common core state standards k-5 mathematics presented by kitty rutherford and amy scrinzi
DESCRIPTION
Our Goals for this afternoon Recognize what makes a good task. Recognize how Standards for Practice mandate better ways of managing instruction. Importance of the relationship between multiplication and division. 1/19/2016 page 3TRANSCRIPT
Common Core State StandardsK-5 Mathematics
Presented by Kitty Rutherford and Amy Scrinzi
Normsbull Listen as an Allybull Value Differencesbull Maintain Professionalismbull Participate Actively
050323 050323 bull page 2
Our Goals for this afternoonbull Recognize what makes a good taskbull Recognize how Standards for Practice
mandate better ways of managing instructionbull Importance of the relationship between
multiplication and division
050323 bull page 3
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 4
There is no other decision that teachers make that has a greater impact on studentsrsquo opportunity to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages the students in studying mathematics
Lappan and Briars (1995 pg 138)
050323 bull page 5
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 6
Multiplication and Rectangles
Make as many different rectangles as you can using 12 square-inch color tiles
050323 bull page 7
What did you notice
bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your
rectanglebull Does that description fit someone
elses rectangle
050323 bull page 8
050323 bull page 9
Possible Arrays with 12 tiles
Commutative Property of Multiplication
050323 bull page 10
2 x 4 = 8 4 x 2 = 8
Multiplication and Rectangles
Find all the rectangles you can make with 18 tiles
Record your rectangles on grid paper
050323 bull page 11
Multiplication and Rectangles
Nowhellip Letrsquos make a class table from
1- 25
050323 bull page 12
050323 bull page 13
050323 bull page 14
What do you notice
Which numbers have rectangles with 3 rows List them from smallest to largest
050323 bull page 15
Which numbers have rectangles with 2 rows
List them from smallest to largest
Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Normsbull Listen as an Allybull Value Differencesbull Maintain Professionalismbull Participate Actively
050323 050323 bull page 2
Our Goals for this afternoonbull Recognize what makes a good taskbull Recognize how Standards for Practice
mandate better ways of managing instructionbull Importance of the relationship between
multiplication and division
050323 bull page 3
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 4
There is no other decision that teachers make that has a greater impact on studentsrsquo opportunity to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages the students in studying mathematics
Lappan and Briars (1995 pg 138)
050323 bull page 5
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 6
Multiplication and Rectangles
Make as many different rectangles as you can using 12 square-inch color tiles
050323 bull page 7
What did you notice
bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your
rectanglebull Does that description fit someone
elses rectangle
050323 bull page 8
050323 bull page 9
Possible Arrays with 12 tiles
Commutative Property of Multiplication
050323 bull page 10
2 x 4 = 8 4 x 2 = 8
Multiplication and Rectangles
Find all the rectangles you can make with 18 tiles
Record your rectangles on grid paper
050323 bull page 11
Multiplication and Rectangles
Nowhellip Letrsquos make a class table from
1- 25
050323 bull page 12
050323 bull page 13
050323 bull page 14
What do you notice
Which numbers have rectangles with 3 rows List them from smallest to largest
050323 bull page 15
Which numbers have rectangles with 2 rows
List them from smallest to largest
Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Our Goals for this afternoonbull Recognize what makes a good taskbull Recognize how Standards for Practice
mandate better ways of managing instructionbull Importance of the relationship between
multiplication and division
050323 bull page 3
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 4
There is no other decision that teachers make that has a greater impact on studentsrsquo opportunity to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages the students in studying mathematics
Lappan and Briars (1995 pg 138)
050323 bull page 5
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 6
Multiplication and Rectangles
Make as many different rectangles as you can using 12 square-inch color tiles
050323 bull page 7
What did you notice
bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your
rectanglebull Does that description fit someone
elses rectangle
050323 bull page 8
050323 bull page 9
Possible Arrays with 12 tiles
Commutative Property of Multiplication
050323 bull page 10
2 x 4 = 8 4 x 2 = 8
Multiplication and Rectangles
Find all the rectangles you can make with 18 tiles
Record your rectangles on grid paper
050323 bull page 11
Multiplication and Rectangles
Nowhellip Letrsquos make a class table from
1- 25
050323 bull page 12
050323 bull page 13
050323 bull page 14
What do you notice
Which numbers have rectangles with 3 rows List them from smallest to largest
050323 bull page 15
Which numbers have rectangles with 2 rows
List them from smallest to largest
Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 4
There is no other decision that teachers make that has a greater impact on studentsrsquo opportunity to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages the students in studying mathematics
Lappan and Briars (1995 pg 138)
050323 bull page 5
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 6
Multiplication and Rectangles
Make as many different rectangles as you can using 12 square-inch color tiles
050323 bull page 7
What did you notice
bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your
rectanglebull Does that description fit someone
elses rectangle
050323 bull page 8
050323 bull page 9
Possible Arrays with 12 tiles
Commutative Property of Multiplication
050323 bull page 10
2 x 4 = 8 4 x 2 = 8
Multiplication and Rectangles
Find all the rectangles you can make with 18 tiles
Record your rectangles on grid paper
050323 bull page 11
Multiplication and Rectangles
Nowhellip Letrsquos make a class table from
1- 25
050323 bull page 12
050323 bull page 13
050323 bull page 14
What do you notice
Which numbers have rectangles with 3 rows List them from smallest to largest
050323 bull page 15
Which numbers have rectangles with 2 rows
List them from smallest to largest
Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
There is no other decision that teachers make that has a greater impact on studentsrsquo opportunity to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages the students in studying mathematics
Lappan and Briars (1995 pg 138)
050323 bull page 5
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 6
Multiplication and Rectangles
Make as many different rectangles as you can using 12 square-inch color tiles
050323 bull page 7
What did you notice
bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your
rectanglebull Does that description fit someone
elses rectangle
050323 bull page 8
050323 bull page 9
Possible Arrays with 12 tiles
Commutative Property of Multiplication
050323 bull page 10
2 x 4 = 8 4 x 2 = 8
Multiplication and Rectangles
Find all the rectangles you can make with 18 tiles
Record your rectangles on grid paper
050323 bull page 11
Multiplication and Rectangles
Nowhellip Letrsquos make a class table from
1- 25
050323 bull page 12
050323 bull page 13
050323 bull page 14
What do you notice
Which numbers have rectangles with 3 rows List them from smallest to largest
050323 bull page 15
Which numbers have rectangles with 2 rows
List them from smallest to largest
Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 6
Multiplication and Rectangles
Make as many different rectangles as you can using 12 square-inch color tiles
050323 bull page 7
What did you notice
bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your
rectanglebull Does that description fit someone
elses rectangle
050323 bull page 8
050323 bull page 9
Possible Arrays with 12 tiles
Commutative Property of Multiplication
050323 bull page 10
2 x 4 = 8 4 x 2 = 8
Multiplication and Rectangles
Find all the rectangles you can make with 18 tiles
Record your rectangles on grid paper
050323 bull page 11
Multiplication and Rectangles
Nowhellip Letrsquos make a class table from
1- 25
050323 bull page 12
050323 bull page 13
050323 bull page 14
What do you notice
Which numbers have rectangles with 3 rows List them from smallest to largest
050323 bull page 15
Which numbers have rectangles with 2 rows
List them from smallest to largest
Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Multiplication and Rectangles
Make as many different rectangles as you can using 12 square-inch color tiles
050323 bull page 7
What did you notice
bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your
rectanglebull Does that description fit someone
elses rectangle
050323 bull page 8
050323 bull page 9
Possible Arrays with 12 tiles
Commutative Property of Multiplication
050323 bull page 10
2 x 4 = 8 4 x 2 = 8
Multiplication and Rectangles
Find all the rectangles you can make with 18 tiles
Record your rectangles on grid paper
050323 bull page 11
Multiplication and Rectangles
Nowhellip Letrsquos make a class table from
1- 25
050323 bull page 12
050323 bull page 13
050323 bull page 14
What do you notice
Which numbers have rectangles with 3 rows List them from smallest to largest
050323 bull page 15
Which numbers have rectangles with 2 rows
List them from smallest to largest
Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
What did you notice
bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your
rectanglebull Does that description fit someone
elses rectangle
050323 bull page 8
050323 bull page 9
Possible Arrays with 12 tiles
Commutative Property of Multiplication
050323 bull page 10
2 x 4 = 8 4 x 2 = 8
Multiplication and Rectangles
Find all the rectangles you can make with 18 tiles
Record your rectangles on grid paper
050323 bull page 11
Multiplication and Rectangles
Nowhellip Letrsquos make a class table from
1- 25
050323 bull page 12
050323 bull page 13
050323 bull page 14
What do you notice
Which numbers have rectangles with 3 rows List them from smallest to largest
050323 bull page 15
Which numbers have rectangles with 2 rows
List them from smallest to largest
Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
050323 bull page 9
Possible Arrays with 12 tiles
Commutative Property of Multiplication
050323 bull page 10
2 x 4 = 8 4 x 2 = 8
Multiplication and Rectangles
Find all the rectangles you can make with 18 tiles
Record your rectangles on grid paper
050323 bull page 11
Multiplication and Rectangles
Nowhellip Letrsquos make a class table from
1- 25
050323 bull page 12
050323 bull page 13
050323 bull page 14
What do you notice
Which numbers have rectangles with 3 rows List them from smallest to largest
050323 bull page 15
Which numbers have rectangles with 2 rows
List them from smallest to largest
Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Commutative Property of Multiplication
050323 bull page 10
2 x 4 = 8 4 x 2 = 8
Multiplication and Rectangles
Find all the rectangles you can make with 18 tiles
Record your rectangles on grid paper
050323 bull page 11
Multiplication and Rectangles
Nowhellip Letrsquos make a class table from
1- 25
050323 bull page 12
050323 bull page 13
050323 bull page 14
What do you notice
Which numbers have rectangles with 3 rows List them from smallest to largest
050323 bull page 15
Which numbers have rectangles with 2 rows
List them from smallest to largest
Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Multiplication and Rectangles
Find all the rectangles you can make with 18 tiles
Record your rectangles on grid paper
050323 bull page 11
Multiplication and Rectangles
Nowhellip Letrsquos make a class table from
1- 25
050323 bull page 12
050323 bull page 13
050323 bull page 14
What do you notice
Which numbers have rectangles with 3 rows List them from smallest to largest
050323 bull page 15
Which numbers have rectangles with 2 rows
List them from smallest to largest
Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Multiplication and Rectangles
Nowhellip Letrsquos make a class table from
1- 25
050323 bull page 12
050323 bull page 13
050323 bull page 14
What do you notice
Which numbers have rectangles with 3 rows List them from smallest to largest
050323 bull page 15
Which numbers have rectangles with 2 rows
List them from smallest to largest
Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
050323 bull page 13
050323 bull page 14
What do you notice
Which numbers have rectangles with 3 rows List them from smallest to largest
050323 bull page 15
Which numbers have rectangles with 2 rows
List them from smallest to largest
Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
050323 bull page 14
What do you notice
Which numbers have rectangles with 3 rows List them from smallest to largest
050323 bull page 15
Which numbers have rectangles with 2 rows
List them from smallest to largest
Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
What do you notice
Which numbers have rectangles with 3 rows List them from smallest to largest
050323 bull page 15
Which numbers have rectangles with 2 rows
List them from smallest to largest
Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
What do you notice
How many different rectangles can you make with 5 tiles
050323 bull page 16
Which numbers on the chart are multiples of 5
How many with 7 tiles
List the prime numbers between 1 and 25Are all odd numbers prime Explain
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Letrsquos look at the number nine
What do you notice
050323 bull page 17
What other numbers have rectangles that are squares
What is the next largest square after 25
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
050323 bull page 18
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
050323 bull page 19
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
How many tiles are in each row
Write a number sentence for this rectangle
050323 bull page 20
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
What standards in third and fourth would this task address
How do these standards build on what fifth grade does
050323 bull page 21
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Criteria Area in Third Grade Students use properties of operations to
calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division
050323 bull page 22
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number
of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =
050323 bull page 23
Operations and Algebraic Thinking 3OA
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Understand properties of multiplication and the relationship between multiplication and division
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when
multiplied by 8
2Students need not use formal terms for these properties
050323 bull page 24
Operations and Algebraic Thinking 3OA
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers
050323 bull page 25
Operations and Algebraic Thinking 3OA
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
x a b c d e f
a g h i j k l
b h m n o p q
c i n r s t u
d j o s w x y
e k p t x z sj
f l q u y sj yt
050323 bull page 26
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection
between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)
050323 bull page 27
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Things to Think Abouthellip How do students demonstrate Computational
Fluency Students exhibit computational fluency when they
demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)
050323 bull page 28
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and
general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities
(Van de Walle)
050323 bull page 29
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Things to Think abouthellip What about timed test Teachers who use timed test believe that the test
help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)
050323 bull page 30
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize
that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite
050323 bull page 31
Operations and Algebraic Thinking 4OA
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
When planning ask
ldquoWhat task can I give that will build student
understandingrdquorather than
ldquoHow can I explain clearly so they will understandrdquo
Grayson Wheatley NCCTM 2002
050323 bull page 32
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Time to Reflect
050323 bull page 33
Summary
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
httpilluminationsnctmorg
050323 bull page 34
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Letrsquos Play the Factor Game
050323 bull page 35
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Math Notebook
050323 bull page 36
1 What skill did you review and practice
2 What strategies did you use while playing the game
3 If you were to play the game a second time what different strategies would you use to be more successful
4 How could you tweak or modify the game to make it more challenging
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
httpilluminationsnctmorg
050323 bull page 37
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
050323 bull page 38
httpnlvmusueduennavvlibraryhtml
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
1 Make sense of problems and persevere in solving them
2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning
of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
050323 bull page 39
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Mathematical practices describe the habits of mind of mathematically proficient studentshellip
bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math
050323 bull page 40
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Letrsquos revisit your poster
Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice
050323 bull page 41
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Think of a NumberMany people have a number that they think is
interesting Choose a whole number between 1 and 25 that you think is special
bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your
numberbull List three or four connections you can make
between your number and your world
050323 bull page 42
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
050323 bull page 54
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
DPI Mathematics Site
httpmathncwiseowlorg
050323 bull page 55
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
wwwcorestandardsorg
050323 bull page 56
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Mathematics Wikki
050323 bull page 57
httpmaccssncdpiwikispacesnetSummer+Institute
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Time to Reflect
050323 bull page 58
Summary
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
PlusDeltabull Please include on the back of the
plusDelta handout topics that you would like to see addressed or discussed during the webinars
ndashNovember 17th
ndashJanuary 10th ndashFebruary 9th
ndashMarch 8th
050323 bull page 59
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-
Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov
Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov
Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov
Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov
050323 bull page 60
- Common Core State Standards K-5 Mathematics
- Norms
- Our Goals for this afternoon
- Think of a Number
- Slide 5
- Slide 6
- Multiplication and Rectangles
- What did you notice
- Slide 9
- Commutative Property of Multiplication
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- What do you notice
- Slide 16
- Letrsquos look at the number nine
- Slide 18
- Slide 19
- If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
- What standards in third and fourth would this task address
- Criteria Area in Third Grade
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Things to Think Abouthellip
- Things to Think Abouthellip
- Slide 29
- Things to Think abouthellip
- Slide 31
- Slide 32
- Time to Reflect
- httpilluminationsnctmorg
- Letrsquos Play the Factor Game
- Math Notebook
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Letrsquos revisit your poster
- Slide 42
- Slide 54
- DPI Mathematics Site
- Slide 56
- Mathematics Wikki
- Slide 58
- PlusDelta
- Contact Information
-