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Standards:

Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.

MCC6.NS.1

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

MCC6.NS.2

Fluently divide multi-digit numbers using the standard algorithm

MCC6.NS.3

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

MCC6.NS.4

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

Transition Standard for 2012-2013:

MCC5.NF.6 (DOK 2) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

6th Grade CCGPS Math

LFS Unit 1: The Number System with Rational Numbers

Douglas County School System

6th Grade Math 8/13/2012

Number System Fluency Page 1

K-U-D Unit 1: Number System Fluency

understand

By the end of the unit, I want my students to understand

how to extend and fluently apply the concept of part(s) of a whole to manipulate numbers (fractions, decimals, multiples, factors, etc.) to solve real world problems.

Know

Do

Vocabulary: Evaluate; Quotient; Dividend; Minuend; Subtrahend; Fraction; Multiple; Factor; Factorization; Prime Number; Composite Number; Exponent; Exponential; Distribution Property; Decompose; Greatest Common Factor (GCF); Least Common Multiple (LCM); Relatively Prime; Array; Model; Sum; Difference; Algorithm

Multiple strategies and models to solve various problems with fractions and decimals. (NS1; NS3)

The standard algorithm for addition, subtraction, multiplication and division of multi-digit numbers and decimals. (NS3; NS4)

The relationship between multiplication and division. (NS1; NS4)

Which operation(s) to apply to a word problem and/or real world situation. (NS1)

What dividing by a fraction means. (NS1)

Ex: ( 3 is asking

"how many 2/5are in 3?)

A number divided by a fraction has a higher quotient than the dividend. (NS1; NS2)

The relationship between the distribution property and factors and multiples. (NS4)

The relationship between multiples and factors. (NS4)

The value of using properties of multiples and factors in real world situations/word problems. (NS1)

Divisibility rules. (NS2)

Divide (NS.1) & multiply fractions. (NS.6) DOK1

Fluently add, subtract, divide and multiply multi-digit decimals. (NS.3) DOK1

Fluently divide multi-digit numbers. (NS.2) DOK1

Divide whole numbers and fractions with fractions. (NS.1) DOK1

Interpret real world situations in expressions and equations by determining if multiplication or division of whole and partial numbers is necessary. (NF.6) DOK2

Model visually multiplication (NF.6) and division of fractions to represent real world situations/word problems. (NS.1) DOK2

Find common multiples of two whole numbers less than or equal to 12. (NS.4) DOK1

Find common factors of two whole numbers less than or equal to 100. (NS.4) DOK1

Find the greatest common factor (GCF) and least common multiple (LCM). (NS.4) DOK1

Factor numbers with prime factorization and write numbers in exponential form. (NS.4) DOK1

Use the distributive property to express a sum of two whole numbers 1 100 (with a common factor) as a multiple of a sum of two whole numbers (with no common factor). (NS.4) DOK1

Ex: Whole numbers (36 & 8) have a common factor of 4. Whole numbers (9 & 2) have no common factor. Use the distributive property to express 36 + 8 as 4 (9 + 2).Notice: 36+8 = 44 & 4(9+2) =44.

SLM Unit 1: Number System Fluency

Key Learning

Extend and fluently apply the uses of the four basic operations (addition, subtraction, multiplication and division) to manipulate numbers (fractions, decimals, multiples, factors, etc.) to solve real world problems.

Unit EQ

How can I effectively use the properties of numbers to understand and solve real world problems?

Concept

Concept

Concept

Fluent addition, subtraction, multiplication and division of multi-digit decimals and whole numbers.

Identification and application of properties of numbers.

Division of whole numbers and of fractions by fractions.

Lesson EQs

Lesson EQs

Lesson EQs

1. How does the answer of multiplying a whole number by a whole number compare with the answer of multiplying a whole number by a decimal?

2. How does the quotient of dividing a decimal by a whole number compare with the quotient of dividing a decimal by a decimal?

3. What strategies can I use to become fluent in adding, subtracting, multiplying and dividing whole numbers and decimals?

4. How can the divisibility rules help me become fluent in adding, subtracting, multiplying and dividing whole numbers and decimals?

1. What is the composition of numbers?

2. What is the relationship between factors and multiples?

3. How can I express the composition of a number?

4. How do I decompose numbers?

5. How can I express the decomposition of a number?

6. When would I use factors and multiples in everyday life?

1. How can I visually model division by fractions?

2. How does the quotient of dividing a whole number by a fraction differ from dividing a whole number by a whole number? Why?

3. When do I need to divide by fractions in everyday life?

4. How does the quotient from dividing by a fraction compare to the quotient from dividing by a decimal?

Vocabulary

Vocabulary

Vocabulary

Quotient; Dividend; Fraction; Sum; Difference

Multiple; Factor; Factorization; Prime Number; Composite Number; Exponent; Distribution Property; Decompose; Greatest Common Factor (GCF); Least Common Multiple (LCM); Relatively Prime; Factor Tree

Array; Model; Mixed Decimals; Mixed Numbers; Improper Fraction; Numerator; Denominator

6th Grade

Unit 1

Number System

Fluency

Unpacked Standards

Explanations, Examples, and Resources

Domain:

Cluster:

Number Systems

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

MCC6.NS.1

What does this standard mean?

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

In this standard contexts and visual models can help students to understand quotients of fractions and begin to develop the relationship between multiplication and division. Model development can be facilitated by building from familiar scenarios with whole or friendly number dividends or divisors. Computing quotients of fractions build upon and extends student understandings developed in Grade 5. In 5th grade students divided whole numbers by unit fractions. Students continue this understanding by using visual models and equations to divide whole numbers by fractions and fractions by fractions to solve word problems.

Examples and Explanations

Mathematical Practice Standards

Students understand that a division problem such as is asking, how many are in 3? One possible visual model would begin with three whole and divide each into fifths. There are 7 groups of two-fifths in the three wholes. However, one-fifth remains. Since one-fifth is half of a two-fifths group, there is a remainder of Therefore, , meaning there are groups of two-fifths. Students interpret the solution, explaining how division by fifths can result in an answer with halves.

Students also write contextual problems for fraction division problems. For example, the problem, can be illustrated with the following word problem:

Susan has of an hour left to make cards. It takes her about of an hour to make each card. About how many cards can she make?

This problem can be modeled using a number line.

1. Start with a number line divided into thirds.

2. The problem wants to know how many sixths are in two-thirds. Divide each third in half to create sixths.

Each circled part represents . There are four sixths in two-thirds; therefore, Susan can make 4 cards.

Examples:

3 people sharepound of chocolate. How much of a pound of chocolate does each person get?

Solution: Each person getslb of chocolate.

Manny has yard of fabric to make book covers. Each book is made from yard of fabric. How many book covers can Manny make? Solution: Manny can make 4 book covers.

yd

Represent in a problem context and draw a model to show your solution.

Context: You are making a recipe that calls for cup of yogurt. You have cup of yogurt from a snack pack. How much of the recipe can you make?

Explanation of Model:

The first model showscup. The shaded squares in all three models show cup.

The second model shows cup and also shows cups horizontally.

The third model shows cup moved to fit in only the area shown by of the model.

is the new referent unit (whole) .

3 out of the 4 squares in the portion are shaded. A cup is only of a cup portion, so you can only make of the recipe.

6.MP.1. Make sense of problems and persevere in solving them.

6.MP.2. Reason abstractly and quantitatively.

6.MP.3. Construct viable arguments and critique the reasoning of others.

6.MP.4. Model with mathematics.

6.MP.7. Look for and make use of structure.

6.MP.8. Look for and express regularity in repeated reasoning.

Suggested Instructional Strategy

Use this problem: How many servings of popcorn are in 4 cups if each person receives 3/4 cup of popcorn

The teacher provides 4 cups of popcorn. Students use a 3/4 cup measuring cup to solve the problem. Record solutions as a group.

1. Think-Pair-Draw-Share: Put students in pairs. Have one solve the problem using a picture/diagram and the other solve using the algorithm. Then they get together and compare.

2. Think-Pair-Share: Students solve the problem on their own, then get together and discuss how their solutions are the same and how they are different.

3. Four Corners: Give students a problem and the quotient. Give each corner in your room a label and have students go to the corner they think would be the correct label for the quotient.

Skill Based Task

Problem Task

Use representations to show that 1/4 divided by is that 2/3 divided by 2/5 is 5/3, that 2/3 divided by 3/4 is 8/9, and that 1 divided by 6/4 is 1.

You have 5/8 pound of Skittles. You want to give your friends 1/4 lb. each. How many friends can you give Skittles to? Explain your answer.

You have a 3/4-acre lot. You want to divide it into 3/8-acre lots. How many lots will you have? Draw a diagram to justify your solution.

You have a 3/4-acre lot. You want to divide it into 2 sections. How many acres in each section will you have? Draw a diagram to justify your solution.

How wide is a rectangular strip of land with length 3/4 mi. and area 1/2 square mi.?

Instructional

Resources/Tools

Models and Algorithms

TEACHER CONTENT

Math Forum - Teacher Tutorial - http://mathforum.org/dr.math/faq/faq.divide.fractions.html

Dividing Fractions - Teacher Tutorial - http://www.tpub.com/math1/5g.htm

STUDENT ACTIVITIES/LESSONS

NLVM - Fraction Number Line Bars- Interactive Applet -

http://nlvm.usu.edu/en/nav/frames_asid_265_g_3_t_1.html?open=activities&from=category_g_3_t_1.html

Visual Fractions - Divide Fractions - Interactive Applets and Game - http://www.visualfractions.com/divide.htm

UEN - Modeling Multiplication and Division of Fractions Lesson - http://www.uen.org/Lessonplan/preview.cgi?LPid=23394

Mixed Numbers and Improper Fractions


LearnAlberta - Improper Fractions and Mixed Numbers Video Lesson -

http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell02.swf

Lessons


Illuminations Feeding Frenzy - Unit Rates; Multiply/Divide Fractions - http://illuminations.nctm.org/LessonDetail.aspx?id=L781

UEN - Sticky Note Math Lesson - http://www.uen.org/Lessonplan/preview?LPid=15443

UEN - Dividing Fractions Lesson - http://www.uen.org/Lessonplan/preview?LPid=5301

Baking Cookies: http://illustrativemathematics.org/illustrations/50

Drinking Juice, Variation 2: http://illustrativemathematics.org/illustrations/412

Drinking Juice, Variation 3: http://illustrativemathematics.org/illustrations/413

How many containers are in one cup/one container: http://illustrativemathematics.org/illustrations/408

Making Hot Cocoa, Variation 1: http://illustrativemathematics.org/illustrations/407

Making Hot Cocoa, Variation 2: http://illustrativemathematics.org/illustrations/411

Running to School, Variation 2: http://illustrativemathematics.org/illustrations/410

Traffic Jam: http://illustrativemathematics.org/illustrations/464

Video Game Credits: http://illustrativemathematics.org/illustrations/267

Literature Connections:

The Doorbell Rang by Pat Hutchins

Full House: An Invitation to Fractions by Dayle Ann Dodds.

CCGPS Internet Resources:

https://ccgps.org/6.NS.html

6.NS.1

Douglas County School System

6th Grade Math 8/13/2012

Number System Fluency Page 21

Domain:

Cluster:

Number Systems

Compute fluently with multi-digit numbers and find common factors and multiples.

MCC6.NS.2


Fluently divide multi-digit numbers using the standard algorithm.

Procedural fluency is defined by the Common Core as skill in carrying out procedures flexibly, accurately, efficiently and appropriately. In the elementary grades, students were introduced to division through concrete models and various strategies to develop an understanding of this mathematical operation (limited to 4-digit numbers divided by 2-digit numbers). In 6th grade, students become fluent in the use of the standard division algorithm. This understanding is foundational for work with fractions and decimals in 7th grade.



Students are expected to fluently and accurately divide multi-digit whole numbers. Divisors can be any number of digits at this grade level.

As students divide they should continue to use their understanding of place value to describe what they are doing. When using the standard algorithm, students language should reference place value. For example, when dividing 32 into 8456, as they write a 2 in the quotient they should say, there are 200 thirty-twos in 8456 and could write 6400 beneath the 8456 rather than only writing 64.

There are 200 thirty twos in 8456.

200 times 32 is 6400.

8456 minus 6400 is 2056.


60 times 32 is 1920.

2056 minus 1920 is 136.


4 times 32 is 128.

The remainder is 8. There is not a full thirty two in 8; there is only part of a thirty two in 8.

This can also be written as or. There is of a thirty two in 8.

8456 = 264 * 32 + 8





1. Think Aloud: Do the problem with a partner while explaining and telling what you are thinking and doing.

2. Have students identify in a problem set when they would use mental math and when they would use the standard algorithm.

3. Connect students existing strategies for division with the standard algorithm.

4. As a starter activity, use division problems that can reasonably be solved by using mental math (e.g., 105/25), estimation (e.g., 150 12, 227 30), and reasoning (e.g., when I think of 105 divided by 25, I think of 4 sets of 25 with 5 left over, the 5 left over is 5/25 which is 1/5, so the answer is 4 1/5). Model for the students your thinking as you work through the problem. (Note: This strategy would not apply to complex division problems for which the algorithm is most appropriate [e.g., 4567 192]).

Skill Based Task

Problem Task

248 divided by 18.

I spent $504 on 28 tickets for a rock concert. How much did I spend on each ticket?

Instructional

Resources/Tools

Elementary & Middle School Mathematics (VanDeWalle, 7th Ed.)

TEACHER CONTENT

Division of Whole Numbers: p. 232-237

STUDENT ACTIVITIES

Division of Whole Numbers: p. 232-237 Figures 12.23-12.27 & problems in bold print


TEACHER CONTENT

Division of Whole Numbers: p. 236-241

STUDENT ACTIVITIES

Division of Whole Numbers: p. 236-241 Figures 13.24-13.28 & problems in bold print

Internet:

Division of Whole Numbers

TEACHER CONTENT

LearnAlberta - Division of Whole Numbers - Video Tutorial http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=9


BBC - Division Strategy Practice - http://www.bbc.co.uk/skillswise/numbers/wholenumbers/division/written/game.shtml

Division by a 2-Digit Number - Algorithm Applet - http://www.doubledivision.org/

http://nlvm.usu.edu/en/nav/frames_asid_197_g_2_t_1.html?open=activities&from=search.html?qt=division

Literature Connection: The Phantom Tollbooth by Norton Juster


https://ccgps.org/6.NS_41B6.html

6.NS.2

Domain:

Cluster:

Number Systems


MCC6.NS.3


Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Procedural fluency is defined by the Common Core as skill in carrying out procedures flexibly, accurately, efficiently and appropriately. In 4th and 5th grades, students added and subtracted decimals. Multiplication and division of decimals was introduced in 5th grade (decimals to the hundredth place). At the elementary level, these operations were based on concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. In 6th grade, students become fluent in the use of the standard algorithms of each of these operations.



The use of estimation strategies supports student understanding of operating on decimals.

Example:

First, students estimate the sum and then find the exact sum of 14.4 and 8.75. An estimate of the sum might be 14 + 9 or 23. Students may also state if their estimate is low or high. They would expect their answer to be greater than 23. They can use their estimates to self-correct.

Answers of 10.19 or 101.9 indicate that students are not considering the concept of place value when adding (adding tenths to tenths or hundredths to hundredths) whereas answers like 22.125 or 22.79 indicate that students are having difficulty understanding how the four-tenths and seventy-five hundredths fit together to make one whole and 25 hundredths.

Students use the understanding they developed in 5th grade related to the patterns involved when multiplying and dividing by powers of ten to develop fluency with operations with multi-digit decimals.





Have students look at student work that contains a common misconception and look at errors and discuss how to correct the error.

Skill Based Task

Problem Task

Skill-based Task:

1. 242.134 + 308.02

2. 38.9 14.334

3. 11.82 x 2.81

4. 341.8 1.2

The school had a bake sale and raised $75.55. If each cookie cost $0.05, how many cookies were sold? Explain how you got your answer.

Instructional

Resources/Tools


TEACHER CONTENT

Computation with Decimals: p. 342-345

STUDENT ACTIVITIES

Computation with Decimals: p. 342-345 Activity 17.11-17.13 & problems in bold print


TEACHER CONTENT

Computation with Decimals: p. 346-350

STUDENT ACTIVITIES

Computation with Decimals: p. 346-350 Activity 18.12-18.14 & problems in bold print

Internet:

Addition/Subtraction of Decimals


NLVM - Base Block Decimals - http://nlvm.usu.edu/en/nav/frames_asid_264_g_3_t_1.html?from=category_g_3_t_1.html

NLVM - Circle 3 - Adding Decimals - Puzzle -

http://nlvm.usu.edu/en/nav/frames_asid_187_g_3_t_1.html?open=instructions&from=category_g_3_t_1.html

LearnAlberta - Solving Problems with Decimals Video Lesson -

http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell05.swf

LearnAlberta - Addition and Subtraction of Decimals Video Lesson -

http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=7

Math Play - Jeopardy - Computation Game - http://www.math-play.com/Decimals-Jeopardy/decimals-jeopardy.html

Multiplication/Division of Decimals

TEACHER CONTENT

LearnAlberta - Multiplication and Division of Decimals - Video Tutorial -

http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=10


https://ccgps.org/6.NS_8KH5.html

6.NS.3

Domain:

Cluster:

Number Systems


MCC6.NS.4


Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

Students will find the greatest common factor of two whole numbers less than or equal to 100. Students also understand that the greatest common factor of two prime numbers will be 1



Students will find the greatest common factor of two whole numbers less than or equal to 100.

For example, the greatest common factor of 40 and 16 can be found by

1) listing the factors of 40 (1, 2, 4, 5, 8, 10, 20, 40) and 16 (1, 2, 4, 8, 16), then taking the greatest common factor (8). Eight (8) is also the largest number such that the other factors are relatively prime (two numbers with no common factors other than one). For example, 8 would be multiplied by 5 to get 40; 8 would be multiplied by 2 to get 16. Since the 5 and 2 are relatively prime, then 8 is the greatest common factor. If students think 4 is the greatest, then show that 4 would be multiplied by 10 to get 40, while 16 would be 4 times 4. Since the 10 and 4 are not relatively prime (have 2 in common), the 4 cannot be the greatest common factor.

2) listing the prime factors of 40 (2 2 2 5) and 16 (2 2 2 2) and then multiplying the common factors (2 2 2 = 8).

Students also understand that the greatest common factor of two prime numbers will be 1. Students use the greatest common factor and the distributive property to find the sum of two whole numbers. For example, 36 + 8 can be expressed as 4 (9 + 2) = 4 (11). Students find the least common multiple of two whole numbers less than or equal to twelve.

For example, the least common multiple of 6 and 8 can be found by

1) listing the multiples of 6 (6, 12, 18, 24, 30, ) and 8 (8, 26, 24, 32, 40), then taking the least in common from the list (24); or

2) using the prime factorization.

Step 1: find the prime factors of 6 and 8.

6 = 2 3

8 = 2 2 2

Step 2: Find the common factors between 6 and 8. In this example, the common factor is 2

Step 3: Multiply the common factors and any extra factors: 2 2 2 3 or 24 (one of the 2s is in common; the other 2 and the 3 are the extra factors.



Solve for LCM and/or GCF using factor towers, Venn diagrams, and factor trees.

Use a model to show that 4(9 + 2) is four groups of 9 and four groups of 2.

Skill Based Task

Problem Task

Find the greatest common factor of 24 and 60.

Find the least common multiple of 6 and 10.

Use the distributive property to show 15 + 75.

Hot dogs come in packs of 8. Buns come in packs of 12. How many packs of hot dogs and bags of buns would you have to buy to have an equal number of hot dogs and buns?

You need to make gift bags for a party with the same number of balloons and candy in each bag. One package of candy has 24 pieces. One package of balloons has 20 balloons. You need to use all the candy and all the balloons. What is the greatest number of gift bags that you can make containing an equal number of items?

Instructional

Resources/Tools


TEACHER CONTENT

Properties of Multiplication and Division: p. 160-161


TEACHER CONTENT

Properties of Multiplication and Division: p. 157-158

Web:

Greatest Common Factor and Least Common Multiple

TEACHER CONTENT

Amby - Teacher Tutorial - http://amby.com/educate/math/


Illuminations - The Venn Factor Lesson - http://illuminations.nctm.org/LessonDetail.aspx?id=L859

Illuminations - Factor Findings Lesson - http://illuminations.nctm.org/LessonDetail.aspx?id=L872

Illuminations - Factor Trail Game Lesson - http://illuminations.nctm.org/LessonDetail.aspx?id=L719

NLVM - Factor Tree - Interactive Applet - http://nlvm.usu.edu/en/nav/frames_asid_202_g_2_t_1.html?from

LearnAlberta Spy Guys - Factors, Multiples, and Prime Factorization Video Lesson - http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell07.swf

IXL - GCF and LCM Word Problems - Assessment - http://www.ixl.com/math/grade-6/greatest-common-factor-word-problems

Greatest Common Factor Lesson

http://www.math.com/school/subject1/lessons/S1U3L2GL.html

This lesson is a resource for teachers or for students after participating in lessons exploring GCF.

Distributive Property


Study Stack - Matching Game - http://www.studystack.com/matching-1870

Illuminations - Distributing and Factoring Using Area Lesson - http://illuminations.nctm.org/LessonDetail.aspx?id=L744


https://ccgps.org/6.NS_B3VJ.html

6.NS.4

More Resources Misconceptions Take Note

Resources:

Lesson Websites:

Visually model word problems with fractions - www.thinkingblocks.com *Great with the SmartBoard!

Factors & Multiples: http://www.math.com/school/subject1/lessons/S1U3L1GL.html

Greatest Common Factor: http://www.math.com/school/subject1/lessons/S1U3L2GL.html

Factoring: http://www.purplemath.com/modules/factnumb.htm

Divisibility Rules: http://mathforum.org/dr.math/faq/faq.divisibility.html

Game Websites:

Higher order fraction addition: http://fen.com/studentactivities/MathSplat/mathsplat.htm

Factor & Multiple Jeopardy: http://www.math-play.com/Factors-and-Multiples-Jeopardy/Factors-and-Multiples-Jeopardy.html *Up to four teams keeps score for you!

Factors/Divisibility Rules: http://www.aaamath.com/g57f-findafactor.html

Prime Factorization/Multiples/Factors Jeopardy: http://www.quia.com/cb/8436.html

Least Common Multiple: http://www.aaamath.com/g57i-lcm.html

Add/Subtract/Multiply/Divide Fractions: http://www.funbrain.com/fractop/index.html

Literature:

My Full Moon is Square by Elinor J. Pinczes

The Doorbell Rang by Pat Hutchins

Spaghetti and Meatballs for All by Marilyn Burns

Dads Diet by Barbara Comer

One Riddle, One Answer by Laura Thompson

Beasts of Burden in the Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan

Misconceptions/Suggestions:

Dividing a number by a fraction does not produce a smaller quotient than the dividend. Instead, dividing a number by a fraction produces a quotient larger than the dividend. Why? Dividing by a fraction is solving how many parts are in the whole.

When dividing decimals, students tend to focus on the algorithm and not consider the actual values of the numbers. Start division of decimals with estimation.

Take Note:

A strong focus is on fluency and on real world application this year! Please visit the corestandards.org Mathematics standards page 4 to read more about how we must shift the students way of thinking and their approach to mathematics.

Addition, subtraction and multiplication of fractions and mixed numbers have been moved from this unit! Division by fraction is the primary focus.

Students should already know, but you may have to review:

Decimal place values to the 10thousandths place;

The standard algorithm for addition, subtraction, multiplication and division;

How to use estimation to predict and assess whether a solution is reasonable;

How to add, subtract and multiply fractions and mixed numbers;

A simplified fraction regardless of the value of the numerator and/or the denominator is always between 0 & 1. (Later this year, they will learn the value of a fraction is also between 0 & -1);

Fractions are just a representation of division.

Just as multiplication is repeated addition, division is repeated subtraction.

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