unit 1 - trenton public schools
TRANSCRIPT
CAR © 2009
Unit title: 5th grade math Understanding Place Value ~ Unit 1 Grade Level: 5
Timeframe: Marking Period 1
45 Days (9 weeks) ~ September through mid-November
8+ weeks MAJOR content + incorporate additional content into 3 instructional days
5.NBT.A.1, 5.NBT.A.2, 5.NBT.B.5, 5.NBT.B.6, 5.NBT.A.3, 5.NBT.A.4 + 5.OA.A.1 + 5.OA.A.2
Unit Focus and Essential Questions
Unit 1 Focus
Understand the place value system
Perform operations with multi-digit whole numbers and with decimals to hundredths
Write and interpret numerical expressions
Essential Questions:
How does “place value” relate to the value of each digit?
In a number where all the digits are the same, how does each identical digit represent a different value?
How do 8 pennies compare to 8 dimes? How do 7 dimes compare to 7 one dollar bills? How do 9 ten dollar bills compare to 9 one dollar bills? How do 6 hundred dollar bills compare to 6 ten dollar bills?
When do digits represent different amounts of the same thing?
How can digits represent the same amount of different things?
What number represents five tens? 8 tens? 8 hundreds? Five hundreds?
How does one hundred differ from one thousand? How does one hundred differ from one ten? They all have 1’s & 0’s.
Which digit of a number tells us the largest amount of some-thing?
Which digit represents the smallest amount of some-thing?
When we write multiple digits beside each other, how can we know the value each digit represents?
When we add the values represented by each digit, what do we get?
What value does the first digit to the right of a decimal point represent? A digit to the immediate left of a decimal point represents what value?
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How does a number’s standard form compare to its expanded form?
How does a number’s written form compare to its standard form?
What value do digits two places to the right of a decimal point represent? When adding or subtracting quantities, why does it make sense to group the same values represented by each digit? When multiplying a single digit number with a multi-digit number, why does it make sense add similar values represented
by the products of each digit? When multiplying a double digit number with another multi-digit number, how do we combine the products represented
by the values of each digit? New Jersey Student Learning Standards
Standards/Cumulative Progress Indicators (Taught and Assessed):
5.NBT.A.1 - 8 days** Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Left # Right
x 10 x 1/10
(10)10 (1)10 (1/10)10 3,160 316 31.6 100 10 1
5.NBT.A.2* - 8 days** Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
5.NBT.B.5* - 5 days Fluently multiply multi-digit whole numbers using the standard algorithm.
5.NBT.B.6* - 5 days
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value,
the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using
equations, rectangular arrays, and/or area models.
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5.NBT.A.3 - 8 days** Read, write, and compare decimals to thousandths.
5.NBT.A.3a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
1 1/10 1/100 1/1000 or or or or
1000 100 10 1
5.NBT.A.3b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
5.NBT.A.4 - 8 days** Use place value understanding to round decimals to any place.
5.OA.A.1 - 1 day (integrate into major content,, i.e., 5.NBT.A.3)
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
5.OA.A.2 - 2 days (integrate into major content,, i.e., 5.NBT.B.5, 5.NBT.A.3)
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
Key:
Green = Major Clusters; Blue = Supporting;
Yellow = Additional Clusters
CAR © 2009
*NJ State benchmarked standard
**OPTIONAL (not required) – entire instructional topics do NOT have to be taught consecutively: consider Spacing Learning Over Time (S.L.O.T.)
http://dwwlibrary.wested.org/media/learning-together-about-spacing-learning-over-time
21st Century Skills Standard and Progress Indicators:
Think like a mathematician & the 8 Mathematical Practices (8MPs)! The Common Core State Standards for mathematical practice (8MPs) describe habits of mind students internalize with practice:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others*
4. Model with mathematics**
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Real-world problem solving is a vital 21st century skill all students need to compete globally. MP4 (modeling/application) Sub-Claim D (18% of raw points) in PARCC math claims structure – only 3 tasks on PARCC. MP3 and MP6 (expressing mathematical reasoning) fall under Sub-Claim C (22% of raw points) in PARCC math claims structure – only 4 tasks on PARCC.
Communication and teamwork are vital 21st century skills students all students should develop. Constructivist, team-building, cooperative learning routines include:
o Think-pair-share
o Group conference o Bounce ideas off each other
o State your claim o Respectfully disagree o Each one teach one
o Group presentation o Team spokesman/spokeswoman
Metacognition and inquiry-based teamwork helps students become self-directed learners, as problem solving and communication skills develop and students take ownership of their own thinking (and hence, learning).Challenging students to “explain” their reasoning helps their metacognition – ability to pay close attention to their own thinking:
o What (exactly) am I doing now? Why am I doing it? o How do I know? Does this really make sense? Why or why not?
PARCC Released items: http://tinyurl.com/gr5PARCCreleaseditems2016
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PARCC Evidence Statements: http://parcc-assessment.org/assessments/test-design/mathematics/math-test-specifications-documents PARCC Model Content Frameworks: http://parcc-assessment.org/resources/educator-resources/model-content-frameworks
Suggested performance tasks from https://illustrativemathematics.org : 5.NBT.A.1 Which number is it?
5.NBT.A.1 Millions and Billions of People
5.NBT.2 Marta’s Multiplication Error: https://www.illustrativemathematics.org/content-standards/5/NBT/A/2/tasks/1524
5.NBT.B.5 Elmer's Multiplication Error
5.NBT.A.3 Placing Thousandths on the Number Line
5.NBT.A.4 Rounding to Tenths and Hundredths
5.OA.A.1 Using Operations and Parentheses
5.OA.A.1 Watch out for Parentheses 1
Additional performance tasks from NC Department of Public Instruction: http://3-5cctask.ncdpi.wikispaces.net/Fifth+Grade+Tasks
Reasoning task: 5.C.7-4/4.NBT (2015 PARCC PBA released item 13)
Units: tens, hundreds, thousands & millions
Part A Write this number in expanded form: 670,503
Part B Show or explain how to write 8,523 in expanded form using 15 hundreds.
Part C A student used 80 ten thousands in the expanded form of the number 6,807,590.
Show or explain how 6 hundred thousands, 80 ten thousands, 7 thousands, 5 hundreds and 9 tens can or cannot be used to represent 6,807,590.
If it cannot be used, show how you would correct it and still use 80 ten thousands.
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Modeling task: 5.D.1/5.NBT.5, 5.NBT.6 (2014 PARCC PBA practice test item 16)
Greg’s water bottles
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Reasoning task: 5.C.4-3/5.NBT.6 (Smarter Balanced sample item 1890, claim 3)
Jasmine’s area model equation
Help Jasmine find the number which equals 363 when divided by 4.
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Modeling task: 5.D.1/5.NBT, 5.OA.2 (2015 PARCC PBA released item 14)
Katie’s jewelry Katie went to a craft store to purchase supplies she needs to make two types of jewelry. This table shows the cost of the supplies Katie needed.
This table shows the supplies needed to make each piece of jewelry.
Katie purchased the exact amount of supplies to make 1 bracelet and 2 necklaces.
Part A Write an expression to determine the cost of supplies to make 1 bracelet.
Part B Write an expression to determine the cost of supplies to make 2 necklaces.
Part C Katie started with $40. How much did she have left after purchasing the supplies?
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Reasoning task: 5.C.4-3/5.NBT.6 (2014 PARCC PBA practice test item 15)
A division & multiplication area model
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Reasoning & Modeling Task: 5.C.4-3, 5.D.1/5.NBT.6 (McGraw-Hill benchmark task)
Division model problem
Now write a brief story or scenario which uses the numbers you put into your division problem. Be sure your story’s conclusion relates to your solution to the division problem modeled.
Farmer Jim solves a problem (Eureka Math 5th grade, Module 1 – Topic A) Farmer Jim keeps 12 hens in every coop. If Farmer Jim has 20 coops, how many hens does he have in all? If every hen lays 9 eggs, how many eggs will Farmer Jim collect? Explain your reasoning using words, numbers, or pictures.
Instructional Plan Standards Based Assessment
Cumulative Pre-Assessment Diagnostic Assessment - MI
Standard/SWBAT Student Strategies Based on Instructional Framework
Formative Assessment
Activities and Resources Standards Based Assessment
CAR © 2009
NJSLS.MATH.CONTENT.5.NBT.1
5.NBT.A.1 - 8 days**
Recognize that in a multi-
digit number, a digit in
one place represents 10
times as much as it
represents in the place to
its right and 1/10 of what
it represents in the place to
its left.
(MAJOR content)
-----------------------------------
Claim: students understand the
quantitative relationships between
digits in the place value positions of
a multi-digit number.
Evidence: students can EXPLAIN
that a digit in one place represents:
a. 1/10 of what it represents in the
place to its left.
And
b. ten times what it represents in
the place to its right.
Tasks: may compare a digit in the
tenths position to a:
Thousandths digit
Or a Tens digit
little to no “context”
Performance: students soon use
whole number exponents to denote
powers of 10 and compare them
when expressed exponentially
(i.e.10⁴ > 10² or 10³ < 10⁴).
Extend the concept to multiple
places…………………………..
Number Talk Direct Instruction
Option 1 - EngageNY
Option 2 – NJCTL presentation
Option 3 - MyMath Centers (rotating)
Teacher Center – teacher works w/ 1-4 students
Standards Based Problem Center – Students work in groups to solve tasks like those in standards-based assessments
Individual Center – Students focus on skills based on , EdConnect, and PARCC data. Use Achieve the Core Coherence Map to guide remediation.
Technology Center – Math
Manipulative Center – Students use tools, such as base 10 blocks.
Interdisciplinary Center – Students solve interdisciplinary math; write their own number stories; listen to music/sing songs to help learn the content.
Record metacognitive thinking in student journals
Review Classwork Exit Ticket
PARCC Released Items 2016, Item #3
http://tinyurl.com/2016PARCCr
eleaseditems
During grade level meetings, teacher PLCs agree on common classwork/question s. Selected tasks most closely match assessment questions in column 5.
Additionally, teachers encourage metacognition– students self- assess during “wait time”: “what am I doing now?” “why am I doing it?” “how do I know…?” “does this answer make sense?” Personal mastery (out-do yourself)
How is the 2 in
542 different from
the value of the 2
in 324?
What does 2 digit
represent in
2897?
How about in
1.026?
EngageNY, 2016, Module 1, Topic A (lessons 1-2)
https://www.engageny.org/resource/grade-5-mathematics-module-1-topic-lesson-1
https://www.engageny.org/resource/grade-5-mathematics-module-1-topic-lesson-2
https://www.engageny.org/resource/math-studio-talk-common-core-instruction-5nbt
NJCTL Decimal Concepts Presentation 2015-11-16, (slides 15-40)
https://njctl.org/courses/math/5th-grade-math/decimal-concepts/
PARCC Released Items 2016, Item #3
http://tinyurl.com/2016PARCCreleaseditems
PARCC Released Items 2015, PBA Item #1, http://tinyurl.com/gr5PARCC-
PBAreleased2015
PARCC EOY Item #28 http://tinyurl.com/gr5PARCC-
EOYreleased2015
Illustrative Mathematics 5.NBT.A.1 Which number is it?
5.NBT.A.1 Millions and Billions of People
Achieve the Core Coherence Map http://achievethecore.org/coherence-
map/#5/22
NJCTL Math Labs – RAFT resources… http://www.raftbayarea.org/readpd
f?isid=600
MyMath (Teacher login available) Ch.1 Lesson 1 Place Value Millions
www.connected.mcgraw-hill.com
(10)10 (1)10 (1/10)10
3,160 316 31.6
100 10 1 1 hundred 1 ten 1 one
The “Touchpoint” standards based assessments (quizzes) are in edConnect nj. Grade 5 Math - Touchpoint – 5.NBT.1 --------------------------------------------------
Build the concept:
The arrows indicate the value is
1/10 of the 5 to the left and 10
times the 5 to the right
--------------------------------------------------
--34.567
In the above number, compare the place which the 5 digit represents to the place represented by the:
a. 7 digit b. 3 digit
Explain the size of each place
compared to the 5’s place.
What value does each digit represent
in this number? Explain.
CAR © 2009
NJSLS.MATH.CONTENT.5.NBT. 2
5.NBT.A.2* - 8 days**
Explain patterns in the
number of zeros of a
product when multiplying
a number by powers of
10, and explain patterns in
the placement of the
decimal point when a
decimal is multiplied or
divided by a power of 10.
Use whole-number
exponents to denote
powers of 10.
(MAJOR content) --------------------------------------------------------------------
Claim: students understand
exponents & scientific notation;
students write powers of 10 using
whole number exponents.
Evidence: students reason about
the place value system (itself)
and
use whole number exponents to
denote powers of ten.
Tasks: focus specifically on place
value; do not serve another goal-
multiplying multi-digit numbers.
Reasoning 5.C.3
Performance: students clearly
communicate well-organized,
complete responses; evaluate and
justify conclusions; critique other
responses; show counterexamples.
Math Practices 7, 3 & 6
Number Talk
Direct Instruction
Option 1 - EngageNY
Option 2 – NJCTL
Option 3 - MyMath Centers (rotating)
Teacher Center –Teacher works with 1-4 students.
Standards Based Problem Center – Students work in groups to solve tasks like those in standards-based assessments (Benchmark; PARCC; etc.).
Individual Center – Students focus on skills based on EdConnect, and PARCC data. Use Achieve the Core Coherence Map to guide remediation.
Technology Center
Manipulative Center – Students use tools, such as base 10 blocks.
Interdisciplinary Center – Students complete math problems interconnected with another subject & write their own number stories; they listen to music/sing songs to help learn the content.
Review Classwork Exit Ticket
PARCC Released Items, EOY Item #9 http://tinyurl.com/gr5PARCC
-EOYreleased2015
During grade level meetings, teacher PLCs agree on common classwork questions. Selected tasks most closely match assessment questions in column 5.
Metacognitive thinking – students self- assess during “wait time”: “what am I doing now?” “why am I doing it?” “how do I know…?” “does this answer make sense?” Personal mastery (out-do yourself)
Record metacognitive
thinking in student journals
EngageNY 2016 Module 1, Topic A (lesson 3)
https://www.engageny.org/resource/grade-5-mathematics-module-1-topic-lesson-3
Module 2, Topic A (lesson 2) https://www.engageny.org/resource/grade-5-
mathematics-module-2-topic-lesson-2
Module 2, Topic B (lesson 24) https://www.engageny.org/resource/grade-5-
mathematics-module-2-topic-g-lesson-24
https://www.engageny.org/resource/grade-5-mathematics-module-2
NJCTL Division Presentation 2015-11-25, (Patterns in Mult. & Division: slides 26-88 ) https://njctl.org/courses/math/5th-grade-
math/division/attachments/unit-3-division/
PARCC Released Items 2016, Item #4 http://tinyurl.com/2016PARCCreleaseditems
Achieve the Core Coherence Map http://achievethecore.org/coherence-
map/#5/22
MyMath (Teacher login available) Ch.1 Lesson 5 Understanding Place Value
www.connected.mcgraw-hill.com
523 x 103 = 523,000 The place value of
523 is increased by 3 places.
5.223 x 102 = 522 The place value of
5.223 is increased by 2 places.
52.3 ÷ 101 = 5.23 The place value of
52.3 is decreased by one place.
Multiplying 0.4 by 1,000 shifts the position of the digits to the left three places, changing the digits’ relationships to the decimal point and producing a product with a value that is 10 × 10 × 10 as large (400.0). Each shift to the left increases 10 times the previous position; 1 thousand = 1,000 = 10³
The standards assessments below are in EdConnect. These are the quiz/test for that standard.
Grade 5 Math – Touchpoint – 5.NBT.2
Illustrative Mathematics: Marta’s multiplication error
https://www.illustrativemathematics. org/content-
standards/5/NBT/A/2/tasks/1524
Multiplying by 104 is multiplying
by 10 four times
102 which is 10 x 10=100
103 = 10 x 10 x 10=1,000
Connect the pattern of zeros when you multiplying by powers of 10.
Decimal moves right…
2.5 x 103 = 2.5 x (10 x 10 x 10) = 2.5 x 1,000 = 2,500.
Decimal moves left… 350. ÷ 103 =
350 ÷ 1,000 = 0.350 = 0.35
Divide by 10 = multiply by 1/10
350/10 = 35
35 /10=3.5
3.5 /10 =.0.35, or 350 x 1/10,
35 x 1/10,
350 x 1/10 =
35 x 1/10 =
3.5 x 1/10 =
36 x 10 = 36 x 101 = 360
36 x 10 x 10= 36x 102 = 3600
36 x 10 x 10 x 10 =
36 x 103 = 36,000
36 x 10 x 10 x 10 x 10 =
36 x 104 = 360,000
See patterns with zeros
CAR © 2009
NJSLS.MATH.CONTENT.5.NBT. 5
5.NBT.B.5* - 5 days**
Fluently multiply multi-
digit whole numbers
using the standard
algorithm.
(MAJOR content) --------------------------------------
Claim: students use the standard
algorithm to fluently multiply
multi-digit whole numbers.
Evidence: students can fluently
multiply multi-digit whole numbers
using the standard algorithm;
Tasks: untimed & assess accuracy,
using up to 3 digit x 4 digit
numbers; pure mental strategy not
obvious – written work required;
little to no “context”
Performance: students (use place
value to) assess reasonableness of
products from multi-digit numbers
after using standard algorithm.
----------------------------------------------------------
Build toward standard algorithm
a. Area model of multiplication
b. Partial products (left to right)
c. Partial products (right to left)
d. Standard w/ regrouping
http://achievethecore.org/pag e/1032/multi-digit- multiplication-using-the- standard-
algorithm-mini- assessment
2639 x 29 =? , 3051 x 882 =?
826 x 3569 =?
Number Talk
Direct Instruction
Option 1 - EngageNY
Option 2 – NJCTL
Option 3 - MyMath Centers
Teacher Center – The teacher works groups of 1-4 students.
Standards Based Problem Center – Students work in groups to solve tasks like those in standards-based assessments (Benchmark; PARCC; etc.). 2639 x 29 =? 3051 x 882 =? 826 x 3569 =?
Individual Center – Students focus on skills based on EdConnect and PARCC data. Use Achieve the Core Coherence Map to guide remediation.
Technology Center
Manipulative Center – Students use tools, such as base 10 blocks
Interdisciplinary Center – Students complete math problems interconnected with another subject
Review Classwork
Exit Ticket PARCC Released Items 2016,
Item #7 http://tinyurl.com/2016PARCCr
eleaseditems
During grade level meetings, teacher PLCs agree on common classwork questions, referring to column 5.
Metacognitive thinking – students self- assess during “wait time”: “what am I doing now?” “why am I doing it?” “how do I know…?” “does this answer make sense?” Personal mastery (out-do yourself)
Illustrative
Mathematics:
5.NBT.B.5 Elmer's
Multiplication Error
EngageNY Math, 2016,
Module 2, Topic B (lessons 3-8) https://www.engageny.org/resource/grade-5-
mathematics-module-2-topic-b-lesson-8
PARCC Released Items EOY #1, 3 & 17 http://tinyurl.com/gr5PARCC-
EOYreleased2015
Illustrative Mathematics:
5.NBT.B.5 Elmer's Multiplication Error
Achieve the Core Coherence Map http://achievethecore.org/coherence-
map/#5/22
MyMath (Teacher login available) Ch.2
Lessons 6-10 Use Partial Products…
www.connected.mcgraw-hill.com
The Partial Products algorithm https://www.sophia.org/search?q=Par
tial%20products%20algorithm
Why learn the partial products algorithm?
1. Students are still developing a sense of
place value, and partial products helps
students better understand place value
than the standard algorithm.
2. The partial products algorithm closely
matches ways people think about
numbers; mental computation easy.
3. The partial products algorithm is
clearly connected to the distributive
property a(b+c) = ab+ac .
4. The partial products algorithm closely
aligns with the ways people handle
algebraic expressions.
Grade 5 Math-Touchpoint- 5.NBT.5
A book company printed 452
books. Each book had 150
pages. How many pages did
the book company print?
There are 225 dozen
cookies in the bakery.
How many cookies
are there?
CAR © 2009
NJSLS.MATH.CONTENT.5.NBT. 6
5.NBT.B.6 - 5 days
Find whole-number
quotients of whole numbers
with up to four-digit
dividends and two-digit
divisors, using strategies
based on place value, the
properties of operations,
and/or the relationship
between multiplication and
division. Illustrate and explain the calculating using
equations, rectangular
arrays, and/or area models.
(MAJOR content)
Claim: Students use division
strategies based on place value,
properties of operations and the
relationship between multiplication
& division to find quotients of whole
numbers with up to 4-digit dividends
and 2-digit divisors
Evidence: Students represent and
explain calculations w/ equations,
rectangular arrays & area models.
Connect diagrams of concrete
referents to symbolic expressions.
Tasks: involve 3- or 4-digit
dividends & 1- or 2- digit divisors.
Performance: students check
reasonableness of answers using
multiplication or area models/arrays
Number Talks
Direct Instruction
Option 1 EngagneNY
Option 2 NJCTL
Option 3 MyMath Centers
Teacher Center – The teacher works groups of 1-4 students.
Standards Based Problem Center – Students work in groups to solve tasks like those in standards-based assessments (benchmarks, PARCC, etc)
Individual work center
Technology center
Review Classwork
Exit Ticket
PARCC Released Items 2016, Item #18b
http://tinyurl.com/2016PARCCreleaseditems
During PLC meetings, teachers agree on common classwork questions similar to ones in column 5.
Metacognitive thinking – students self- assess during wait time. does
this answer make sense?” Personal mastery (out-do yourself)
NJCTL Division Presentation 2015-11-25, (Patterns in Mult& Division:slides 124-184)
https://njctl.org/courses/math/5th-grade-math/division/attachments/unit-3-
division/ EngageNY 2016,
Module 2, Topics E & F (lessons 17-23)
Multi-digit whole number division
Mental strategies (1-2 days) https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-e-overview
Partial quotients (3-4 days) https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-f-overview
MyMath (Teacher login available) Ch.3 Lessons 7 &8, Ch.4 Lessons 1-6
www.connected.mcgraw-hill.com Achieve the Core Coherence Map http://achievethecore.org/coherence-map/#5/22
2682 ÷ 25 =
(2000 + 600 + 80 + 2) ÷ 25 25 x n = 2682
25 x 100 = 2500
2682-2500 = 182
25 x m=182
25 x 7 = 175
182-175= 7 remainder… So 25 x 107 = 2500+175 + 7
1,716 students participate in Field Day.
Each team has 16 students.How many
teams get created? What to do with any
left over students?
There are 100 16’s in 1,716
Grade 5 Math- Touchpoint-5.NBT.6
PARCC Released Items EOY #12 http://tinyurl.com/gr5PARCC-
EOYreleased2015
Each ticket for a concert cost $14. The amount of ticket sales for the concert was $8,792. How many tickets were sold?
Common Core Sheets http://www.commoncoresheets.com /SortedByGrade.php?Sorted=5nbt6
9984 ÷ 6
1716 -1600
100
116 80
5
36 -32
2
4
CAR © 2009
NJSLS.MATH.CONTENT.5.NBT. 3
5.NBT.A.3 - 8 days**
Read, write, and compare
decimals to thousandths.
(MAJOR content)
5.NBT.A.3a. Read and
write decimals to
thousandths using base-
ten numerals, number
names, and expanded
form, e.g., 347.392 = 3 ×
100 + 4 × 10 + 7 × 1 + 3 ×
(1/10) + 9 × (1/100) + 2 ×
(1/1000).
5.NBT.A.3b. Compare
two decimals to thousandths based on
meanings of the digits in
each place, using >, =, &
< symbols to record the
results of comparisons. -------------------------------------------------------------------------------------
Claim: students compare two
decimals to thousandths using >, =,
and < in expanded form, number
names and/or base 10 numerals.
Evidence: students use >, =, and <
symbols to represent numbers to the
thousandths in multiple (different)
forms, including base 10 numerals,
expanded form & number names.
Tasks: mixture of #representations
reflects conceptual understanding.
Performance: students read, write
& compare decimals to any place
using >, =, <, expanded form,
number names and numerals.
Number Talk
Direct Instruction
Option 1 - EngageNY
Option 2 – NJCTL
Option 3 - MyMath Centers
Teacher Center – The teacher works groups of 1-4 students.
Standards Based Problem Center – Students work in groups to solve tasks like those in standards-based assessments (Benchmark; PARCC; etc.).
Individual Center – Students focus on skills based on EdConnect, and PARCC data. Use Achieve the Core Coherence Map to guide remediation.
Technology Center –
Manipulative Center – Students use tools, such as base 10 blocks & etc., to solve problems.
Interdisciplinary Center – Students complete math problems interconnected with another subject & write their own number stories; they listen to music/sing songs to help learn the content.
Review Classwork Exit Ticket PARCC Released Items 2016,
Items #5 & 6 http://tinyurl.com/2016PARCCr
eleaseditems
During grade level meetings, teacher PLCs agree on common classwork questions. Selected tasks most closely match assessment questions in column 5.
Metacognitive thinking – students self- assess during “wait time”: “what am I doing now?” “why am I doing it?” “how do I know…?” “does this answer make sense?” Personal mastery (out-do yourself)
Illustrative
Mathematics:
5.NBT.A.3 Placing
Thousandths on the
Number Line
EngageNY 2016 Module 1, Topic B (lessons 5-6)
https://www.engageny.org/resource/grade-5-mathematics-module-1-topic-b-overview
NJCTL Decimal Concepts Presentation 2015-11-16, (slides 56-93 & 94-126)
https://njctl.org/courses/math/5th-grade-math/decimal-concepts/
MyMath (Teacher login available) Ch.1 Lesson 6 Place Value through the
Thousandths
www.connected.mcgraw-hill.com
Illustrative Mathematics:
5.NBT.A.3 Placing Thousandths on the
Number Line
Achieve the Core Coherence Map
http://achievethecore.org/coherence-map/#5/22
Use the same blocks 2 different ways:
Thousands Hundreds Tens
1000 100 10 (100)10 (10)10 (1)10
1000(1/1000) 10(1/100) 100(1/10) 1 1/10 1/100
1.0 0.1 0.01 One One-tenth One-
hundredth
Grade 5 Math- Touchpoint-5.NBT.3
CAR © 2009
NJSLS.MATH.CONTENT.5.NBT. 4
5.NBT.A.4 - 8 days**
Use place value
understanding to round
decimals to any place.
(MAJOR content) ------------------------------------------ Claim: students round decimals to
any place value.
Evidence: students use
understanding of place value to
round decimals to any place.
Tasks: have thin or no context.
Performance: students round
decimals to any place and choose
appropriate context given a rounded
number.
Number Talk
Direct Instruction
Option 1 - Eureka Math modules
Option 2 – SMART Presentation NJCTL
Option 3 - MyMath Centers
Teacher Center – The teacher works groups of 1-4 students.
Standards Based Problem Center – Students work in groups to solve tasks like those in standards-based assessments (Benchmark; PARCC; etc.).
Individual Center – Students focus on skills based on , EdConnect, and PARCC data. Use Achieve the Core Coherence Map to guide remediation.
Technology Center – Math
Manipulative Center – Students use tools, such as base 10 blocks & etc., to solve problems.
Interdisciplinary Center – Students complete math problems interconnected with another subject & write their own number stories; they listen to music/sing songs to help learn the content.
Review Classwork Exit Ticket
During grade level meetings, teacher PLCs agree on common classwork questions. Selected tasks most closely match assessment questions in column 5.
Metacognitive thinking – students self- assess during “wait time”: “what am I doing now?” “why am I doing it?” “how do I know…?” “does this answer make sense?” Personal mastery (out-do yourself)
Illustrative
Mathematics:
5.NBT.A.4
Rounding to Tenths
and Hundredths
EngageNY, 2016 Module 1, Topic C (lessons 7- 8)
https://www.engageny.org/resource/grade-5-mathematics-module-1-topic-c-overview
NJCTL Decimal Concepts Presentation 2015-11-16, (slides 127-178)
https://njctl.org/courses/math/5th-grade-math/decimal-concepts/
PARCC Released Items, EOY Item #28
http://tinyurl.com/gr5PARCC-EOYreleased2015
MyMath (Teacher login available) Ch.5 Lesson 1 Rounding Decimals
www.connected.mcgraw-hill.com
Illustrative Mathematics 5.NBT.A.4 Rounding to Tenths and
Hundredths
Achieve the Core Coherence Map http://achievethecore.org/coherence-
map/#5/22
Common Core Sheets
http://www.commoncoresheets.com/Sorte
dByGrade.php?Sorted=5nbt4
MyMath (Teacher login available) Ch. Lesson Pl
www.connected.mcgraw-hill.com
NJCTL Math Labs
https://njctl.org/courses/math/5th-grade-math/decimal-concepts/
Gr 5 Math- Touchpoint-5.NBT.4
CAR © 2009
NJSLS.MATH.CONTENT.5.OA.1
5.OA.A.1 - 1 day (integrate into major content,
i.e., 5.NBT.A.3, 5.NBT.B.5)
Use parentheses, brackets,
or braces in numerical
expressions, and evaluate
expressions with these
symbols.
(Additional content)
Claim: students evaluate numerical
expressions containing parentheses,
brackets and braces.
Evidence: students can use nested
grouping symbols (parentheses,
brackets or braces) to evaluate
numerical expressions: for example
3 x [5 + (7 - 3)].
Tasks: Depth of nested grouping
symbols no greater than two; e.g.
3 x [6-(2+4)] ok because it has only
two sets of parenthesis or brackets.
However, 3 x [6-(2+{5-1})] has
three sets of grouping symbols, so it
is not ok.
Performance: students write and
evaluate numerical expressions w/
parentheses, brackets or braces of no
greater depth than two.
Number Talk
Direct Instruction
Option 1 - EngageNY
Option 2 – SMART Presentation NJCTL
Option 3 - MyMath Centers
Teacher Center – The teacher works groups of 1-4 students.
Standards Based Problem Center – Students work in groups to solve tasks like those in standards-based assessments (Benchmark; PARCC; etc.).
Individual Center – Students focus on skills based on , EdConnect, and PARCC data. Use Achieve the Core Coherence Map to guide remediation.
Technology Center – Math
Manipulative Center – Students use tools, such as base 10 blocks & etc., to solve problems.
Interdisciplinary Center – Students complete math problems interconnected with another subject & write their own number stories; they listen to music/sing songs to help learn the content.
Review Classwork Exit Ticket
During grade level meetings, teacher PLCs agree on common classwork questions. Selected tasks most closely match assessment questions in column 5.
Metacognitive thinking – students self- assess during “wait time”: “what am I doing now?” “why am I doing it?” “how do I know…?” “does this answer make sense?” Personal mastery (out-do yourself)
Are we working from the inside-out?
Illustrative
Mathematics
5.OA.A.1 Using
Operations and
Parentheses
5.OA.A.1 Watch out
for Parentheses 1
Incorporate this standard into major content during one
instructional session. EngageNY, 2016 Module 4, Topic D
(lesson 10) https://www.engageny.org/resource/grade-5-mathematics-module-4-topic-d-lesson-10
NJCTL Algebraic Concepts Presentation 2015-11-16, (slides 24-57)
https://njctl.org/courses/math/5th-grade-math/algebraic-concepts/
2 x (8 + 7) means:
“add 8 and 7, then multiply by 2” or
“2 times the quantity of 8 & 7.”
3 x (18932 + 921) means:
“three times as large as 18932 + 921”
MyMath (Teacher login available) Ch.7 Lesson 2 Order of Operations
www.connected.mcgraw-hill.com
Illustrative Mathematics:
5.OA.A.1 Using Operations and
ParenthesesD
5.OA.A.1 Watch out for Parentheses 1
Achieve the Core Coherence Map
http://achievethecore.org/coherence-
map/#5/24
Gr 5 Math- Touchpoint-5.OA.1
Hint: pinch your fingers together, then slowly open them apart. This is how we work from the “inside” of an expression “out.”
CAR © 2009
NJSLS.MATH.CONTENT.5.OA.2
5.OA.A.2 - 2 days (incorporate into major content,
i.e., 5.NBT.B.5, 5.NBT.6)
Write simple expressions
that record calculations with
numbers, and interpret
numerical expressions
without evaluating them. For
example, express the
calculation “add 8 and 7, then
multiply by 2” as 2 × (8 + 7).
Recognize that 3 × (18932 +
921) is three times as large as
18932 + 921, without having
to calculate the indicated sum
or product.
(Additional content) ------------------------------------------ Claim: students write simple
numerical expressions when given
verbal descriptions or word
problems, without evaluating
(simplifying) them.
Evidence: students can write simple
expressions which record
calculations with numbers.
Tasks: to express the calculation,
“add 5 and 6, then multiply by 3,”
students write 3x(5+6). integrated
into major content, where possible.
Performance: Students interpret
numerical expressions without
evaluating them.
Number Talk
Direct Instruction
Option 1 – EngageNY
Option 2 – NJCTL
Option 3 - MyMath Centers
Teacher Center – The teacher works groups of 1-4 students.
Standards Based Problem Center – Students work in groups to solve tasks like those in standards-based assessments (Benchmark; PARCC; etc.).
Individual Center – Students focus on skills. Use Achieve the Core Coherence Map to guide remediation.
Technology Center – Math
Manipulative Center – Students use tools, such as base 10 blocks etc., to solve problems.
Interdisciplinary Center – Students complete math problems interconnected with another subject & write their own number stories.
Review Classwork Exit Ticket PARCC Released Items 2016,
Item #14 http://tinyurl.com/2016PARCCr
eleaseditems
During grade level meetings, teacher PLCs agree on common classwork questions. Selected tasks most closely match assessment questions in column 5.
Metacognitive thinking – students self- assess during “wait time”: “what am I doing now?” “why am I doing it?” “how do I know…?” “does this answer make sense?” Personal mastery (out-do yourself)
Incorporate this standard into major content instruction over the course of 2 days.
EngageNY, 2016 Module 2, Topic B (lesson 6)
https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-
b-lesson-6
NJCTL Algebraic Concepts Presentation 2015-11-16, (slides 58-92)
https://njctl.org/courses/math/5th-grade-math/algebraic-concepts/
MyMath (Teacher login available) Ch.7
Lessons 3 & 4 Numerical Expressions
www.connected.mcgraw-hill.com
Achieve the Core Coherence Map
http://achievethecore.org/coherence-
map/#5/24
“double five and then add 26”
(2x5) +26 = 2x5 + 26
5(10 x 10)
“5 groups of (10 x 10)”
3(100) + 3(10) + 3(1)
3(100 + 10 + 1)
2(5+13)
Gr 5 Math- Touchpoint-5.OA.1 Grade 5 Math – – 5.OA.1