Name

Daily Spiral Review

10-1

1. Look at the model.

4. Which of the following numbers is divisible by 9? 15 198 682

A _12 B _13

5. What fraction of the squares below are white?

C _23 D _34 2. Which number can be divided evenly by 2, 3, 5, 9, and 10? A B C D

255 309 425 450

6. There are 540 students at Central Valley Elementary School. At a rally, the students are arranged into 6 equal groups. How many students are in each group?

7. Estimate the product of 91 ! 27.

© Pearson Education, Inc. 4

3. Maria is reading a book that has 217 pages. She wants to finish reading the book in 1 week. She is going to read the same number of pages each day. How many pages does Maria have to read each day to finish the book in a week? A 37 B 33 C 31 D 28

Daily Spiral Review 10-1

Which fraction is shown by the shaded part of the model?

Topic 10

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29 1/30/08 2:29:32 PM

Name

Daily Spiral Review

10-1

1. Look at the model.

A _12 B _13

198 5. What fraction of the squares below are white?

C _23

3 __

D _34 2. Which number can be divided evenly by 2, 3, 5, 9, and 10? A B C D

255 309 425 450

6. There are 540 students at Central Valley Elementary School. At a rally, the students are arranged into 6 equal groups. How many students are in each group?

There are 90 students in each group. 7. Estimate the product of 91 ! 27.

2,700

© Pearson Education, Inc. 4

3. Maria is reading a book that has 217 pages. She wants to finish reading the book in 1 week. She is going to read the same number of pages each day. How many pages does Maria have to read each day to finish the book in a week? A 37 B 33 C 31 D 28

4

Daily Spiral Review 10-1

Which fraction is shown by the shaded part of the model?

4. Which of the following numbers is divisible by 9? 15 198 682

Topic 10

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29 1/30/08 11:41:09 AM

30

Nat_AncTopic_10.indb 30

Problem of the Day 10-1

Topic 10

Problem

of the

Day

10-1

10-1

1/30/08 2:29:34 PM

© Pearson Education, Inc. 4

Problem of the Day

Hillary and Sarah painted a fence. Each hour, Hillary painted 6 boards and Sarah painted 9 boards. How many boards had Hillary painted when Sarah had painted 45 boards? (Hint: Make a table.)

Name 1. Which fraction represents the part of the rectangle that is shaded?

Quick Check

10-1 2. Which of the following shows a flag 2 white? that is __ 5

C

B

D

Quick Check 10-1

A

A _16 B _36 C _24 D _26

© Pearson Education, Inc. 4

3. Writing to Explain A rectangle is divided into 9 equal sections. One section is blue. One section is green. Two sections are orange. Five sections are red. Explain why the fractions comparing the colors of the sections to the numbers of sections all have the same denominator.

Topic 10

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31 1/30/08 2:29:34 PM

Name 1. Which fraction represents the part of the rectangle that is shaded?

Quick Check

10-1 2. Which of the following shows a flag 2 white? that is __ 5

C

B

D

Quick Check 10-1

A

A _16 B _36 C _24 D _26

3. Writing to Explain A rectangle is divided into 9 equal sections. One section is blue. One section is green. Two sections are orange. Five sections are red. Explain why the fractions comparing the colors of the sections to the numbers of sections all have the same denominator.

© Pearson Education, Inc. 4

See student samples to the right.

Topic 10

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31 1/30/08 11:41:12 AM

Name

Reteaching

10-1

Regions and Sets

Reteaching 10-1

The top number, the numerator, tells the number of equal parts described. The bottom number, the denominator, tells how many equal parts there are in all.

2 3

3 5

Numerator: 2 parts are shaded. Denominator: There are 3 parts total.

2 of the circle is shaded. 3

Numerator: 3 parts are shaded. Denominator: There are 5 parts total.

3 of the set is shaded. 5

Write a fraction for the part of the region that is shaded. 1.

2.

3.

4.

Shade in the models to show each fraction. 5.

!5! 15

6.

!7! 9

© Pearson Education, Inc. 4

7. Reasoning Tara says that !21! of a salad is always the same amount. Lynn says that it could be different amounts, depending on how large the salad is. Who is correct? Why?

32 Nat_AncTopic_10.indb 32

Topic 10

1/30/08 2:29:37 PM

Name

Reteaching

10-1

Regions and Sets

Reteaching 10-1

The top number, the numerator, tells the number of equal parts described. The bottom number, the denominator, tells how many equal parts there are in all.

2 3

3 5

Numerator: 2 parts are shaded. Denominator: There are 3 parts total.

Numerator: 3 parts are shaded. Denominator: There are 5 parts total.

3 of the set is shaded. 5

2 of the circle is shaded. 3

Write a fraction for the part of the region that is shaded. 1.

!2 4! 1 !3!

3.

2.

!1! 4 4.

Shade in the models to show each fraction. 5.

!5! 15

6.

5 !5!

Sample answers: !7! 9

Lynn, because a fraction describes a part of a whole. The size of the part depends on the size of the whole.

32 Nat_AncTopic_10.indb 32

© Pearson Education, Inc. 4

7. Reasoning Tara says that !21! of a salad is always the same amount. Lynn says that it could be different amounts, depending on how large the salad is. Who is correct? Why?

Topic 10

1/30/08 11:41:15 AM

Name

Practice

10-1

Regions and Sets Write a fraction for the part of the region below that is shaded. 1.

2.

Practice 10-1

Shade in the models to show each fraction. 3.

7 4. __ 10

!2! 4

5. What fraction of the pizza is cheese? cheese green peppers

6. What fraction of the pizza is mushroom?

mushrooms

7. A set has 12 squares. Which is the number of squares in !13! of the set? A 3

B 4

C 6

D 9

8. Writing to Explain Explain why !12! of Region A is not larger than !12! of Region B.

Region B

© Pearson Education, Inc. 4

Region A

Topic 10

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33 1/30/08 2:29:39 PM

Name

Practice

10-1

Regions and Sets Write a fraction for the part of the region below that is shaded. 1.

2.

Practice 10-1

4 !8!

3 !4! Shade in the models to show each fraction. 3.

Sample models are given.

!2! 4

7 4. __ 10

5. What fraction of the pizza is cheese?

3 __

cheese green peppers

8 2 __ 8

6. What fraction of the pizza is mushroom?

mushrooms

7. A set has 12 squares. Which is the number of squares in !13! of the set? A 3

B 4

C 6

D 9

8. Writing to Explain Explain why !12! of Region A is not larger than !12! of Region B.

!1 2!

Region A

Region B

© Pearson Education, Inc. 4

of each is the same, 6 squares.

Topic 10

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33 1/30/08 11:41:18 AM

Name

Enrichment

10-1

Look-Alikes Write the fraction from the box that shows the smaller part of each group. You will not use all of the fractions.

Enrichment 10-1

Fraction Box

3 __

3 __

1 __ 5 __

4

7

3 __

5 __

1 __

3 __

1 __

2 __

4 __

2 __

8 6

8 3

3 7

5

Visual Thinking

4 6

5

1.

2.

3.

4.

5.

34 Nat_AncTopic_10.indb 34

© Pearson Education, Inc. 4

6.

Topic 10

1/30/08 2:29:40 PM

Name

Enrichment

10-1

Look-Alikes Write the fraction from the box that shows the smaller part of each group. You will not use all of the fractions. 3 __

3 __

1 __ 5 __

4

7

3 __

5 __

1 __

3 __

1 __

2 __

4 __

2 __

8 6

8 3

3 7

5

4 6

5

1.

2 __

2.

1 __

3.

1 __

4.

3 __

5.

3 __

6.

1 __

34 Nat_AncTopic_10.indb 34

5

3

6 7

8

4

© Pearson Education, Inc. 4

Enrichment 10-1

Fraction Box

Visual Thinking

Topic 10

1/30/08 11:41:20 AM

Name

Daily Spiral Review

10-2

1. Which fraction of these coins are nickels?

4. What fraction is represented by the shaded part of the drawing below?

2 A __ 5

1 B __ 2

3 C __ 4

3 D __

Daily Spiral Review 10-2

5

2. Look at the model.

Which fraction is shown by the shaded part of the model?

5. How do you write 4 ! 7 as a fraction?

4 A ___ 10

4 B __ 8

6 C __ 8 __ D 4 5

3. There are 18 berries in a bowl. Six are blueberries. What fraction of the berries are blueberries? 6 A ___

7. What are the next three numbers in the pattern? 5, 14, 24, 35, 47, ,

,

© Pearson Education, Inc. 4

18 __ B 6 6 ___ C 18 6 ___ D 1 16

6. Jan and 3 of her friends went skiing. Each lift ticket cost $34. How much did they have to pay altogether?

Topic 10

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35 1/30/08 2:29:42 PM

Name

Daily Spiral Review

10-2

1. Which fraction of these coins are nickels?

4. What fraction is represented by the shaded part of the drawing below?

2 A __ 5

3 __

1 B __ 2 3 C __ 4 3 D __ 5

8

Daily Spiral Review 10-2

2. Look at the model.

Which fraction is shown by the shaded part of the model?

5. How do you write 4 ! 7 as a fraction?

4 __

4 A ___

7

10

4 B __ 8

6 C __ 8 4 D __ 5

3. There are 18 berries in a bowl. Six are blueberries. What fraction of the berries are blueberries? 6 A ___

$102

7. What are the next three numbers in the pattern? 5, 14, 24, 35, 47,

60 , 74 , 89

© Pearson Education, Inc. 4

18 __ B 6 6 ___ C 18 6 ___ D 1 16

6. Jan and 3 of her friends went skiing. Each lift ticket cost $34. How much did they have to pay altogether?

Topic 10

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35 1/30/08 11:41:23 AM

36

Nat_AncTopic_10.indb 36

Problem of the Day 10 -2

Topic 10

Problem

of the

Day

10-2

Write a fraction to describe which part of the shapes shown are trapezoids.

10-2

© Pearson Education, Inc. 4

Problem of the Day

1/30/08 2:29:44 PM

Draw the two polygons that come next in the pattern to complete the set.

Name 1. If 6 friends divided 3 pies equally, which division sentence shows how much pie each friend will get? A 6!6

Quick Check

10-2 2. Which represents the fraction that each of four persons will receive if they share 3 oranges? A

C

B

D

B 3!3 C 3!6 Quick Check 10-2

D 6!3

© Pearson Education, Inc. 4

3. Writing to Explain Mary and some of her friends are having a sleepover. Mary’s mother orders a pizza, which is cut into 8 slices. Each girl ate _28 of the pizza. The entire pizza was eaten. Explain how to use this information to find out how many girls were at the sleepover.

Topic 10

Nat_AncTopic_10.indb 37

37 1/30/08 2:29:45 PM

Name 1. If 6 friends divided 3 pies equally, which division sentence shows how much pie each friend will get? A 6!6

Quick Check

10-2 2. Which represents the fraction that each of four persons will receive if they share 3 oranges? A

C

B

D

B 3!3 C 3!6 Quick Check 10-2

D 6!3

3. Writing to Explain Mary and some of her friends are having a sleepover. Mary’s mother orders a pizza, which is cut into 8 slices. Each girl ate _28 of the pizza. The entire pizza was eaten. Explain how to use this information to find out how many girls were at the sleepover.

© Pearson Education, Inc. 4

See student samples to the right.

Topic 10

Nat_AncTopic_10.indb 37

37 1/30/08 11:41:26 AM

Name

Reteaching

10-2

Fractions and Division To show how you can share items, you can divide to find a fraction of the total. Four people shared two submarine sandwiches equally.

Reteaching 10-2

What fraction of the sandwiches did each person receive? Divide each sandwich into 4 equal parts. 1. Each part is 1 ! 4 or __ 4

Each person received one equal slice from each sandwich for a total of 2 slices.

Portion received by each

There are 8 slices altogether, so each 2 of the person received __ 8 shared sandwiches. Tell what fraction each person gets when they share equally. 2. Two friends share a bag of pretzels.

3. Eight runners run an equal part in a 5-mile relay.

4. Five rabbits share 4 carrots equally.

5. Five people use 2 cans of paint.

6. Two children share 2 small boxes of cereal. © Pearson Education, Inc. 4

1. Six friends divide 2 apples.

38 Nat_AncTopic_10.indb 38

Topic 10

1/30/08 2:29:46 PM

Name

Reteaching

10-2

Fractions and Division To show how you can share items, you can divide to find a fraction of the total. Four people shared two submarine sandwiches equally.

Reteaching 10-2

What fraction of the sandwiches did each person receive? Divide each sandwich into 4 equal parts. 1. Each part is 1 ! 4 or __ 4

Portion received by each

Each person received one equal slice from each sandwich for a total of 2 slices. There are 8 slices altogether, so each 2 of the person received __ 8 shared sandwiches.

Tell what fraction each person gets when they share equally.

Each friend gets 2 of an apple. __ 6

3. Eight runners run an equal part in a 5-mile relay.

Each runner runs 5 of a mile. __ 8

5. Five people use 2 cans of paint.

Each person uses 2 of a can of paint. __ 5

38 Nat_AncTopic_10.indb 38

2. Two friends share a bag of pretzels.

Each friend 1 of the bag gets __ 2 of pretzels.

4. Five rabbits share 4 carrots equally.

Each rabbit gets 4 of a carrot. __ 5

6. Two children share 2 small boxes of cereal.

Each child gets 2 or 1 box of cereal. __ 2

© Pearson Education, Inc. 4

1. Six friends divide 2 apples.

Topic 10

1/30/08 11:41:28 AM

Name

Practice

10-2

Fractions and Division What fraction does each person get when they share equally? 1. Eight friends share 3 bags of toys. 2. Five people share 2 jugs of water.

Five friends are sharing supplies on a camping trip. Tell what fraction each person gets when they share equally. 3. Two boxes of trail mix. Practice 10-2

4. Three packages of water purifying tablets. 5. There are 3 bottles of Vermont maple syrup. If four people are sharing the syrup, how much of a bottle does each person get? 6. Which model represents 6 people sharing 1 five-foot sub? A

C

B

D

© Pearson Education, Inc. 4

7. Writing to Explain Several friends are taking turns flying a kite. Each friend flies the kite for the same amount of time. They spend 6 hours flying the kite altogether. Explain what information you need to find how long each friend flew the kite.

Topic 10

Nat_AncTopic_10.indb 39

39 1/30/08 2:29:49 PM

Name

Practice

10-2

Fractions and Division What fraction does each person get when they share equally? 1. Eight friends share 3 bags of toys. 2. Five people share 2 jugs of water.

3 of a bag of toys __ 8 2 of a jug __ 5

Five friends are sharing supplies on a camping trip. Tell what fraction each person gets when they share equally. 3. Two boxes of trail mix.

4. Three packages of water purifying tablets.

5

5. There are 3 bottles of Vermont maple syrup. If four people are sharing the syrup, how much of a bottle does each person get?

6. Which model represents 6 people sharing 1 five-foot sub? A

C

B

D

Practice 10-2

2 of a box of trail mix __ 5 3 of a package __ 3 of __ 4

a bottle

7. Writing to Explain Several friends are taking turns flying a kite. Each friend flies the kite for the same amount of time. They spend 6 hours flying the kite altogether. Explain what information you need to find how long each friend flew the kite.

© Pearson Education, Inc. 4

You need to know how many friends there are.

Topic 10

Nat_AncTopic_10.indb 39

39 1/30/08 11:41:31 AM

Name

Paper Fun Read the steps in the box. Then answer the questions.

Enrichment

10-2 Reasoning

Step 1: Tyler and Ashley each have a rectangular sheet of paper. Step 2: Tyler folds his paper in half and Ashley folds her paper into three equal parts. Step 3: Tyler and Ashley open their papers and label the creased lines Enrichment 10-2

with a fraction that represents the length of the paper at the creased line. Step 4: Tyler and Ashley refold the paper as in step 2. Step 5: Tyler folds his paper into three equal parts and Ashley folds her paper into two equal parts. Step 6: Tyler and Ashley open their papers and label the creased lines with fractions that represent the length of the paper at each creased line.

1. What fraction did Tyler and Ashley write on the creased line of their papers in step 3?

2. What fractions did Tyler and Ashley write on the creased lines of their papers in step 6?

3. Are there any creases on Ashley’s paper that are labeled differently than those on Tyler’s paper? What are they?

© Pearson Education, Inc. 4

4. Are there any creases on Tyler’s paper that are labeled differently than those on Ashley’s paper? What are they?

40 Nat_AncTopic_10.indb 40

Topic 10

1/30/08 2:29:59 PM

Name

Enrichment

10-2

Paper Fun Read the steps in the box. Then answer the questions.

Reasoning

Step 1: Tyler and Ashley each have a rectangular sheet of paper. Step 2: Tyler folds his paper in half and Ashley folds her paper into three equal parts. Step 3: Tyler and Ashley open their papers and label the creased lines Enrichment 10-2

with a fraction that represents the length of the paper at the creased line. Step 4: Tyler and Ashley refold the paper as in step 2. Step 5: Tyler folds his paper into three equal parts and Ashley folds her paper into two equal parts. Step 6: Tyler and Ashley open their papers and label the creased lines with fractions that represent the length of the paper at each creased line.

1. What fraction did Tyler and Ashley write on the creased line of their papers in step 3?

1

1 2

Tyler wrote !2! and Ashley wrote !3!, !3!. 2. What fractions did Tyler and Ashley write on the creased lines of their papers in step 6?

1 2 3 4 5

They both wrote !6!, !6!, !6!, !6!, !6!.

3. Are there any creases on Ashley’s paper that are labeled differently than those on Tyler’s paper? What are they?

1

2

Yes; !3! and !3! 4. Are there any creases on Tyler’s paper that are labeled differently than those on Ashley’s paper? What are they?

1

© Pearson Education, Inc. 4

Yes; !2!

40 Nat_AncTopic_10.indb 40

Topic 10

1/30/08 11:41:44 AM

Name

Daily Spiral Review

10-3

1. Look at the model.

4. Tamara is having a birthday party. She has invited 23 guests. Each table can seat 6 guests. How many tables does Tamara need to set up?

Which fraction is shown by the shaded part of the model? 1 A __ 5

2 B __ 5 5

5 D __

Daily Spiral Review 10-3

4 C __

5. At the basketball game, Luis scored 35 points. He made three 3-point shots. How many 2-point shots did Luis make?

5

2. A teacher put some books on a bookshelf. Look at the diagram below. The bookshelf is 8 ft long. How much of the shelf does NOT hold a book?

A 6 ft B 5 ft

6. Tyler’s mom made a dozen muffins. Tyler ate 2 muffins. His brother ate 1 muffin. What fraction shows how many muffins were eaten?

7. About what fraction of the pie has been eaten?

C 4 ft D 3 ft 3. Look at the model.

© Pearson Education, Inc. 4

Which fraction is shown by the shaded part of the model? 1 A ___ 10

5 B ___ 10

7 C ___ 10

9 D ___ 10

Topic 10

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41 1/30/08 2:29:59 PM

Name

Daily Spiral Review

10-3

1. Look at the model.

Which fraction is shown by the shaded part of the model? 1 A __ 5

2 B __ 5 5

5 D __ 5

2. A teacher put some books on a bookshelf. Look at the diagram below. The bookshelf is 8 ft long. How much of the shelf does NOT hold a book?

4

5. At the basketball game, Luis scored 35 points. He made three 3-point shots. How many 2-point shots did Luis make?

13

6. Tyler’s mom made a dozen muffins. Tyler ate 2 muffins. His brother ate 1 muffin. What fraction shows how many muffins were eaten? 3

Daily Spiral Review 10-3

4 C __

4. Tamara is having a birthday party. She has invited 23 guests. Each table can seat 6 guests. How many tables does Tamara need to set up?

__ 12

A 6 ft B 5 ft

7. About what fraction of the pie has been eaten?

C 4 ft D 3 ft 3. Look at the model.

About _24 or _12

© Pearson Education, Inc. 4

Which fraction is shown by the shaded part of the model? 1 A ___ 10

5 B ___ 10

7 C ___ 10

9 D ___ 10

Topic 10

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41 1/30/08 11:41:46 AM

42

Nat_AncTopic_10.indb 42

Problem of the Day 10-3

Topic 10

Problem

of the

Day

10-3

How many times can Mel make macaroni and cheese with one package of butter?

10-3

Problem of the Day

1/30/08 2:30:01 PM

© Pearson Education, Inc. 4

Name 1. About how much of this rectangle is shaded?

Quick Check

10-3 2. Which of the following shows a rectangle that is about _19 shaded? A

A _16

B

B _36 D _56

C

Quick Check 10-3

C _46

D

© Pearson Education, Inc. 4

3. Writing to Explain Is _47 a benchmark fraction? If it is not, draw a comparison between _47 and a benchmark fraction.

Topic 10

Nat_AncTopic_10.indb 43

43 1/30/08 2:30:04 PM

Name 1. About how much of this rectangle is shaded?

Quick Check

10-3 2. Which of the following shows a rectangle that is about _19 shaded? A

A _16

B

B _36 D _56

C

Quick Check 10-3

C _46

D

3. Writing to Explain Is _47 a benchmark fraction? If it is not, draw a comparison between _47 and a benchmark fraction.

© Pearson Education, Inc. 4

See student samples to the right.

Topic 10

Nat_AncTopic_10.indb 43

43 1/30/08 11:41:53 AM

Name

Reteaching

Estimating Fractional Amounts

10-3

Benchmark fractions are fractions that are commonly used, such as !14!, !13!, !12!, !23!, and !34!. They are useful when you estimate fractional parts. For example: A

B

1 1 Point A is at about . 4 1 Point B is at about . 2 0

Reteaching 10-3

1 About of the 2 rectangle is shaded.

1 of the 3 length is shaded. About

Estimate the fractional part of each that is shaded. 1.

2.

3.

4.

5.

6.

Estimate the fraction that should be written at each point. B

M C 1

0

7. L

8. A

10. M

11. C

12. Number Sense There is a pan of food. About !14! of the food has been eaten. About how much food is left?

44 Nat_AncTopic_10.indb 44

9. B

© Pearson Education, Inc. 4

L A

Topic 10

1/30/08 2:30:06 PM

Name

Reteaching

10-3

Estimating Fractional Amounts Benchmark fractions are fractions that are commonly used, such as !14!, !13!, !12!, !23!, and !34!. They are useful when you estimate fractional parts. For example: A

B

1 1 Point A is at about . 4 1 Point B is at about . 2 0

1 of the 3 length is shaded. About

Estimate the fractional part of each that is shaded. 1.

About

2.

!1! 2

1

About !3!

3.

4.

3

2

About !4!

About !3!

5.

6.

1

1

About !3!

About 4!!

Estimate the fraction that should be written at each point. L A 0

7. L 10. M

!1! 4 !2 3!

B

M C 1

8. A 11. C

1 !3! 3 !4!

12. Number Sense There is a pan of food. About !14! of the food has been eaten. About how much food is left?

44 Nat_AncTopic_10.indb 44

9. B

Sample answers: !1 2!

3

About !4!

© Pearson Education, Inc. 4

Reteaching 10-3

1 About of the 2 rectangle is shaded.

Topic 10

1/30/08 11:41:57 AM

Name

Practice

10-3

Estimating Fractional Amounts Estimate the fractional amount of each that is shaded. 1.

2.

3.

A B

Estimate the fraction that should be written at each point. 5. A

6. B

Practice 10-3

4. Reasonableness Is !16! a reasonable estimate for the shaded part in the region to the right? Explain.

C D

0

1

7. C

8. D

9. Part of the region to the right is shaded. Which is the best estimate? A

!3! 3

B

!2! 3

C

!1! 3

D

!0! 3

© Pearson Education, Inc. 4

10. Writing to Explain Explain how you estimated the shaded region in Exercise 9.

Topic 10

Nat_AncTopic_10.indb 45

45 1/30/08 2:30:08 PM

Name

Practice

10-3

Estimating Fractional Amounts Estimate the fractional amount of each that is shaded. 1.

2.

3.

!2! 3

2 !3!

!1! 2

Practice 10-3

4. Reasonableness Is !16! a reasonable estimate for the shaded part in the region to the right? Explain.

No; Sample answer: About 1 !2! of the region is shaded.

A B

Estimate the fraction that should be written at each point.

1 !4!

5. A

6. B

!1! 3

C D

0

7. C

2 !3!

8. D

!3! 4

1

9. Part of the region to the right is shaded. Which is the best estimate? A

!3! 3

B

!2! 3

C

!1! 3

D

!0! 3

© Pearson Education, Inc. 4

10. Writing to Explain Explain how you estimated the shaded region in Exercise 9.

Sample answer: The region is divided into 3 sections. Each section seems equal and 1 of them is shaded. So, 1 about !3! of the region is shaded.

Topic 10

Nat_AncTopic_10.indb 45

45 1/30/08 11:42:00 AM

Name

Enrichment

10-3

Time After Time JANUARY

Enrichment 10-3

S M T 1 6 7 8 13 14 15 20 21 22 27 28 29

S M 1 7 8 14 15 21 22 28 29

W 2 9 16 23 30

T 3 10 17 24 31

JULY

T 2 9 16 23 30

W 3 10 17 24 31

T 4 11 18 25

APRIL

F 4 11 18 25

S 5 12 19 26

S M 1 7 8 14 15 21 22 28 29

T 2 9 16 23 30

F 5 12 19 26

S 6 13 20 27

S M T 1 6 7 8 13 14 15 20 21 22 27 28 29

W 3 10 17 24

T 4 11 18 25

Estimation F 5 12 19 26

OCTOBER W 2 9 16 23 30

T 3 10 17 24 31

F 4 11 18 25

S 6 13 20 27

S 5 12 19 26

Estimate the fraction of each month that passed before the date given. 1. January 8 2. October 17 3. April 16 4. July 5 5. October 10 6. January 25 7. July 6

© Pearson Education, Inc. 4

8. April 30

46 Nat_AncTopic_10.indb 46

Topic 10

1/30/08 2:30:10 PM

Name

Enrichment

10-3

Time After Time JANUARY

Enrichment 10-3

S M T 1 6 7 8 13 14 15 20 21 22 27 28 29

S M 1 7 8 14 15 21 22 28 29

W 2 9 16 23 30

T 3 10 17 24 31

JULY

T 2 9 16 23 30

W 3 10 17 24 31

T 4 11 18 25

APRIL

F 4 11 18 25

S 5 12 19 26

S M 1 7 8 14 15 21 22 28 29

T 2 9 16 23 30

F 5 12 19 26

S 6 13 20 27

S M T 1 6 7 8 13 14 15 20 21 22 27 28 29

W 3 10 17 24

T 4 11 18 25

Estimation F 5 12 19 26

OCTOBER W 2 9 16 23 30

T 3 10 17 24 31

F 4 11 18 25

S 6 13 20 27

S 5 12 19 26

Estimate the fraction of each month that passed before the date given.

_1

4 _1 2. October 17 2 _1 2 3. April 16 1 _ 6 4. July 5 _1 5. October 10 3 _5 6. January 25 6 _1 5 7. July 6 30 __ 30 8. April 30

Sample answers have been given.

or _11 © Pearson Education, Inc. 4

1. January 8

46 Nat_AncTopic_10.indb 46

Topic 10

1/30/08 11:42:02 AM

Name 1. Which of these is the number 3,200,601 in word form? A Three million, two hundred thousand, six hundred one B Three million, two hundred one C Three million, two hundred six thousand, one D Three million, two thousand, six hundred one

4. Alex is building bookshelves. Each shelf can hold 14 books. He has built 9 shelves. How many books can Alex put on the shelves?

5. Carl cut 2 feet off a rope that measured 10 feet. Write a fraction to represent the part of the rope he cut off.

6. If Zachary takes 3 steps for every 2 steps Ritchie takes, how many steps will Zachary take if Ritchie takes 18 steps? Make a table to help you.

© Pearson Education, Inc. 4

3. Pedro has started a car-washing business. He charges $5 for each car he washes. On Saturday, Pedro washed 4 cars. On Sunday, he washed 7 cars. How much money did Pedro earn? A $20 B $27 C $35 D $55

10-4

Daily Spiral Review 10-4

2. Isabel walked 1,357 steps to get to school. Harold walked 935 steps to get to school. How many more steps did Isabel walk? A 492 B 422 C 392 D 122

Daily Spiral Review

Topic 10

Nat_AncTopic_10.indb 47

47 1/30/08 2:30:11 PM

Name 1. Which of these is the number 3,200,601 in word form? A Three million, two hundred thousand, six hundred one B Three million, two hundred one C Three million, two hundred six thousand, one D Three million, two thousand, six hundred one

4. Alex is building bookshelves. Each shelf can hold 14 books. He has built 9 shelves. How many books can Alex put on the shelves?

126 books

5. Carl cut 2 feet off a rope that measured 10 feet. Write a fraction to represent the part of the rope he cut off.

2 Sample answer: ___ 10

6. If Zachary takes 3 steps for every 2 steps Ritchie takes, how many steps will Zachary take if Ritchie takes 18 steps? Make a table to help you.

27 steps

© Pearson Education, Inc. 4

3. Pedro has started a car-washing business. He charges $5 for each car he washes. On Saturday, Pedro washed 4 cars. On Sunday, he washed 7 cars. How much money did Pedro earn? A $20 B $27 C $35 D $55

10-4

Daily Spiral Review 10-4

2. Isabel walked 1,357 steps to get to school. Harold walked 935 steps to get to school. How many more steps did Isabel walk? A 492 B 422 C 392 D 122

Daily Spiral Review

Topic 10

Nat_AncTopic_10.indb 47

47 1/30/08 11:42:04 AM

48

Nat_AncTopic_10.indb 48

Problem of the Day 10-4

Topic 10

Problem

of the

Day

10-4

Is _13 of the flag white? Explain why or why not. Yellow Blue Red 10-4

Problem of the Day

1/30/08 2:30:12 PM

© Pearson Education, Inc. 4

Name

Quick Check

10-4

6 1. Which fraction is equivalent to __ ? 16

2 A __ 4

3 B __ 4 __ C 3 8 2 D __ 6

2. Which picture shows a fraction equivalent to _16 ? A

B

Quick Check 10-4

C

D

© Pearson Education, Inc. 4

3. Writing to Explain Use fraction strips to show _13 and _26 of one whole strip. Are _13 and _26 the same part of the strip?

Topic 10

Nat_AncTopic_10.indb 49

49 1/30/08 2:30:13 PM

Name

Quick Check

10-4

6 1. Which fraction is equivalent to __ ? 16

2 A __ 4

3 B __ 4 __ C 3 8 __ D 2 6

2. Which picture shows a fraction equivalent to _16 ? A

B

Quick Check 10-4

C

D

3. Writing to Explain Use fraction strips to show _13 and _26 of one whole strip. Are _13 and _26 the same part of the strip?

© Pearson Education, Inc. 4

See student samples to the right.

Topic 10

Nat_AncTopic_10.indb 49

49 1/30/08 11:42:07 AM

Name

Reteaching

10-4

Equivalent Fractions If two fractions name the same amount, they are called equivalent fractions. Are _12 and _36 equivalent fractions? Multiply the numerator and denominator by the same number. "3 _1

!

2

"3

_3 6

three times as many parts in all

three times as many shaded parts

Reteaching 10-4

6 . Use division to write a fraction that is equivalent to __ 24

Think of a number that is a factor of both 6 and 24. 3 is a factor of 6 and 24. Divide the numerator and the denominator by 3. #3 #2 6 _2 and _1 are both equivalent to __ . 6 8 4 24 __ _2 _1 ! ! 24 8 4 #3

#2

Find the missing number. 1 ! __ 1. __ 4

8

15 ! __ 2. ___ 20

4

2 ! ___ 3. __

9 ! __ 4. ___

5! 7. __

3! 8. __

7

21

27

3

Multiply to find an equivalent fraction. 3 ! 5. ___ 10

1! 6. __ 2

6

4

Divide to find an equivalent fraction. 10 ! 9. ___

9 ! 10. ___

21 ! 11. ___

25 ! 12. ___

8 ! 13. ___

9 ! 14. ___

8 ! 15. ___

15 ! 16. ___

15

18

28

18

35

40

© Pearson Education, Inc. 4

20

24

50 Nat_AncTopic_10.indb 50

Topic 10

1/30/08 2:30:14 PM

Name

Reteaching

10-4

Equivalent Fractions If two fractions name the same amount, they are called equivalent fractions. Are _12 and _36 equivalent fractions? Multiply the numerator and denominator by the same number. "3 _1

_3

!

2

6

"3

three times as many parts in all

three times as many shaded parts

Reteaching 10-4

6 . Use division to write a fraction that is equivalent to __ 24

Think of a number that is a factor of both 6 and 24. 3 is a factor of 6 and 24. Divide the numerator and the denominator by 3. #3 #2 6 _2 and _1 are both equivalent to __ . 6 8 4 24 __ _2 _1 ! ! 24 8 4 #3

#2

Find the missing number. 1 ! __ 1. __ 4

8

2

2.

Sample answers given for 5-16. 15 ! __ 9 ! __ 2 ! ___ ___ 3. __ 4. ___ 7 20 4 3 21 6 27 3 1

Multiply to find an equivalent fraction. 3 ! 5. ___ 10

9 ___ 30

1! 6. __ 2

4 __ 8

5! 7. __ 6

25 ___ 30

Divide to find an equivalent fraction. 10 ! 9. ___ 15

8 ! 13. ___

3 2 __ 5

9 ! 10. ___ 24

9 ! 14. ___ 18

3 __

8 1 __ 2

21 ! 11. ___ 28

8 ! 15. ___ 18

3 __

4 4 __ 9

4

24 ___ 32

25 ! 12. ___ 35

15 ! 16. ___ 40

5 __

7 3 __ 8 © Pearson Education, Inc. 4

20

2 __

3! 8. __

50 Nat_AncTopic_10.indb 50

Topic 10

1/30/08 11:42:08 AM

Name

Practice

10-4

Equivalent Fractions Find the missing number. 1 ! ___ 1. __ 2

12

6 ! __ 2. ___ 10

4 ! 2 ___ 4. 2___

4 ! __ 3. ___ 16

5

20

4

40

Multiply or divide to find an equivalent fraction. 6 6. ___

11 5. ___

9 7. ___

36

22

5 8. ___

10

35

7 9. ___ 12

2 10. Is __ equivalent to _37? 14

Practice 10-4

11. In Mark’s collection of antique bottles, _49 of the bottles are dark green. Write three equivalent fractions for _49 .

12. Write a pair of equivalent fractions for the picture above.

13. At the air show, _13 of the airplanes were gliders. Which fraction is not an equivalent fraction for _13 ? 5 A ___ 15

7 B ___ 21

6 C ___ 24

9 D ___ 27

© Pearson Education, Inc. 4

14. Writing to Explain In Missy’s sports-cards collection, _57 of the cards are 12 are baseball. Frank says they have the baseball. In Frank’s collection, __ 36 same fraction of baseball cards. Is he correct?

Topic 10

Nat_AncTopic_10.indb 51

51 1/30/08 2:30:16 PM

Name

Practice

10-4

Equivalent Fractions Find the missing number. 1 ! ___ 1. __ 2

12

6 ! __ 2. ___

4 ! __ 3. ___

3

1

10

16

5

6

4 ! 2 ___ 4. 2___ 20

4

40

8

Multiply or divide to find an equivalent fraction. 11 5. ___ 22

1 __ 2

6 6. ___

1 __

36

6

2 10. Is __ equivalent to _37? 14

9 7. ___ 10

18 ___ 20

5 8. ___ 35

1 __

7 9. ___ 12

7

14 ___ 24

Sample answers given for 5-9.

No

Practice 10-4

11. In Mark’s collection of antique bottles, _49 of the bottles are dark green. Write three equivalent fractions for _49 .

8 , ___ 16 12 , ___ Sample answers: ___ 18 27 36

12. Write a pair of equivalent fractions for the picture above.

3 and ___ 6. 2 and ___ 4 , or __ Possible answers are __ 5

5

10

10

13. At the air show, _13 of the airplanes were gliders. Which fraction is not an equivalent fraction for _13 ? 5 A ___ 15

7 B ___ 21

6 C ___ 24

9 D ___ 27

14. Writing to Explain In Missy’s sports-cards collection, _57 of the cards are 12 are baseball. Frank says they have the baseball. In Frank’s collection, __ 36 same fraction of baseball cards. Is he correct?

5 12 are not equivalent fractions. ___ No. __ and 7

© Pearson Education, Inc. 4

36

Topic 10

Nat_AncTopic_10.indb 51

51 1/30/08 11:42:11 AM

Name

Enrichment

10-4

Playing the Part 1. You have 6 tiles. _26 of the tiles are rectangles. The rest of the tiles are triangles. Draw a design using the tiles.

Visual Thinking

4 of the tiles are 2. You have 10 tiles. __ 10 rectangles. The rest of the tiles are triangles. Draw a design using the tiles.

Enrichment 10-4

8 3. You have 10 triangular tiles. Use __ 10 of them to draw a design.

Students in Jeremy’s class are working on 20 projects for the Science Fair. 4. _15 of the projects are about plants. How many are about plants?

5. _14 of the projects are about animals. How many are about animals?

Use the table at the right for Exercises 6 through 8.

7. One fourth of the cars are red. How many cars are red?

8. What fraction would represent all the cars in the train?

52 Nat_AncTopic_10.indb 52

Train Cars Number 7 1 7 9

Cars Flatcar Engine Tanker Boxcar

© Pearson Education, Inc. 4

6. What fraction of the train cars are tankers? What fraction are flatcars and boxcars altogether?

Topic 10

1/30/08 2:30:17 PM

Name

Enrichment

10-4

Playing the Part 1. You have 6 tiles. _26 of the tiles are rectangles. The rest of the tiles are triangles. Draw a design using the tiles.

Visual Thinking

Sample answers are shown for Exercises 1–3

4 of the tiles are 2. You have 10 tiles. __ 10 rectangles. The rest of the tiles are triangles. Draw a design using the tiles.

Enrichment 10-4

8 3. You have 10 triangular tiles. Use __ 10 of them to draw a design.

Students in Jeremy’s class are working on 20 projects for the Science Fair. 4. _15 of the projects are about plants. How many are about plants?

5. _14 of the projects are about animals. How many are about animals?

4

5

Use the table at the right for Exercises 6 through 8. 6. What fraction of the train cars are tankers? What fraction are flatcars and boxcars altogether?

16 or __ 7 ; ___ 2 ___ 24 24

3

7. One fourth of the cars are red. How many cars are red?

Train Cars Number 7 1 7 9

Cars Flatcar Engine Tanker Boxcar

8. What fraction would represent all the cars in the train?

24 ___ 24

52 Nat_AncTopic_10.indb 52

© Pearson Education, Inc. 4

6 cars

Topic 10

1/30/08 11:42:12 AM

Name

Daily Spiral Review

10-5

1. Terry has 38 marbles. She gives each of her 5 friends the same number of marbles. How many marbles does she have left over? A 2 B 3 C 4 D 5 2. Which fraction is equivalent to _34? 9 A ___ 27

4. What fraction of the balls is striped?

5. Richard rides his bike 14 miles a day, 7 days a week. Amelia rides her bike 17 miles a day, 6 days a week. Who rides more miles in a week?

6 B ___ 12 3

12 D ___ 16

3. What number sentence do these counters model?

6. Gail’s soccer team played 27 games in one season and lost 9 of them. Write a fraction to represent how many games were won by the team in relation to the total of games played.

18 ! 4 " 4 R2 18 ! 5 " 5 R3 16 ! 4 " 4 16 ! 8 " 2

© Pearson Education, Inc. 4

A B C D

Daily Spiral Review 10-5

2 C __

Topic 10

Nat_AncTopic_10.indb 53

53 1/30/08 2:30:20 PM

Name

Daily Spiral Review

10-5

1. Terry has 38 marbles. She gives each of her 5 friends the same number of marbles. How many marbles does she have left over? A 2 B 3 C 4 D 5 2. Which fraction is equivalent to _34? 9 A ___ 27

6 B ___

3. What number sentence do these counters model?

18 ! 4 " 4 R2 18 ! 5 " 5 R3 16 ! 4 " 4 16 ! 8 " 2

10

5

5. Richard rides his bike 14 miles a day, 7 days a week. Amelia rides her bike 17 miles a day, 6 days a week. Who rides more miles in a week?

Amelia

6. Gail’s soccer team played 27 games in one season and lost 9 of them. Write a fraction to represent how many games were won by the team in relation to the total of games played.

Gail’s soccer 2 of the team won __ 3 games played.

© Pearson Education, Inc. 4

A B C D

4 ! __ 2 ___

Daily Spiral Review 10-5

12 __ C 2 3 ___ D 12 16

4. What fraction of the balls is striped?

Topic 10

Nat_AncTopic_10.indb 53

53 1/30/08 11:42:16 AM

54

Nat_AncTopic_10.indb 54

Problem of the Day 10-5

Topic 10

Problem

of the

Day

10-5

Draw a picture to solve.

10-5

1/30/08 2:30:21 PM

© Pearson Education, Inc. 4

Problem of the Day

Patrick and Luis are building a brick wall. Patrick says that the wall is _46 of a yard tall. Luis says that the wall is 8 __ 12 of a yard tall. Who is right? How do you know?

Name 5 1. What is __ in simplest form? 15

3 A ___

15 1 B __ 5 __ C 1 3 3 D __ 5

Quick Check

10-5 2. Which fraction strip model shows _3 ! _1 ? 9 3 A

1 1 9

1 3 1 9

1 9

1 3 1 9

B

1 3

1 9

1 3

1

C

1 9

1 1 9

D

1 3

1 3

1 3

1

1 9

1 3 1 3 1 3 1 9

1 9

1 9

1 3 1 3 1 3 1 9

1 9

1 9

1 3 1 3 1 3 1 9

1 9

Quick Check 10-5

© Pearson Education, Inc. 4

4 3. Writing to Explain Cliff used a _12 strip to model __ in simplest 12 form. Is Cliff correct? If not, explain his error and correct his model using fraction strips.

Topic 10

28450_ANC-NATGR4_T10-5_working.i55 55

55 2/5/08 12:19:43 PM

Name 5 1. What is __ in simplest form? 15

3 A ___

15 1 B __ 5 __ C 1 3 __ D 3 5

Quick Check

10-5 2. Which fraction strip model shows _3 ! _1 ? 9 3 A

1 1 9

1 3 1 9

1 9

1 3 1 9

B

1 3

1 9

1 3

1

C

1 9

1 1 9

D

1 3

1 3

1 3

1

1 9

1 3 1 3 1 3 1 9

1 9

1 9

1 3 1 3 1 3 1 9

1 9

1 9

1 3 1 3 1 3 1 9

1 9

Quick Check 10-5

4 3. Writing to Explain Cliff used a _12 strip to model __ in simplest 12 form. Is Cliff correct? If not, explain his error and correct his model using fraction strips.

© Pearson Education, Inc. 4

See student samples to the right.

Topic 10

28450_ANC-NATGR4_T10-5_working.i55 55

55 2/5/08 12:20:09 PM

Name

Reteaching

10-5

Fractions in Simplest Form 6 Use division to write a fraction that is equivalent to __ . 24

Think of a number that is a factor of both 6 and 24. 3 is a factor of 6 and 24. Divide the numerator and the denominator by 3. If you continue to divide until 1 is the only factor of both the numerator and denominator, you will find the fraction in simplest form. 3 6 24

= 3

2 2 8

6 _2 and _1 are both equivalent to __ . 8 4 24

1 4

= 2

Only _14 is in simplest form.

Find the missing number. 2 ! __ 1. __ Reteaching 10-5

8

4

15 ! __ 2. ___ 20

4

7 ! __ 3. ___

9 ! __ 4. ___

21

3

27

3

Write each fraction in simplest form. 6 5. ___

4 6. ___

25 7. ___

24 8. ___

10 9. ___

9 10. ___

21 11. ___

25 12. ___

8 13. ___

9 14. ___

8 15. ___

15 16. ___

2 17. ___

6 18. ___

32 19. ___

12 20. ___

10

15

20

24

18

24

30

28

18

34

32

35

40

26

© Pearson Education, Inc. 4

18

10

56 Nat_AncTopic_10.indb 56

Topic 10

1/30/08 2:30:24 PM

Name

Reteaching

10-5

Fractions in Simplest Form 6 Use division to write a fraction that is equivalent to __ . 24

Think of a number that is a factor of both 6 and 24. 3 is a factor of 6 and 24. Divide the numerator and the denominator by 3. If you continue to divide until 1 is the only factor of both the numerator and denominator, you will find the fraction in simplest form. 3 6 24

= 3

2 2 8

6 _2 and _1 are both equivalent to __ . 8 4 24

1 4

= 2

Only _14 is in simplest form.

Find the missing number. 2 ! __ 1. __ Reteaching 10-5

8

4

1

15 ! __ 2. ___ 20

4

3

7 ! __ 3. ___ 21

Write each fraction in simplest form. 6 5. ___ 10

10 9. ___ 15

8 13. ___ 20

2 17. ___

5 2 __ 3 2 __ 5 1 __ 9

4 6. ___ 10

9 10. ___ 24

9 14. ___ 18

6 18. ___ 24

2 __ 5 3 __ 8 1 __ 2 1 __ 4

25 7. ___ 30

21 11. ___ 28

8 15. ___ 18

32 19. ___ 34

5 __

6 3 __ 4 4 __ 9 16 ___ 17

1

9 ! __ 4. ___ 27

24 8. ___ 32

25 12. ___ 35

15 16. ___ 40

12 20. ___ 26

3

1

3 __

4 5 __ 7 3 __ 8 6 ___ 13

© Pearson Education, Inc. 4

18

3 __

3

56 Nat_AncTopic_10.indb 56

Topic 10

1/30/08 11:42:21 AM

Name

Practice

10-5

Fractions in Simplest Form For 1 through 18, write each fraction in simplest form. If it is in simplest form, write “simplest form.” 13 1. ___ 14

2. __78

1 3. ___ 23

15 4. ___ 20

2 5. ___ 18

6 6. ___ 30

5 7. ___ 18

13 8. ___ 26

9 9. ___ 12

7 10. ___ 21

7 11. ___ 10

40 12. ___ 50

18 13. ___ 36

25 14. ___ 35

12 15. ___ 14

16. __89

60 17. ___ 80

18. __28 Practice 10-5

6 19. Sheldon has scored __ of the points in a basketball game. 18 How can you use division to simplify the fraction of the points 6 in simplest form? he scored? What is __ 18

40 ? 20. What is the simplest form of the fraction ___ 80

1 A __ 4

4 B __ 8

2 C __ 4

1 D __ 2

© Pearson Education, Inc. 4

21. Writing to Explain If the numerator of a fraction is a prime number, can the fraction be simplified? Why or why not?

Topic 10

Nat_AncTopic_10.indb 57

57 1/30/08 2:30:25 PM

Name

Practice

10-5

Fractions in Simplest Form For 1 through 18, write each fraction in simplest form. If it is in simplest form, write “simplest form.” 13 1. ___ 14

2. __78

simplest form

simplest form

4. 7.

15 ___ 20

3 __

5.

4

5 ___ 18

8.

simplest form

7 ___

2 ___ 18 13 ___ 26

1 __

1 3. ___ 23

simplest form

6.

6 ___ 30

1 __

9.

9 ___ 12

3 __

9

1 __ 2

5

4

40 ___

7 ___

10. 21

1 __

11. 10

12. 50 __ 4

18 13. ___ 36

1 __

25 __ 5 14. ___ 35

12 15. ___ 6 14 __

60 17. ___ 3 80 __

18. __28

simplest form

3

7

2

16. __89

7

4

1 __ 4

Practice 10-5

simplest form

5

6 19. Sheldon has scored __ of the points in a basketball game. 18 How can you use division to simplify the fraction of the points 6 in simplest form? he scored? What is __ 18

6 in Divide both numbers by 6; ___ 18 1 __ simplest form is . 3

40 ? 20. What is the simplest form of the fraction ___ 80

1 A __ 4

4 B __ 8

2 C __ 4

1 D __ 2

© Pearson Education, Inc. 4

21. Writing to Explain If the numerator of a fraction is a prime number, can the fraction be simplified? Why or why not?

Yes. The fraction can be simplified if the numerator is a factor of the denominator.

Topic 10

Nat_AncTopic_10.indb 57

57 1/30/08 11:42:23 AM

Name

Enrichment

10-5

Parts of a Region

Visual Thinking

A fraction names equal parts of a region. The numerator tells the number of equal parts shaded. ____________________________________________________ The denominator tells the total number of equal parts.

3 shaded parts ________________ 5 parts in all

3 out of 5 equal parts of the rectangle are shaded. There are five equal parts, so the shaded parts are three fifths, or _35 , of the rectangle. Circle the fraction for the shaded parts of each region.

Enrichment 10-5

1.

2.

5 1 __ 1 __ __

1 1 __ 1 __ __

3 1 __ 1 __ __

5 6 6

4 3 2

4.

3.

5.

5 __ 3 5 __ __

4 3 4

6.

3 __ 3 1 __ __

3 8 8

5 __ 5 __ 1 __ 6 5 6

4 1 4

Write the fraction for the shaded parts of each region. 8.

9.

© Pearson Education, Inc. 4

7.

58 Nat_AncTopic_10.indb 58

Topic 10

1/30/08 2:30:26 PM

Name

Enrichment

10-5

Parts of a Region

Visual Thinking

A fraction names equal parts of a region. The numerator tells the number of equal parts shaded. ____________________________________________________ The denominator tells the total number of equal parts.

3 shaded parts ________________ 5 parts in all

3 out of 5 equal parts of the rectangle are shaded. There are five equal parts, so the shaded parts are three fifths, or _35 , of the rectangle. Circle the fraction for the shaded parts of each region.

Enrichment 10-5

1.

2.

5 1 __ 1 __ __

1 1 __ 1 __ __

3 1 __ 1 __ __

5 6 6

4 3 2

4.

3.

5.

5 __ 3 5 __ __

4 3 4

6.

3 __ 3 1 __ __

3 8 8

5 __ 5 __ 1 __ 6 5 6

4 1 4

Write the fraction for the shaded parts of each region. 7.

8.

1 __

2 __ 4

7 __ 8

© Pearson Education, Inc. 4

3

9.

58 Nat_AncTopic_10.indb 58

Topic 10

1/30/08 11:42:25 AM

Name

Daily Spiral Review

10-6

1. The model is shaded to represent a fraction.

Which of the following is an equivalent fraction? 3 A ___ 12

3 B __ 9

3 C __

4. Jamie has seen her favorite movie 95 times! Derrek has seen it 113 times! How many more times has Derrek seen the movie?

5. A number has a 4 in the thousands place, a 1 in the tens place, a 0 in the ones place, and a 9 in the hundreds place. What is the number?

4

9 D __ 3

6. Find the product of 29 ! 3.

Daily Spiral Review 10-6

2. Each of the three fourth-grade classes at Woodrow Wilson Elementary has 22 students. About how many students are in all three classes? A 90 B 60 C 30 D 25

© Pearson Education, Inc. 4

3. Angel bought 5 books for $45. How much did each book cost if each book was the same price? A $5 B $6 C $8 D $9

Topic 10

Nat_AncTopic_10.indb 59

59 1/30/08 2:30:31 PM

Name

Daily Spiral Review

10-6

1. The model is shaded to represent a fraction.

4. Jamie has seen her favorite movie 95 times! Derrek has seen it 113 times! How many more times has Derrek seen the movie?

18

Which of the following is an equivalent fraction? 3 A ___ 12

3 B __ 9

3 C __ 4 __ D 9 3

4,910

6. Find the product of 29 ! 3.

87

Daily Spiral Review 10-6

2. Each of the three fourth-grade classes at Woodrow Wilson Elementary has 22 students. About how many students are in all three classes? A 90 B 60 C 30 D 25

5. A number has a 4 in the thousands place, a 1 in the tens place, a 0 in the ones place, and a 9 in the hundreds place. What is the number?

© Pearson Education, Inc. 4

3. Angel bought 5 books for $45. How much did each book cost if each book was the same price? A $5 B $6 C $8 D $9

Topic 10

Nat_AncTopic_10.indb 59

59 1/30/08 11:42:30 AM

60

Nat_AncTopic_10.indb 60

Problem of the Day 10-6

Topic 10

Problem

of the

Day

10-6

10-6

© Pearson Education, Inc. 4

Problem of the Day

1/30/08 2:30:33 PM

Melissa and Jennifer went apple picking. Melissa picked _12 of a bushel. Jennifer picked _48 of a bushel. Melissa says that they picked the same amount, but Jennifer says that she picked more. Which girl is correct? Explain how you know.

Name

Quick Check

10-6

1. Look at the model below. Which mixed number and improper fraction describe the shaded part of the model? A B C D

3_34; 4_14; 4_34; 3_14;

15 __ 4 15 __ 4 _6 4 _6 4

2. Which choice below shows the 11 written as a improper fraction __ 3 mixed number? A 4_13 B 3_23 C 2_12 D 2_13

3. Writing to Explain Write the mixed number 4_12 as an improper fraction. Draw a model and explain your thinking.

© Pearson Education, Inc. 4

Quick Check 10-6

Topic 10

Nat_AncTopic_10.indb 61

61 1/30/08 2:30:34 PM

Name 1. Look at the model below. Which mixed number and improper fraction describe the shaded part of the model? 15 A 3_34; __ 4 15 B 4_14; __ 4

C 4_34; _64 D 3_14; _64

Quick Check

10-6 2. Which choice below shows the 11 written as a improper fraction __ 3 mixed number? A 4_13 B 3_23 C 2_12 D 2_13

3. Writing to Explain Write the mixed number 4_12 as an improper fraction. Draw a model and explain your thinking.

See student samples to the right.

© Pearson Education, Inc. 4

Quick Check 10-6

Topic 10

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61 1/30/08 11:42:33 AM

Name

Reteaching

10-6

Reteaching 10-6

Improper Fractions and Mixed Numbers You can use fraction strips to write a mixed number as an improper fraction.

You can also use fraction strips to write an improper fraction as a mixed number.

3_12 of the model below is shaded.

_8 of the model below is shaded. 3

1 2

1 2

1 3

1 3

1 3

1 2

1 2

1 3

1 3

1 3

1 2

1 2

1 3

1 3

1 3

1 2

1 2

Into how many parts is each strip divided? 2. This is your denominator.

How many strips are completely shaded? 2. This is your whole number.

Count the shaded halves. There are 7. This is your numerator.

What fraction of the third strip is shaded? _23 . This is your fraction.

3_12 is the same as the improper fraction _72.

_8 is the same as the mixed number 2_2 . 3 3

Write each mixed number as an improper fraction. 1. 2 !13!

2. 4 !15!

3. 2 !34!

4. 5 !26!

Write each improper fraction as a mixed number or a whole number. 5.

13 ! ! 12

6.

50 ! ! 10 Is !45!5

7.

23 ! ! 10

8.

17 ! ! 15

© Pearson Education, Inc. 4

9. Writing to Explain equal to a whole number or a mixed number? Explain how you know.

62 Nat_AncTopic_10.indb 62

Topic 10

1/30/08 2:30:35 PM

Name

Reteaching

10-6

Reteaching 10-6

Improper Fractions and Mixed Numbers You can use fraction strips to write a mixed number as an improper fraction.

You can also use fraction strips to write an improper fraction as a mixed number.

3_12 of the model below is shaded.

_8 of the model below is shaded. 3

1 2

1 2

1 3

1 3

1 3

1 2

1 2

1 3

1 3

1 3

1 2

1 2

1 3

1 3

1 3

1 2

1 2

Into how many parts is each strip divided? 2. This is your denominator.

How many strips are completely shaded? 2. This is your whole number.

Count the shaded halves. There are 7. This is your numerator.

What fraction of the third strip is shaded? _23 . This is your fraction.

3_12 is the same as the improper fraction _72.

_8 is the same as the mixed number 2_2 . 3 3

Write each mixed number as an improper fraction. 1.

7 !3!

2 !13!

2.

4 !15!

21 !5!

3.

2 !34!

11 !4!

4.

32 ! 6!

5 !26!

Write each improper fraction as a mixed number or a whole number.

1

5.

13 ! ! 12

1!1! 2

6. !510! 0 4 Explain Is !5!5

5

3

7.

23 ! ! 10

2 !1! 0

8.

17 ! ! 15

2

1 !15!

Sample answer: Whole number, because if you divide the numerator by the denominator, the quotient is 9 and there is no remainder.

62 Nat_AncTopic_10.indb 62

© Pearson Education, Inc. 4

9. Writing to equal to a whole number or a mixed number? Explain how you know.

Topic 10

1/30/08 11:42:34 AM

Name

Practice

10-6

Improper Fractions and Mixed Numbers Write each mixed number as an improper fraction. 1. 3 !25!

2. 6 !14!

3. 2 !112!

4. 2 !79!

Write each improper fraction as a mixed number or whole number. 5.

12 ! ! 5

6.

2! 7 ! 9

7.

32 ! ! 3

8.

20 ! ! 12

9. Number Sense Matt had to write 3 !284! as an improper fraction. Write how you would tell Matt the easiest way to do so.

Practice 10-6

11 10. Jill has __ 8 ounces of trail mix. Write the weight of Jill’s trail mix as a mixed number.

11. Nick had 1 !43! gal of milk. Write the amount of milk Nick has as an improper fraction. 12. Which is NOT an improper fraction equal to 8? A

24 ! ! 3

B

49 ! ! 7

C

5! 6 ! 7

D

6! 4 ! 8

© Pearson Education, Inc. 4

13. Writing to Explain Write three different improper fractions that equal 4 !32!. (Hint: find equivalent fractions.)

Topic 10

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63 1/30/08 2:30:37 PM

Name

Practice

10-6

Improper Fractions and Mixed Numbers Write each mixed number as an improper fraction. 1.

3 !25!

17 ! ! 5

2.

6 !14!

25 ! ! 4

3.

25 ! 1! 2

2 !11! 2

Write each improper fraction as a mixed number or whole number.

2

5.

12 ! ! 5

2 !5!

6.

27 ! ! 9

3

7.

32 ! ! 3

4.

2 !79!

8.

20 ! ! 12

2

25 !9!

2

10 !3!

1 !3!

9. Number Sense Matt had to write 3 !284! as an improper fraction. Write how you would tell Matt the easiest way to do so.

11 10. Jill has __ 8 ounces of trail mix. Write the weight of Jill’s trail mix as a mixed number.

11. Nick had 1 !43! gal of milk. Write the amount of milk Nick has as an improper fraction.

Practice 10-6

Sample answer: The easiest way is to 8 _1 . first write __ in simplest form as 24 3 That makes the multiplication easier. 10 . (3 ! 3) " 1 # 10, so 3_13 # __ 3 1_38 oz _7 gal 4

12. Which is NOT an improper fraction equal to 8? A

24 ! ! 3

B

4! 9 ! 7

C

5! 6 ! 7

D

6! 4 ! 8

13. Writing to Explain Write three different improper fractions that equal 4 !32!. (Hint: find equivalent fractions.)

© Pearson Education, Inc. 4

28 __ 14 __ Sample answer: __ , , 42 3 6 9

Topic 10

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63 1/30/08 11:42:37 AM

Name

Recreation Time! 1. Timothy has computer class 3 times a week. Each class is 45 minutes long. How many hours of computer class does Timothy have per week? In 4 weeks?

Enrichment

10-6 Reasoning

2. Alex practices soccer 4 times a week for 50 minutes each practice. How many total hours does Alex practice soccer per week? In 2 weeks? 3. Laurel went swimming 7 times in 3 weeks. One time she swam for 1!12! hours. The other 6 times she swam for 30 minutes each time. How many hours did Laurel swim in 3 weeks?

Enrichment 10-6

4. Caitlin, Cindy, and Connie went jogging at the recreation center. Caitlin jogged for 40 minutes, Cindy jogged for 30 minutes, and Connie jogged for 70 minutes. What was the total amount of time they jogged altogether? 5. Dena takes karate classes every Tuesday and Thursday. Each class is 55 minutes long. How many hours of class will Dena have in 3 weeks? 6. Jack spent 9!34! hours practicing ice hockey with his team. How many !14! hours is that?

8. Carlos practices piano every Monday, Wednesday, and Friday for 35 minutes each day. He also practices guitar every Tuesday, Thursday, and Saturday for 30 minutes each day. How many hours does Carlos spend practicing musical instruments each week?

64 Nat_AncTopic_10.indb 64

© Pearson Education, Inc. 4

7. Misa takes 3 dance classes each week. Ballet class is 45 minutes long, modern dance is 50 minutes long, and jazz dance is 35 minutes long. How many hours of dance class does Misa have in 2 weeks?

Topic 10

1/30/08 2:30:38 PM

Name

Enrichment

10-6

Recreation Time! 1. Timothy has computer class 3 times a week. Each class is 45 minutes long. How many hours of computer class does Timothy have per week? In 4 weeks?

Reasoning

1

2!4! h, 9 h

2. Alex practices soccer 4 times a week for 50 minutes each practice. How many total hours does Alex practice soccer per week? In 2 weeks?

1

3. Laurel went swimming 7 times in 3 weeks. One time she swam for 1!12! hours. The other 6 times she swam for 30 minutes each time. How many hours did Laurel swim in 3 weeks?

4!2! h

1

4. Caitlin, Cindy, and Connie went jogging at the recreation center. Caitlin jogged for 40 minutes, Cindy jogged for 30 minutes, and Connie jogged for 70 minutes. What was the total amount of time they jogged altogether?

2!3! h

5. Dena takes karate classes every Tuesday and Thursday. Each class is 55 minutes long. How many hours of class will Dena have in 3 weeks?

5!2! h

2

Enrichment 10-6

3!3! h, 6!3! h

6. Jack spent 9!34! hours practicing ice hockey with his team. How many !14! hours is that?

1 1

39

7. Misa takes 3 dance classes each week. Ballet class is 45 minutes long, modern dance is 50 minutes long, and jazz dance is 35 minutes long. How many hours of dance class does Misa have in !1 3! 2 weeks? 8. Carlos practices piano every Monday, Wednesday, and Friday for 35 minutes each day. He also practices guitar every Tuesday, Thursday, and Saturday for 30 minutes each day. How many hours does Carlos spend practicing musical instruments each week?

1

3!4! h

64 Nat_AncTopic_10.indb 64

© Pearson Education, Inc. 4

4 h

Topic 10

1/30/08 11:42:38 AM

Name 1. Look at the model.

Which fraction is shown by the model?

Daily Spiral Review

10-7 4. Estimate the product 9 # 231. Show your work.

5. Write 3_17 as an improper fraction.

A _15 B _34 C _33 D _31

6. Marsha’s school has 345 students. If all the students are separated into 5 equal groups, how many are in each group?

Daily Spiral Review 10-7

2. Janelle and Howard combined all their pennies. Janelle had 213 pennies, and Howard had 468 pennies. How many pennies did they have in all? A 781 B 681 C 671 D 255

© Pearson Education, Inc. 4

3. Where would placing the number 3 make the number sentence true? A 15 ! 5 " B 42 ! "7 C !5 "9 D 27 ! "3

Topic 10

Nat_AncTopic_10.indb 65

65 1/30/08 2:30:39 PM

Name 1. Look at the model.

Which fraction is shown by the model? A _15 B _34 C _33 D _31

10-7 4. Estimate the product 9 # 231. Show your work.

Sample answer: about 1,800; 9 ! 200 " 1,800

5. Write 3_17 as an improper fraction.

22 ___ 7

6. Marsha’s school has 345 students. If all the students are separated into 5 equal groups, how many are in each group?

69 students

Daily Spiral Review 10-7

2. Janelle and Howard combined all their pennies. Janelle had 213 pennies, and Howard had 468 pennies. How many pennies did they have in all? A 781 B 681 C 671 D 255

Daily Spiral Review

© Pearson Education, Inc. 4

3. Where would placing the number 3 make the number sentence true? A 15 ! 5 " B 42 ! "7 C !5 "9 D 27 ! "3

Topic 10

Nat_AncTopic_10.indb 65

65 1/30/08 11:42:39 AM

66

Nat_AncTopic_10.indb 66

Problem of the Day 10-7

Topic 10

Problem

of the

Day

10-7

Is more or less than _14 of all the fruit in the basket bananas? (Hint: Use fraction strips.) Fruit in the Basket Fruit

Number of Pieces 5

Bananas

3

Grapefruits

2

Oranges

6

10-7

1/30/08 2:30:40 PM

© Pearson Education, Inc. 4

Problem of the Day

Apples

Name

Quick Check

10-7

1. Use the fraction strips shown. Which choice shows a correct comparison?

2. Use the fraction strips shown. Which choice shows a correct comparison?

1 1/4

1/4

1 1/4

1/4

1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8

1/3 1/6

1/6

A _38 ! _34

A _13 ! _16

B _34 ! _38

B _36 ! _13

C _18 " _14

C _46 " _36

D _14 " _38

D _23 ! _46

1/3 1/6

1/6

1/3 1/6

1/6

3. Writing to Explain Which fraction is greater, _45 or _48? Use words and draw models to explain your answer.

© Pearson Education, Inc. 4

Quick Check 10-7

Topic 10

Nat_AncTopic_10.indb 67

67 1/30/08 2:30:41 PM

Name

Quick Check

10-7

1. Use the fraction strips shown. Which choice shows a correct comparison?

2. Use the fraction strips shown. Which choice shows a correct comparison?

1 1/4

1/4

1 1/4

1/4

1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8

1/3 1/6

1/6

A _38 ! _34

A _13 ! _16

B _34 ! _38

B _36 ! _13

C _18 " _14

C _46 " _36

D _14 " _38

D _23 ! _46

1/3 1/6

1/6

1/3 1/6

1/6

3. Writing to Explain Which fraction is greater, _45 or _48? Use words and draw models to explain your answer.

See student samples to the right.

© Pearson Education, Inc. 4

Quick Check 10-7

Topic 10

Nat_AncTopic_10.indb 67

67 1/30/08 11:42:42 AM

Name

Reteaching

10-7

Comparing Fractions Leanne wanted to compare !46! and !34!. She used fraction strips to help. 1 6

1 6 1 4

4 6 3 4

She compared the amounts that were shaded in each picture. Because the amount shaded in !34! is more than the amount shaded in !46!, she knew that !34! is greater than !46!. So, !34! " !46!. . Use fraction strips or benchmark

Write " or # for each fractions to help. 1.

!5! 6

!2! 3

2.

!1! 5

!2! 8

3.

!9! 10

5.

!8! 9

!5! 10

6.

!2! 5

!2! 6

7.

!6! 9

!6! 8 !7! 9

4.

!3! 4

8.

!2! 10

!1! 4 !3! 5

Reteaching 10-7

The same number of students attended school all week. Day Monday Tuesday Wednesday Thursday Friday

Fraction of students buying lunch !1! 2 !2! 5 !3! 4 !5! 8 !4! 6

10. Did more students buy lunch on Thursday or on Friday?

68 Nat_AncTopic_10.indb 68

© Pearson Education, Inc. 4

9. Did more students buy lunch on Tuesday or on Wednesday?

Topic 10

1/30/08 2:30:43 PM

Name

Reteaching

10-7

Comparing Fractions Leanne wanted to compare !46! and !34!. She used fraction strips to help. 1 6

1 6 1 4

4 6 3 4

She compared the amounts that were shaded in each picture. Because the amount shaded in !34! is more than the amount shaded in !46!, she knew that !34! is greater than !46!. So, !34! " !46!. . Use fraction strips or benchmark

Write " or # for each fractions to help. 1.

!5! 6

5.

!8! 9

> >

!2! 3

2.

!1! 5

!5! 10

6.

!2! 5

< >

!2! 8

3.

!9! 10

!2! 6

7.

!6! 9

> !68! < !79!

4. 8.

> !14! !2! < !3! 10 5 !3! 4

Day Monday Tuesday Wednesday Thursday Friday

Fraction of students buying lunch !1! 2 !2! 5 !3! 4 !5! 8 !4! 6

9. Did more students buy lunch on Tuesday or on Wednesday? 10. Did more students buy lunch on Thursday or on Friday?

68 Nat_AncTopic_10.indb 68

Wednesday Friday

© Pearson Education, Inc. 4

Reteaching 10-7

The same number of students attended school all week.

Topic 10

1/30/08 11:42:44 AM

Name

Practice

10-7

Comparing Fractions Write > or < for each

. You may use fraction strips to help.

1.

!1! 2

!3! 13

2.

!8! 9

!5! 9

3.

!3! 8

1! 1 ! 22

4.

!3! 3

!7! 8

5.

!3! 5

!1! 3

6.

!1! 4

!2! 4

7.

!5! 6

!5! 8

8.

!7! 12

9.

!3! 7

!6! 7

!4! 5

!2! 10. Number Sense Explain how you know that !321! 0 is greater than 3 .

11. Tina completed !23! of her homework before dinner. George completed !47! of his homework before dinner. Who completed a greater fraction of homework? 12. Jackson played a video game for !16! hour. Hailey played a video game for !13! hour. Who played the video game for a greater amount of time? Practice 10-7

13. Which fraction is greater than !34!? A

!5! 9

B

17 ! ! 24

C

15 ! ! 20

D

!7! 9

© Pearson Education, Inc. 4

9! 9 14. Writing to Explain James says that !55! is greater than ! 100 . Is he correct? Explain.

Topic 10

Nat_AncTopic_10.indb 69

69 1/30/08 2:30:44 PM

Name

Practice

10-7

Comparing Fractions Write > or < for each 1.

!1! 2

4.

!3! 3

7.

!5! 6

. You may use fraction strips to help.

> !13!3 > !78! > !58!

2. 5. 8.

> !59! !3! !1! 5 > 3 !7! !4! 12 < 5 !8! 9

3.

!3! 8

6.

!1! 4

9.

!3! 7

< <