Common Core State Standards Fractions

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Outcomes:

 Participants will unwrap the fraction and decimal standards to determine the concepts, procedures and type of problems students are expected to master. Participants will engage in learning activities that build fraction meaning, relationships, and operations along with decimal meaning and relationships using various tools and strategies.

Agenda

 Unwrap standards

 Building meaning of fractions and decimals

 Make fraction equivalencies using areas and number lines

 Compare fractions using the same whole by comparing same numerators, same denominators, or benchmark values.

 Instructional Planning

My Reflection on Multiplication and Division:

Standards that Impact Student Achievement for Grades 3-5

Grade 3

Operations and Algebraic Thinking

Numbers and Fractions Measurement

3.OA.1 3.OA.2

Interpret products and interpret quotients

3.OA.7 Multiply and divide within 100

3.NF.1 Defining a fraction

3.NF.3 Equivalent fractions and comparing fractions

3.MD.2

Solve problems of mass and volume using all operations

3.MD.7

Concepts of area as it relates to multiplication and division.

Grade 4

Numbers and Base Ten Numbers and Fractions 4.NBT.4

Add and subtract to 100,000

4.NBT.5 Multiply 4- digit x 1-digit and 2-digit x 2-digit

4.NBT.6 Division including understanding remainders

4.NF.1 Equivalent fractions

4.NF.3 Addition and subtraction of fractions

including word problems.

4.NF.4 Multiplication of fractions including word problems.

Grade 5

Numbers and Base Ten Numbers and Fractions Measurement 5.NBT.1

Powers of 10 and our place value system

5.NBT.6 Division up to 4- digit by 2-digit (equations, arrays, area model)

5.NF.2

Word problems involving addition and subtraction of fractions.

5.NF.3

Interpret a fraction as a division problem and solve problems leading to a fractional quotient

5.MD.5 Concept of volume

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My Notes:

Fraction Meaning

Fraction Relationships:

Equivalence and Comparisons

Fraction Operations

Decimal Meaning

Decimal Relationships

Fraction Meaning

Models: Area, Line or Set Defining a Fraction:

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Naming Fractions, Representing Fractions

Part A:

Now you will need to think differently. Each shape represents a part of the whole described by the fraction. Complete the shape by representing the whole.

Part B:

The line on top of the number line represents a fractional value. Draw the line underneath the number line that would represent the whole.

1.

2.

Part C:

In problems 3-5, find the value of x and locate 1 on each number line. Justify your solutions.

3 2

4 3

2 1

3 2 3

1 2

4 3

4

1

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3.

4.

5.

Part D:

6. If ½ of this set should be red, which ones are red?

7. What fraction of this set is gray?

8. If 4 circles are 1/5 of a set, how many circles are in the set?

9. If 6 triangles are 2/3 of a set, how many triangles are in the set?

0

0 0

3 x 4

x

5 8

12 3

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For problems 10 - 12, use this set below. By adding and subtracting cards, describe what you will do to this set to show that . . .

10.

1

2 of the cards are clubs?

11.

5

8of the cards are diamonds?

12.

1

4 of the cards are black and

1

2 are hearts?

Notes for Pattern Blocks, Cuisenaire Rods, and Number Lines

   

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Fraction Relationships: Equivalent Fractions

Using the pattern blocks, we will find several equivalent areas. For each representation, think about how you would use a fraction to describe what you are showing.

1. Let one hexagon represent the whole.

a. 1 red trapezoid ( ) represents _______ of the whole.

2 red trapezoid ( ) represents _______ of the whole.

b. What is another name for the 1 whole hexagon? ______________________

3 green triangles ( ) cover the same area as 1 red trapezoid and represent ______ of the whole.

c. What are two fractions that are equivalent? ______________________ How do you know?

d. How many green triangles ( ) cover the entire hexagon? _____________ How do you write this as a fraction?

2. Now let two hexagons represent the whole.

a. 1 red trapezoid ( ) represents _______ of the whole.

b. 3 green triangles ( ) cover the same area but represent ______ of the whole.

c. What are two fractions that are equivalent? ______________________

3. Again, let two hexagons represent the whole.

a. 1 hexagon represents ______ of the whole.

b. The area can also be represented by ___ green triangles. This value is written as _______.

c. You can also represent this region with ____ blue parallelograms. This value is written using the fraction ______.

d. What are the three fractions that represent equivalent areas? _____________________

4. Again, let two hexagons represent the whole.

G r e e n Red (R) Red (R)

Red (R)

G r e e n

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a. 2 blue parallelograms represent ______ of the whole.

b. 4 green triangles cover this same area but represent ___________ of the whole.

c. What are two fractions that are equivalent? _______________________

d. What is another name for this area? Why?

Fraction Relationships: Equivalent Fractions

1. Compose the shaded fraction into larger fractional units. Write the equivalent fractions.

2. Compose the shaded fraction into larger fractional units. Write the equivalent fractions.

3. Draw an area model to represent each number sentence below.

𝟐 𝟑=^𝟔

𝟗 ^𝟗

𝟏𝟐= ^𝟑

𝟒

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Building Meaning of Equivalence in Context

1. In the pictures shown below, each group is made up of two cakes. The shaded (gray) section show how much is left of each cake. Compare the two cakes within each group. Determine if the cakes in each group have the same amount of cake or different amounts of cake left to be eaten Be ready to justify your thinking.

Group A Group B Group C Group D

Group A: same amount or different amount Group B: same amount or different amount Group C: same amount or different amount Group D: same amount or different amount

2. Create two different cakes from those above that would be cut differently but would show how the two cakes have the same amount of cake left to eat. Show in symbols how you know your cakes have equivalent amounts left to eat?

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Fraction Relationships - Comparing

1. Comparing has to begin with the same whole.

2. Comparing with like size pieces (same denominator).

Example: Compare each of the following sets of fractions by placing them on a number line.

a. ⁵

8 ⁶

8 ³

8 ¹

8 b. ⁵

7 ³

7 ⁶

7 ¹⁰

7

3. Comparing with same number of pieces (same numerator).

Example 1: Compare unit fractions using >, < or =.

a. 1 fourth 1 eighth

b. 1 seventh 1 fifth

c. 1 eighth ¹

8

d. 1 twelfth ¹

10

e. 1

15 1 thirteenth

f. 3 thirds 1 whole

Example 2: Compare each of the following sets of fractions using a number line.

a. ⁴

8 ⁴

5 ⁴

6

b. ⁴

10 ⁴

12 ⁴

3 ⁴

37

4. Comparing to benchmark numbers.

Example: Compare by determining how close a fraction it to zero or to one.

Close to Zero Close to 1

Example: Compare by determining how close a fraction it to zero, to ½ or to one.

Close to Zero Close to ½ Close to 1

Example: Use these estimations to write problems about sums or differences. Write a problem (using these fractions) whose sum would be approximately 1?

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Part A

Circle the fraction in each pair that is greater in value. Use a model and/or strategy to justify your thinking and try to figure out each one using concepts versus an algorithm.

Remember to think about how a value relates to zero, ½, and 1.

A. ⁵

8 𝑜𝑟 ³

8

B. ⁵

6 𝑜𝑟 ⁵

9

C. ⁵

12 𝑜𝑟 ³

8

D. ⁵

6 𝑜𝑟 ⁹

10

E. ⁴

7 𝑜𝑟 ⁵

9

Part B – Putting it into Context

Use what you know about benchmark numbers and making comparison to answer these questions.

F. There are two parking lots shown below. Which one is more occupied? Why? Use table and diagrams and numbers to explain your thinking.

Parking Lot A Parking Lot B

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Adding and Subtracting Fractions

 Ken and Barbie are eating pizza. Ken ate 3/6 of the pizza and Barbie at 2/6 of the pizza.

How much did they eat altogether? Show this with your pattern blocks.

 You need 8 ¹/8 yards of ribbon for your project. You have 4 ³/8 yards and your sister has 3 ⁵/8 yards of ribbon. How much ribbon do you have altogether? and is this enough to complete the project? Show this with the Cuisenaire Rods. Use Brown as your whole.

 Timothy has 4 ⅙ pizzas left over from his soccer party. After giving some pizza to his friend, he has 2 ⅚ of a pizza left. How much pizza did Timothy give to his friend?

1. Solve by modeling and writing the sum in unit form.

2. Solve by using a number bond to decompose to find the sum. Record your sum as a mixed number.

3. Solve by modeling and then writing the difference in unit form

4. Solve by using a number bond to decompose to find the difference. Record your sum as a mixed number.

5. Mrs. Smith too her bird to the vet. Tweety weighted 1 3/10 pounds. The vet said that Tweety weighted 4/10 pound more last year. How much did Tweety weigh last year?

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6. Ally’s little sister wanted to help her make some oatmeal cookies. First, she put 5/8 cup of oatmeal in the bowl. Next, she added another 5/8 cut of oatmeal. Finally, she added another 3/8 cup oatmeal. How much oatmeal did she put in the bowl?

Part A – Putting it into Context

What are three different ways you can find the solutions to these problems. What would be a word problem that would go with each one?

Problem A: ¹

8+²

8+⁴

8

Problem B: ¹ 6+²

6+⁴

6

Problem C: ¹¹ 10− ⁴

10− ¹

10

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Multiplying Fractions

 You plan on having 6 people to your party. The recipe for cupcakes calls for 2 teaspoons of chips per cupcake. How many teaspoons of chips will you need?

 You plan on having 6 people to your party. The recipe for shredded beef sandwiches calls for 3/8 pound of beef for every person. How much beef will you need to buy?

Part A: Problem in Context

1. Mrs. Smith needs ½ cup of milk for a cake recipe. If she makes 4 cakes, how much milk will she need?

2. Sally is making bows for the cheer squad. Each bow requires ¼ of a yard of ribbon. If she makes 8 bows, how much ribbon will she need? How much ribbon will she need for 13 bows?

3. Mr. Jacobs is making punch for dinner. The recipe calls for ¾ a cup of orange juice for a single serving. He is making 8 servings. How much orange juice does he need?

4. Jose uses cable to tie up a sunblock that is triangular. He needs 4 ½ feet of cable for each corner. The spool of cable contains 15 feed of cable. Will he have enough? If so, how much cable will be left? If not, how much cable does he need?

Part B: Generalizing Patterns for Multiplication

What does this question ask students to know about multiplication of fractions?

1. Kara wrote an expression that has a value of 12/5. Choose YES or NO to indicate whether each expression has a value of 12/5.

a) 12 x 1/5

o

^Yes

o

^No

b) 12 x 5/5

o

^Yes

o

^No

c) 3 x 4/5

o

^Yes

o

^No

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Naming and Representing Decimals

Connecting decimals to fractions and using visuals helps with the misconceptions of how we say decimal values.

1 Model Z is shaded to represent a value that is less than 1 whole. Determine if each value represents Model Z. .

a) 30/100

o

^Yes

o

^No

b) 3/10

o

^Yes

o

^No

c) 0.03

o

^Yes

o

^No

Circle the equivalent ways to represent each number.

2 . 3 . 4 .

5 .

Find the sum and color in the appropriate areas of each box to show the value of each addend and the sum.