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on Core

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atics Instruction

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4Common CoreInstruction

Mathematics

Table of Contents

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CCSSUnit 1: Number and Operations in Base Ten, Part 1 . . . . . . . 1

Lesson 1 Understand .Place .Value . . . . . . . . . . . . . . . . . . . . . . 2 . 4 NBT 1, .4 NBT 2

Lesson 2 Compare .Whole .Numbers . . . . . . . . . . . . . . . . . . . . 8 . 4 NBT 2

Lesson 3 Add .and .Subtract .Whole .Numbers . . . . . . . . . . . . . . . 16 . 4 NBT 4

Lesson 4 Round .Whole .Numbers . . . . . . . . . . . . . . . . . . . . . .26 . 4 NBT 3

Unit 1 Interim Assessment . . . . . . . . . . . . . . . . . . . . . . . . . .34

Unit 2: Operations and Algebraic Thinking . . . . . . . . . . . . .37

Lesson 5 Understand .Multiplication . . . . . . . . . . . . . . . . . . . .38 . 4 OA 1

Lesson 6 Multiplication .and .Division .in .Word .Problems . . . . . . . .44 . 4 OA 2

Lesson 7 Multiples .and .Factors . . . . . . . . . . . . . . . . . . . . . . 54 . 4 OA 4

Lesson 8 Number .and .Shape .Patterns . . . . . . . . . . . . . . . . . . .66 . 4 OA 5

Lesson 9 Model .Multi-Step .Problems . . . . . . . . . . . . . . . . . . 76 . 4 OA 3

Lesson 10 Solve .Multi-Step .Problems . . . . . . . . . . . . . . . . . . . .84 . 4 OA 3

Unit 2 Interim Assessment . . . . . . . . . . . . . . . . . . . . . . . . . 92

Unit 3: Number and Operations in Base Ten, Part 2 . . . . . . .95

Lesson 11 Multiply .Whole .Numbers . . . . . . . . . . . . . . . . . . . . .96 . 4 NBT 5

Lesson 12 Divide .Whole .Numbers . . . . . . . . . . . . . . . . . . . . . 106 . 4 NBT 6

Unit 3 Interim Assessment . . . . . . . . . . . . . . . . . . . . . . . . 116

Unit 4: Number and Operations—Fractions . . . . . . . . . . . 119

Lesson 13 Understand .Equivalent .Fractions . . . . . . . . . . . . . . . 120 . 4 NF 1

Lesson 14 Compare .Fractions . . . . . . . . . . . . . . . . . . . . . . . . 126 . 4 NF 2

Lesson 15 Understand Fraction .Addition .and .Subtraction . . . . . . 136 . 4 NF 3 a, .4 NF 3 b

Lesson 16 Add .and .Subtract .Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142 . 4 NF 3 a, .4 NF 3 d

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Table of Contents

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CCSSUnit 4: Number and Operations—Fractions (continued)

Lesson 17 Add .and .Subtract .Mixed .Numbers . . . . . . . . . . . . . . 152 . .4 NF 3 b, .4 NF 3 c, .4 NF 3 d

Lesson 18 Understand .Fraction .Multiplication . . . . . . . . . . . . .162 . 4 NF 4 a, .4 NF 4 b

Lesson 19 Multiply .Fractions . . . . . . . . . . . . . . . . . . . . . . . . . 168 . 4 NF 4 c

Lesson 20 Fractions .as .Tenths .and .Hundredths . . . . . . . . . . . . . 176 . 4 NF 5

Lesson 21 Relate .Decimals .and .Fractions . . . . . . . . . . . . . . . . . 184 . 4 NF 6

Lesson 22 Compare .Decimals . . . . . . . . . . . . . . . . . . . . . . . . 194 . 4 NF 7


Unit 5: Measurement and Data . . . . . . . . . . . . . . . . . . . . . 207

Lesson 23 Convert .Measurements . . . . . . . . . . . . . . . . . . . . . 208 . .4 MD 1

Lesson 24 Time .and .Money . . . . . . . . . . . . . . . . . . . . . . . . .218 . 4 MD 2

Lesson 25 Length, .Liquid .Volume, .and .Mass . . . . . . . . . . . . . . . 228 . 4 MD 2

Lesson 26 Perimeter .and .Area . . . . . . . . . . . . . . . . . . . . . . . . 240 . 4 MD 3

Lesson 27 Line .Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 . 4 MD 4

Lesson 28 Understand .Angles . . . . . . . . . . . . . . . . . . . . . . . . 262 . 4 MD 5 a, .4 MD 5 b

Lesson 29 Measure .and .Draw .Angles . . . . . . . . . . . . . . . . . . 268 . 4 MD 6

Lesson 30 Add .and .Subtract .With .Angles . . . . . . . . . . . . . . . . . 278 . .4 MD 7


Unit 6: Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

Lesson 31 Points, .Lines, .Rays, .and .Angles . . . . . . . . . . . . . . . . . 292 . 4 G 1

Lesson 32 Classify .Two-Dimensional .Figures . . . . . . . . . . . . . . . 304 . 4 G 2

Lesson 33 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .316 . 4 G 3


Common Core State Standards for Mathematics, Grade 4 . . . . . 329


©Curriculum Associates, LLC Copying is not permitted.L15: Understand Fraction Addition and Subtraction136

Understand Fraction Addition and SubtractionLesson 15 Part 1: Introduction

Focus on Math Concepts

What’s really going on when we add numbers?

Adding means joining or putting things together.

Think about how you could explain adding 2 1 3 to a first grader. You could start at 2, count on 3 more, and see where you end up: 2 . . . 3 . . . 4 . . . 5.

Or, you could put a segment with a length of 2 and a segment with a length of 3 next to each other on a number line to show 2 1 3.

0 1 2 3 4 5 6 7 8 9 10

1 1 1 1 1

When you add 2 1 3, you are putting ones together.

Think

Adding fractions means joining or putting together parts of the same whole.

You can put a segment with a length of 2 ·· 4 and a segment

with a length of 3 ·· 4 next to each other to show 2 ·· 4 1 3 ·· 4 .

0 1 2

14

04

44

84

24

34

54

64

74

14

14

14

14

14

When you add 2 ·· 4 1 3 ·· 4 , you are putting one-fourths together.

Underline the sentence that explains what adding fractions means.

CCSS4.NF.3.a4.NF.3.b


©Curriculum Associates, LLC Copying is not permitted.137L15: Understand Fraction Addition and Subtraction

Lesson 15Part 1: Introduction

Think

Subtracting means separating or taking away.

On a number line, you can start with a segment of length 5 and take away a segment of length 2 to show 5 2 2.

0 1 2 3 4 5 6 7 8 9 10

1 1 1 1 1

1 1

When you subtract 5 2 2, you are taking away ones.

You can show subtracting fractions on a number line. Start with a segment of

length 5 ·· 4 and take away a segment of length 2 ·· 4 to show 5 ·· 4 2 2 ·· 4 .

14

24

34

54

64

74

84

44

04

0 1 2

14

14

14

14

14

14

14

When you subtract 5 ·· 4 2 2 ·· 4 , you are taking away one-fourths.

Now you’ll have a chance to think more about how adding or subtracting fractions is like adding or subtracting whole numbers. You may find that using number lines or area models can help you explain your thinking.

Reflect

1 Use your own words to describe what you just learned about adding and subtracting fractions.

Look at the whole numbers. Now look at the numerators of the fractions. I think I see a connection.


Part 2: Guided Instruction Lesson 15

©Curriculum Associates, LLC Copying is not permitted.

L15: Understand Fraction Addition and Subtraction138

Explore It

Counting on and using a number line are two ways to think about adding fractions.

2 Count by fourths to fill in the blanks: 1 ·· 4 , 2 ·· 4 , , 4 ·· 4 , 5 ·· 4 , , , ,

Now label the number line.

0 1

424

44

54

10 4

3 Count by fifths to fill in the blanks: 1 ·· 5 , 2 ·· 5 , , ,

Now label the number line.

0 1

525

65

Use the number lines above to answer numbers 4 and 5.

4 What is 1 ·· 4 more than 6 ·· 4 ?

5 What is 1 ·· 5 more than 3 ·· 5 ?

Now try these two problems.

6 Label the number line below and use it to show 2 ·· 4 1 1 ·· 4 .



Part 2: Guided Instruction Lesson 15


Talk About It

Solve the problems below as a group.

8 Look at your answers to problems 2 and 3. How is counting by fractions the same as counting with whole numbers?

How is it different?



Try It Another Way

Work with your group to use the area models to show adding or subtracting fractions.

11 Show 1 ·· 8 1 2 ·· 8 .

12 Show 6 ·· 10 2 2 ·· 10 .


Part 3: Guided Practice Lesson 15


L15: Understand Fraction Addition and Subtraction140

Connect It

Talk through these problems as a class, then write your answers below.

13 Compare: Draw two different area models to show 2 ·· 3 2 1 ·· 3 .

14 Explain: Rob had a large pizza and

a small pizza. He cut each pizza into

fourths. He took one fourth from each

pizza and used the following problem

to show their sum: 1 ·· 4 1 1 ·· 4 5 2 ·· 4 .

What did Rob do wrong?

15 Demonstrate: Think about how you would add three whole numbers. You add two of the numbers first, and then add the third to that sum. You add three fractions the same way.

Use the number line and area model below to show 1 ·· 10 1 3 ·· 10 1 4 ·· 10 .


Part 4: Common Core Performance Task Lesson 15


Put It Together

16 Use what you have learned to complete this task.

Jen has 4 ··

 10

of a kilogram of dog food. Luis has 3 ··

 10

of a kilogram of dog food.

A large dog eats 2 ··

 10

of a kilogram in one meal.

A Write two different questions about this problem that involve adding or subtracting fractions.

i

ii

B Choose one of your questions to answer. Circle the question you chose. Show how to find the answer using a number line and an area model.


©Curriculum Associates, LLC Copying is not permitted.L16: Add and Subtract Fractions142

Add and Subtract FractionsLesson 16 Part 1: Introduction

In Lesson 15, you learned that adding fractions is a lot like adding whole numbers. Take a look at this problem.

Lynn, Paco, and Todd split a pack of 12 baseball cards. Lynn got 4 cards, Paco

got 3 cards, and Todd got the rest of the cards. What fraction of the pack did

Todd get?

Explore It

Use the math you already know to solve the problem.

How many cards did Lynn and Paco get altogether?

How many cards did Todd get?

There are 12 cards in the pack. What fraction represents the whole pack of cards?

If Lynn got 4 cards out of 12, that means she got 4 ·· 12 of the pack. If Paco got 3 cards

out of 12, what fraction of the pack did he get?

What fraction of the pack did Lynn and Paco get altogether?

Explain how you could find the fraction of the pack that Todd got.

CCSS4.NF.3.a4.NF.3.d


©Curriculum Associates, LLC Copying is not permitted.143L16: Add and Subtract Fractions

Lesson 16Part 1: Introduction

Find Out More

We often use fractions in real life. Sometimes they refer to parts of a set of objects, like the baseball card problem. In that problem, the “whole” is the pack, and 12 cards means there are 12 parts of the whole.

Each person got baseball cards from the same pack, so each fraction refers to the same whole. When you add or subtract baseball cards, the whole will stay the same because the cards are all from the same pack of 12.

412

312

512

Fractions in real life can also refer to equal parts of a whole object. Lynn, Paco, and Todd might share a pizza cut into 8 slices. The “whole” is the pizza, and 8 slices means there are 8 equal parts of the whole. No matter if a person takes away 1 slice or 3 slices from the pizza, the whole will stay the same.

Reflect

1 Describe another example of a set of objects or a whole object divided into fractions.


Lesson 16


L16: Add and Subtract Fractions144

Part 2: Modeled Instruction

Read the problem below. Then explore different ways to understand it.

Josie and Margo made 10 clay pots in art class. Josie painted 3 ··

 10

of the pots.

Margo painted 4 ··

 10

of the pots. What fraction of the clay pots did they paint?

Picture It

You can use models to help understand the problem.

The following model shows the pots. Each pot is 1 ·· 10 of the total number of pots.

Josie painted 3 pots, and Margo painted 4 pots. They painted a total of 7 pots.

1

3 tenths 4 tenths 7 tenths

5J J J J J JJ J

M M M M

J M M M M

Model It

You can also use a number line to help understand the problem.

The following number line is divided into tenths, with a point at 3 ·· 10 .

0 11

10210

310

410

510

610

710

810

910

Start at 3 ·· 10 and count 4 jumps to the right to add 4 tenths.

0 11

102

103

104

105

106

107

108

109

10


Lesson 16


Part 2: Guided Instruction

Connect It

Now you will solve the problem from the previous page using equations.

2 How do you know that each pot is 1 ·· 10 of the total number of pots?

3 What do the numerators, 3 and 4, tell you?

4 How many clay pots did Josie and Margo paint altogether?

5 Write equations to show what fraction of the clay pots Josie and Margo painted altogether.

Use words: 3 tenths 1 4 tenths 5 tenths

Use fractions: 3 ·· 10 1 4 ·· 10 5 ···· 10

6 Explain how you add fractions with the same denominator.

Try It

Use what you just learned to solve these problems. Show your work on a separate sheet of paper.

7 Lita and Otis are helping their mom clean the house. Lita cleaned 1 ·· 3 of the rooms.

Otis cleaned 1 ·· 3 of the rooms. What fraction of the rooms did Lita and Otis clean

altogether?

8 Mark’s string is 1 ·· 5 of a meter long. Bob’s string is 3 ·· 5 of a meter long. How long are

the two strings combined?


Lesson 16



Read the problem below. Then explore different ways to understand it.

Alberto’s water bottle had 5 ··

 6 of a liter in it. He drank 4

·· 

6 of a liter. What fraction

of the bottle still has water in it?

Picture It

You can use models to help understand the problem.

The following model shows the water bottle divided into 6 equal parts. Each part

is 1 ·· 6 of a liter. Five shaded parts show how much water is in the bottle.

Alberto drank 4 parts of the water in the bottle, so take away 4 shaded parts of the bottle. There is 1 part of the bottle left with water in it.

2 5

5 sixths 4 sixths 1 sixth

Model It

You can use a number line to help understand the problem.

The following number line is divided into sixths, with a point at 5 ·· 6 .

0 11

626

36

46

56

Start at 5 ·· 6 and count 4 jumps to the left to subtract 4 sixths.

0 11

626

36

46

56

Part 3: Modeled Instruction


Lesson 16


Connect It

Now you will solve the problem from the previous page using equations.

9 How do you know that each part is 1 ·· 6 of a liter?

10 What do the numerators, 5 and 4, tell you?

11 How many parts of water are left in the bottle after Alberto drank 4 parts?

12 Write equations to show what fraction of the bottle has water left in it.

Use words: 5 sixths 2 4 sixths 5 sixth

Use fractions: 5 ·· 6 2 4 ·· 6 5 ···· 6

13 Explain how you subtract fractions with the same denominator.

Try It

Use what you just learned to solve these problems. Show your work on a separate sheet of paper.

14 Mrs. Kirk had 3 ·· 4 of a carton of eggs. She used 2 ·· 4 of the carton to make breakfast.

What fraction of the carton of eggs does Mrs. Kirk have left?

15 Carmen had 8 ·· 10 of the yard left to mow. She mowed 5 ·· 10 of the yard. What fraction

of the yard is left to mow?

Part 3: Guided Instruction


Student Model




How did you and your partner decide what fraction to start with?

Pair/Share

Whatfractionrepresentsthewholefruitsmoothie?

How else could you solve this problem?

Pair/Share

Thestudentusedlabelsand“jump”arrowstoshoweachpartofthehikeonanumberline.Itisjustlikeaddingwholenumbers!

Study the model below. Then solve problems 16–18.

Jessica hiked 2 ··

 5 mile on a trail before she stopped to get a drink

of water. After her drink, Jessica hiked another 2 ··

 5 mile. How far

did Jessica hike in all?

Look at how you could show your work using a number line.

0 115

25

35

45

25

25

before drink after drink

Solution:

16 Ruth made a fruit smoothie. She drank 1 ·· 3 of it. What fraction of the

fruit smoothie is left?

Show your work.

Solution:

4 ·· 5 mile




Ithinkthatthereareatleasttwodifferentstepstosolvethisproblem.

How is this problem different from the others you’ve seen in this lesson?

Pair/Share

TofindthefractionofthebagEmilyandNickatealtogether,shouldyouaddorsubtract?

Does Rob’s answer make sense?

Pair/Share

17 Mr. Chang has a bunch of balloons. 3 ·· 10 of the balloons are red.

2 ·· 10 of the balloons are blue. What fraction of the balloons are

neither red nor blue?

Show your work.

Solution:

18 Emily ate 1 ·· 6 of a bag of carrots. Nick ate 2 ·· 6 of the bag of carrots.

What fraction of the bag of carrots did Emily and Nick eat

altogether? Circle the letter of the correct answer.

A 1 ·· 6

B 1 ·· 3

C 3 ·· 6

D 3 ·· 12

Rob chose D as the correct answer. How did he get that answer?


Part 5: Common Core Practice Lesson 16



Solve the problems. Mark your answers to problems 1–4 on the Answer Form to the right. Be sure to show your work.

1 Lee’s muffin mix calls for 2 } 3 cup of milk, 1 } 

3 cup of oil, and 1 } 

3 cup of sugar. How much

more milk than oil does she need for the muffin mix?

A 4 } 3 cups

B 3 } 3 cup

C 2 } 3 cup

D 1 } 3 cup

2 Liang bought some cloth. He used 5 } 8 of a yard for a school project. He has 2 } 

8 of a yard

left. How much cloth did Liang buy?

A 3 } 8 of a yard

B 7 }} 16

of a yard

C 7 } 8 of a yard

D 8 } 8 of a yard

3 Carmela cut a cake into 12 equal-sized pieces. She ate 2 }} 12

of the cake, and her brother

ate 3 }} 12

of the cake. What fraction of the cake is left?

A 1 }} 12

of the cake

B 5 }} 12

of the cake

C 7 }} 12

of the cake

D 12 }} 12

of the cake

1 B C D

2 B C D

3 B C D

4 B C D

Answer Form

Number Correct 4


Part 5: Common Core Practice Lesson 16


Self Check Go back and see what you can check off on the Self Check on page 119.

4 Maria practiced piano for 1 } 4 hour on Monday and 1 } 

4 hour on Tuesday. She was

supposed to practice for 3 } 4 hour on each day. How much practice time did she skip?

A 5 } 4 hours

B 4 } 4 hour

C 2 } 4 hour

D 1 } 4 hour

5 In all, Cole and Max picked 9 }} 10

of a bucket of blueberries. Cole picked 3 }} 10

of the

bucket of blueberries. What fraction of the bucket of blueberries did Max pick?

Show your work.

Answer Max picked of the bucket of blueberries.

6 A pizza is cut into 8 equal slices. Together, Regan and Juanita will share 5 } 8 of the pizza.

What is one way the girls could share the pizza?

Show your work.

Answer Regan could eat of the pizza, and

Juanita could eat of the pizza.


Documents

Ready Common Core Instruction 4 - casamples.com · 4 OA 1 Lesson 6 Multiplication .and .Division .in .Word ... Lesson 29 Measure .and .Draw .Angles ... Common Core Performance Task