Please copy and paste this embed script to where you want to embed

Comparing and Ordering Fractions

Objectives To review equivalent fractions; and to provide experience with comparing and ordering fractions. e www.everydaymathonline.com

ePresentations

eToolkit

Algorithms Practice

EM Facts Workshop Game™

Teaching the Lesson

Assessment Management

Common Core State Standards

Ongoing Learning & Practice

Key Concepts and Skills

1 2 4 3

• Find equivalent fractions using a length model. [Number and Numeration Goal 5] • Compare fractions to the benchmarks 0, and 1. [Number and Numeration Goal 6] • Order fractions from least to greatest.

Family Letters

1 _ 2,

[Number and Numeration Goal 6]

• Solve fraction number stories using a number-line model. [Operations and Computation Goal 4]

• Use fraction sticks to add fractions.

Playing Fraction Top-It Student Reference Book, p. 316 Fraction Cards (Math Journal 2, Activity Sheets 5–7) Students practice comparing fractions by playing Fraction Top-It.

Math Boxes 5 3

Math Journal 1, p. 133 Students practice and maintain skills through Math Box problems.

Study Link 5 3

[Operations and Computation Goal 4]

Key Activities Students use the Fraction-Stick Chart to find equivalent fractions and compare fractions to the benchmarks 0, _12 , 1, and 1_12 . They use the fraction-stick model to compare pairs of fractions, find equivalent fractions, and continue their exploration of fraction addition.

Math Masters, p. 131 Students practice and maintain skills through Study Link activities.

Curriculum Focal Points

Interactive Teacher’s Lesson Guide

Differentiation Options READINESS

Making Fraction Strips 6 strips of colored paper, each 2" by 8_12 " Students use a length model to explore comparing and ordering fractions by making fraction strips. ENRICHMENT

Exploring a Fraction-Stick Chart Math Masters, p. 130 Students explore relationships between the numerators and denominators of equivalent fractions. ELL SUPPORT

Building a Math Word Bank Differentiation Handbook, p. 142 Students add the term equivalent fractions to their Math Word Banks.

Ongoing Assessment: Recognizing Student Achievement Use journal page 129. [Number and Numeration Goal 6]

Ongoing Assessment: Informing Instruction See page 305. Key Vocabulary benchmark fraction stick equivalent fractions

Materials Math Journal 1, pp. 129–132 Study Link 52 transparency of Math Masters, p. 137 slate Geometry Template straightedge (optional)

Advance Preparation For Part 1, make a transparency of the chart on Math Masters, page 137. For the optional Readiness activity in Part 3, each student will need 6 strips of colored paper, each 2" by 8_12 ". These can be prepared ahead of time or during the activity.

Teacher’s Reference Manual, Grades 4–6 pp. 38, 44, 45, 60–74, 88, 89 302

Unit 5

Fractions, Decimals, and Percents

302_EMCS_T_TLG1_G5_U05_L03_576825.indd 302

2/14/11 1:20 PM

Getting Started Mental Math and Reflexes

Math Message Use the benchmarks 0, _ , 2 and 1 to answer Problems 1–5 on journal page 129. 1

Have students use the rulers on their Geometry Templates. Find 2_ inches on a ruler. How many half-inches is that? 5 2 1

Find 6 cm on a ruler. How many _ cm is that? 12 2 1

Study Link 5 2 Follow-Up

Find 2_ inches on a ruler. How many quarter-inches is that? 10 8 4

Find 3_ cm on a ruler. How many _ cm is that? 7 2 2 1

1

1 1 1 _ inch is what fraction of 2_ inches? _

Allow students five minutes to compare answers and correct any errors. Have volunteers share their mixed-number problems.

5 2 2 3 3 1 _ _ _ inch is what fraction of 2 inches? 4 2 10

1 Teaching the Lesson ▶ Math Message Follow-Up

WHOLE-CLASS DISCUSSION

(Math Journal 1, p. 129)

Remind students that a benchmark is a well-known count or measure that can serve as a reference point when estimating. 1 When working with fractions, the benchmarks 0, _ , and 1 are often 2 used. Discuss how students applied their knowledge of numerators, denominators, and benchmarks to tell if each measurement is 1 closest to 0, _ , or 1. 2

Ongoing Assessment: Recognizing Student Achievement

Journal Page 129 Problem 5

Student Page Date

Time

LESSON

Use journal page 129, Problem 5 to assess students’ understanding of the structure of fractions. Students are making adequate progress if their explanations correctly represent the relationship between the numerator and denominator and 1 the use of benchmarks such as 0, _ 2 , and 1. [Number and Numeration Goal 6]

Comparing and Ordering Fractions

53

Math Message 1 Decide whether each of these measurements is closer to the benchmark 0, _ 2 , or 1 inch. Circle the closest benchmark. 1 _ 1. 8

inch is closest to . . .

15 inch 2. _ 16 5 3. _ 8

is closest to . . .

inch is closest to . . .

3 inch is closest to . . . 4. _ 8

▶ Ordering Fractions

PARTNER ACTIVITY

(Math Journal 1, p. 129)

5.

0 inches.

1 _ 2 inch.

1 inch.

0 inches.

1 _ 2 inch.

1 inch.

0 inches.

1 _ 2 inch.

1 inch.

0 inches.

1 _ 2 inch.

1 inch.

Explain your solution for Problem 4.

3 1 _ Sample answer: I know that _ 8 is only 8 away 3 4 1 1 _ _ _ from , which is . So must be closest to _ . 8

2

8

2

Ordering Fractions

On the board or a transparency, draw 4 horizontal lines in a row to order the fractions from Problems 1–4 of the journal page. Volunteers explain which of the Math Message fractions is least 1 is the least because it is the closest to 0; and which is greatest. _ 8 15 is the greatest because it is closest to 1. Write these fractions _ 16 5 and _ 3 are on the first and last lines, respectively. Ask: Since _ 8 8 1 , how do we decide where to write them? Both equally close to _ 2 fractions are eighths, and 5 is more than 3, which means that 3 is the smaller fraction so it is closer to 0. _ 8

For each problem below, write the fractions in order from least to greatest. 6 _ 3 _ 5 _ 8 _ 6. 8 , 8 , 8 , 8 2 _ 2 _ 2 _ 2 _ 7. 7 , 9 , 5 , 12 3 2 _ 1 _ 1 _ _ 8. 3 , 4 , 3 , 4 3 _ 9 _ 4 _ 1 _ 9. 5 , 10 , 20 , 25 3 _ 5 1 _ 7 _ _ 10. 7 , 10 , 8 , 7 5 _ 9 2 _ 1 _ _ 11. 9 , 5 , 6 , 10 3 _ 4 _ 4 _ 4 _ 12. 8 , 7 , 5 , 9

3 _

8 2 _ 12 1 _ 4 1 _ 25 1 _ 10 1 _ 6 4 _ 9

5 _

, , , , , , ,

8 2 _ 9 1 _ 3 4 _ 10 3 _ 7 2 _ 5 4 _ 8

6 _

, , , , , , ,

8 2 _ 7 2 _ 3 9 _ 20 5 _ 7 5 _ 9 4 _ 7

8 _

, , , , , , ,

8

2 _ 5

3 _ 4

3 _ 5

7 _ 8

9 _ 10 3 _ 5

Math Journal 1, p. 129 EM3MJ1_G5_U05_121-163.indd 129

1/20/11 8:34 AM

Lesson 5 3

303-307_EMCS_T_TLG1_G5_U05_L03_576825.indd 303

303

2/14/11 1:26 PM

Student Page Date

Time

LESSON

Fraction-Stick Chart

53 䉬

0 1 4

1 8

1 10 1 12 1 16

9

—

7

6

2 3

—

4

9

—

8

12

12

3 4

14 8

—

1 2 1 3 1 1 4 4 1 1 5 5 1 1 1 6 6 6 1 1 1 7 7 7 1 1 1 8 8 8 1 1 1 1 9 9 9 9 1 1 1 1 10 10 10 10 1 1 1 1 1 12 12 12 12 12 1 1 1 1 1 1 1 16 16 16 16 16 16 16

—

6

4

2 1. 3

8

12

1

2 4

1

—

16

Examples:

4 7

or 8 ?

4 or 5 ?

6.

3.

2 Which is 5 closest to:

Which is closer to 1 2:

1 0 or 2 or 1?

1 3 or 1 5 ?

3 4

Which is larger:

4 7

Ask students to describe the fractions in Problem 6. The denominators are the same. So we know that all the unit fractions are the same size. Only the number of pieces (the numerators) need to be compared.

1 3

2.

Which is larger:

7 12

1 9 1 10

5.

Which is larger:

13 or 3 ? 12. Which is 8 closest to:

1 16

8.

Which is larger:

1 4

1 12

1 5

1 6 1 7 1 8 1 9 1 10 1 12 1 16

1 16

1 1

3

1 4

1 8

1

143

1 3

1 9 1 10

1 16

1 4

1 12

1

1 5

2

1 6 1 7 1 8 1 9 1 10 1 12 1 16

1 16

1

2

0 or 2 or 1?

1 2 1 3 1 4 1 1 5 5 1 1 6 6 1 1 1 7 7 7 1 1 1 8 8 8 1 1 1 9 9 9 1 1 1 10 10 10 1 1 1 1 12 12 12 12 1 1 1 1 1 16 16 16 16 16

142

1 10 1 12 1 16

5

1

3 1 4 or 6 ? 9. Which is 1 6 closest to: 0 or 2 or 1?

4

1 2 1 3 1 1 4 4 1 1 5 5 1 1 1 6 6 6 1 1 1 7 7 7 1 1 1 8 8 8 1 1 1 1 9 9 9 9 1 1 1 1 10 10 10 10 1 1 1 1 1 12 12 12 12 12 1 1 1 1 1 1 1 16 16 16 16 16 16 16

2

11.

1 2 1 3 1 4 1 1 5 5 1 1 6 6 1 1 1 7 7 7 1 1 1 8 8 8 1 1 1 9 9 9 1 1 1 10 10 10 1 1 1 1 12 12 12 12 1 1 1 1 1 16 16 16 16 16

—

12

12

2 3

—

8

3 4

16

28

12

11 6

—

22

14

3

Fill in the blanks. Circle the correct answer.

—

6

5

3 4. 4

4

—

5

8

—

3

15

20 7. 16

10.

Explain that examining numerators and denominators is the first step when comparing and ordering fractions. Refer students to journal page 129.

Math Journal 1, p. 130

Ask students to describe the fractions in Problem 7. The numerators are the same. Now what do we know? There are the same number of pieces for each fraction. So only the size of the pieces (the denominators) needs to be compared. Remind students that the smaller the denominator is, the larger the piece is. Ask students to describe the fractions in Problem 8. There are two different denominators; there are two unit fractions. First 1 and _ 1 . The smaller denominator is compare the unit fractions _ 3 4 the larger fraction. The remaining fractions are within one 3 is _ 1 away from 1, and _ 2 is _ 1 away from 1. piece of 1—that is, _ 4 4 3 3 1 is greater than _ 1 , that makes _ 2 farther away from 1. Since _ 3

4

3

Ask partners to complete the problems on the journal page. When most students are finished, discuss their strategies for Problems 9–12, including the following: 1 . That leaves the other three Problem 9: The least fraction is _ 25

to compare. Change each to an equivalent fraction with a denominator of 20. Problem 10: One of these fractions is close to 0, one is close to 1. 1, and the other two are close to _ 2 1 is to see if the Problem 11: One way to compare a fraction to _ 2 1 _ numerator is more or less than 2 of the denominator. Two of 1 . Their order is determined the fractions are greater than _ 2 5 9 1 _ _ _ because 9 is close to 2 and 10 is close to 1. Of the two fractions 1 , the denominators are close to each other, that are less than _

Student Page Date

Time

LESSON

Adding with Fraction Sticks

5 3 䉬

1.

2.

2 halves

8 eighths

4 quarters

16 sixteenths

and one numerator is 2 times the numerator of the other. 1 (the numerator is _ 1 of the Problem 12: One fraction equals _ 2 2 1 , and _ 4 is less than _ 1. denominator). The others are close to _ 2

Use the fraction sticks to find equivalent fractions.

2

a. 1 8

—

d. 1 2

—

b.

16

2

4

4 —

8

6 —

8

12 16

8

3 4

e.

—

16

2 —

2

6

c.

—

4 4

—

8

8 —

8

3 4

1 2 8 8

3 8

2 4

1 4

9 1 6

12 , 16

or

3 4

5 8 1 6 16

14 , 16

or

7 8

a.

3 16

b.

1 c. 16

16

16 —

16

3 4

5

1 2

1 4

b.

1 2

3 8

c.

5 8

1 4

d.

1 4

7

2

WHOLE-CLASS ACTIVITY

Fraction-Stick Chart

3 4 7 8 7 8

8 1 6

2

7

▶ Introducing the

Use the fraction sticks to add fractions with different denominators. a.

9

1 but only by _ 1 of a piece The other two are greater than _ 2 2 3 is _ 4 1 1 , and _ 1 of _ _ each—that is, 7 is 2 of a seventh greater than _ 2 5 2 1 . Because fifths are greater than sevenths, a fifth greater than _ 2 3 is greater than _ 4. _

12 —

Use the fraction sticks to add fractions with the same denominator. Example:

3.

2

1

A whole stick is worth 1.

(Math Journal 1, p. 130; Math Masters, p. 137)

20 16 ,

4

1

116, or 14

Use a transparency of the chart from Math Masters, page 137 to demonstrate how to use the Fraction-Stick Chart.

Math Journal 1, p. 131

304

Unit 5

Fractions, Decimals, and Percents

EM3cuG5TLG1_303-307_U05L03.indd 304

12/4/10 7:59 AM

1. Skip-Counting with Fractions Please refer students to journal page 130. Explain that a fraction stick is a model for the whole, or the ONE, that shows unit fractions for the interval between 0 and 1. Each row of the Fraction-Stick Chart combines 2 fraction sticks to show the interval from 0 to 2, divided into unit fractions for a particular denominator.

NOTE A fraction stick is a narrow rectangle divided into pieces that represents fractions. Sometimes it is helpful to make physical fraction sticks, as in Part 3 of this lesson.

Example: The third row shows two sticks, each divided into 1 . The pieces thirds. There are 6 pieces in this row, each labeled _ 3 can be used to count by thirds.

2. Finding Equivalent Fractions The Fraction-Stick Chart on Math Masters, page 137 can be used to find equivalent fractions. Survey the class for examples of pairs of fractions that name the same part of a whole. Emphasize that these are equivalent fractions and list the examples on the 3 is equivalent to _ 1. board. For example, _ 6 2 2. Example: Find equivalent fractions for _

1 3

1 3

1 3

0 3

1 3

1 3

2 3

1 3

3 3

1 3

4 3

5 3

6 3

The third row of the Fraction-Stick Chart

3

Step 1: The denominator is 3, so use the thirds stick to locate the 2 . Count the pieces from left to right. The right edge of the fraction _ 3 2. second piece is _ 3 2 , that is, along the Step 2: Place one edge of a straightedge at _ 3 1 piece. The straightedge should be right edge of the second _ 3

parallel to the sides of the Fraction-Stick Chart. Now look for other fraction sticks on the chart along the straightedge. On the sixths stick, the straightedge touches the right edge of a piece. Count the sixths-stick pieces from left to right. The 4 . So _ 4 is straightedge is at the end of the fourth piece, which is _ 6 6 2 _ equivalent to 3 .

Ongoing Assessment: Informing Instruction Watch for students who confuse the fraction labels with the actual end of the fraction stick. Remind students that the labels are in the center of a portion, not at its end. Have students draw a light pencil line along the straightedge and use the line instead of the straightedge to identify equivalent portions.

On the ninths stick, the straightedge touches the end of the sixth 6 . So _ 6 =_ 2. piece, which is _ 9 9 3 On the twelfths stick, the straightedge touches the end of the 8 . So _ 8 =_ 6 , and _ 8 2 . The fractions _ 2, _ 4, _ eighth piece, which is _ 12 12 3 3 6 9 12 are equivalent. They name the same distance on the FractionStick Chart.

0

1 4

On the other sticks, the straightedge cuts through some of the 2 cannot be written as an equivalent fraction using the pieces, so _ 3 denominator on those sticks.

1 1 2 1 3

3. Comparing Fractions The Fraction-Stick Chart on Math Masters, page 137 can be used 3 . (See margin.) 4 and _ to compare fractions, for example, compare _ 9 8 Step 1: The denominator of the first fraction is 9, so use the 4 . Count the pieces from left to right. The ninths stick to locate _ 9 4 . Place the straightedge along right edge of the fourth piece is _ 9 this edge.

2 4

1 3

1 4 1 5

eighths ninths

1 4 1 5

1 5

1 1 1 6 6 6 1 1 1 7 7 7 1 1 1 8 8 8 1 1 1 1 9 9 9 9 1 1 1 1 10 10 10 10 1 1 1 1 1 12 12 12 12 12 1 1 1 1 1 1 1 16 16 16 16 16 16 16

1 7 1 8 1 9 1 10 1 12 1 16

Lesson 5 3

EM3cuG5TLG1_303-307_U05L03.indd 305

305

12/4/10 7:59 AM

Student Page Date

3 (the right edge of the third piece on the eighths Step 2: Locate _ 8 3 is to the left of _ 4 , it is less than _ 4 . Conversely, _ 4 is stick). Since _ 8 9 9 9 3 3 _ _ to the right of 8 , so it is greater than 8 . Ask partners to complete journal page 130. Ask volunteers to explain their solutions.

Time

LESSON

Fraction Number Stories

5 3 䉬

Shade the fraction sticks to help you solve these fraction number stories. Write a number model for each story. 1.

2.

3.

5

ᎏ7ᎏ 8 1 ᎏᎏ ⫽ ᎏ7ᎏ 4 8

a.

How much flour did he use in all?

b.

Number model:

ᎏ5ᎏ 8

⫹

cup

1

Sheryl’s puppy weighed 1ᎏ2ᎏ pounds when it was born. After two weeks, 3 the puppy had gained ᎏ8ᎏ pounds. a.

How much did the puppy weigh after two weeks?

b.

Number model:

1ᎏ12ᎏ ⫹

ᎏ3ᎏ 8

⫽ 1ᎏ78ᎏ

1ᎏ78ᎏ

▶ Adding with Fraction Sticks

pounds

5 8

⫹ ᎏᎏ =

1ᎏ38ᎏ

The five fraction sticks at the top of journal page 131 provide a length model for fraction work. Note that the denominators are restricted to 1, 2, 4, 8, and 16. This model will be used to formally introduce the addition of fractions. All these problems can be solved visually. The correct amount of shading for any fraction can be decided by using the appropriate fraction stick at the top of the page.

Answers vary.

Number story:

b.

Make up your own fraction number story. Draw and shade fraction sticks to solve it. Write a number model for your story.

Answers vary. a.

Number story:

b.

Number model:

c.

Solution:

PARTNER ACTIVITY

(Math Journal 1, p. 131)

Shade the fraction sticks to solve the number model. Then write a fraction number story that fits the number model. 3 a. ᎏᎏ 4

4.

1

Chris made pizza dough with ᎏ8ᎏ cup of white flour and ᎏ4ᎏ cup of whole wheat flour.

▶ Solving Fraction Number Stories

Math Journal 1, p. 132

(Math Journal 1, p. 132)

INDEPENDENT ACTIVITY PROBLEM PRO PR P RO R OB BLE BL L LE LEM EM SO S SOLVING OL O LV VIN IIN NG

Students solve the fraction number stories on journal page 132. Circulate and assist. Encourage students to use the benchmarks 1 , and 1 when explaining their solutions and assessing the 0, _ 2 reasonableness of answers. Discuss the answers and write the strategies on the board.

2 Ongoing Learning & Practice ▶ Playing Fraction Top-It

Student Page Date

Math Boxes

53 䉬

1.

(Student Reference Book, p. 316; Math Journal 2, Activity Sheets 5–7)

Time

LESSON

Write a 10-digit numeral that has 9 3 5 7 1 6

in in in in in in

2.

the tens place, the millions place, the billions place, the hundred-millions place, the thousands place, and all other places.

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

4ᎏ14ᎏ 8 2ᎏ12ᎏ

17 a. ᎏᎏ ⫽ 4 24 b. ᎏᎏ 3

5, 7 6 3, 6 6 1, 6 9 6

Write the numeral in words.

Five billion, seven hundred sixty-three million, six hundred sixty-one thousand, six hundred ninety-six

⫽

5 c. ᎏᎏ 2

⫽

9 d. ᎏᎏ 8

⫽

32 e. ᎏᎏ 5

1ᎏ18ᎏ 6ᎏ25ᎏ

⫽

what fraction of the students traveled within their state?

b.

what fraction traveled to Europe?

c.

62 63

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 5-1. The skill in Problem 5 previews Unit 6 content.

Vacation Travel 11 ᎏ ᎏ 32 ᎏ4ᎏ 32

, or

what fraction traveled to Canada or Mexico?

ᎏ8ᎏ 32

, or

within state 11

ᎏ1ᎏ 8

Canada or Mexico 8

stayed home 3

another state 6 Europe 4

ᎏ1ᎏ 4

59 125

4.

Divide.

5.

a.

21冄4 苶9 苶3 苶∑

23 R10

b.

35冄6 苶2 苶3 苶∑

17 R28

INDEPENDENT ACTIVITY

(Math Journal 1, p. 133)

Where 32 students vacationed, ... a.

Students practice comparing fractions by playing Fraction Top-It. Students use the Fraction Cards that were stored in Lesson 5-1.

▶ Math Boxes 5 3

4

3.

PARTNER ACTIVITY

22–24

Find the following landmarks for this set of numbers: 929, 842, 986, 978, 869, 732, 898, 986, 900, 899, 986, 920, 842 a.

Minimum:

b.

Maximum:

c.

Mode:

d.

Range:

e.

Median:

732 986 986 254 900

Writing/Reasoning Have students write a response to the following: Explain how you converted the fractions to mixed numbers in Problem 2. Sample answer: For the whole number part, I found how many groups of the denominator were in the numerator. The fraction part was what was left.

119

Math Journal 1, p. 133

306

Unit 5

Fractions, Decimals, and Percents

EM3cuG5TLG1_303-307_U05L03.indd 306

1/20/11 11:59 AM

Study Link Master

▶ Study Link 5 3

INDEPENDENT ACTIVITY

(Math Masters, p. 131)

Name

Date

STUDY LINK

Time

Fraction-Stick Problems

53 䉬

Shade the fraction sticks to help you find equivalent fractions. 59

Home Connection Students find equivalent fractions, add fractions, and solve fraction number stories using fraction sticks.

3 Differentiation Options

4

1 1. 2

— 8

3 2. 4

— 16

12

1

4

2 8

— 16

—

3.

4

Shade the fraction sticks to help you solve the addition problems. 1 4. 4

1 5. 2

1 6. 2

4 1 4 6 3 8 4 5 1 1 4 4

3 4 2 8 3 4

Shade the fraction sticks to help you solve the fraction number stories. 3

3

Joe was baking a cake. He added cup of white sugar and cup of brown 4 8 sugar. How much sugar did he use in all?

7.

9 , 8

118 cups

or

(unit)

READINESS

▶ Making Fraction Strips

SMALL-GROUP ACTIVITY

On the back of this page, write a number story using fractions. Then write a number model to show how you solved it.

8.

Practice

15–30 Min

To explore comparing and ordering fractions using a length model, have students make fraction strips. Students cut 6 strips of paper, 1 " and then fold and label them to represent halves, each 2" by 8_ 2 thirds, fourths, fifths, sixths, and eighths. (See margin.)

297

3冄苶8 苶9 苶1 苶

9.

74 R3

12冄苶8 苶9 苶1 苶→

11.

→

10.

6冄苶8 苶9 苶1 苶

12.

24冄苶8 苶9 苶1 苶 →

148 R3 37 R3

Math Masters, p. 131

To fold into thirds, fold one end in so the doubled parts and the single part are the same size. To fold into sixths, fold a strip into thirds and then in half. For fifths, fold the two outside edges of the strip in toward the middle but not together. Fold them so the doubled parts and the space between them look like three equal parts. Now fold the doubled parts back the other way at the point where the folded ends first came down.

When folded into thirds, the edge of the folded end divides the rest into halves.

Have students label the fractions on the folds. As they finish, ask students to fold two strips so only the unit fraction shows and then 1 is less than _ 1. make a comparison statement. For example, _ 5 3

When folded into fifths, the two folded ends are equal in size to the space in the middle.

ENRICHMENT

▶ Exploring a Fraction-Stick Chart

PARTNER ACTIVITY 15–30 Min

Teaching Master Name

Date

LESSON

Time

Fraction-Stick Chart

53 䉬

1 4

0

2 4

3 4

124

114

1

1 1 2

(Math Masters, p. 130)

1 2

1 3

1 3

1 4 1 5

To apply students’ understanding of fractions, have them explore the relationships between the numerators and denominators of equivalent fractions. When they finish, have them share one of their discoveries.

1 4 1 5

1 5

1 3

1 4 1 5

1 6 1 7 1 8 1 1 9 9 1 1 10 10 1 1 12 12 1 1 1 16 16 16

1 3

1 4

1 5

1 5

1 4

1 4

1 5

1 5

1 5

1 1 1 1 1 6 6 6 6 6 1 1 1 1 1 1 7 7 7 7 7 7 1 1 1 1 1 1 1 8 8 8 8 8 8 8 1 1 1 1 1 1 1 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 12 1 1 1 1 1 1 1 1 1 1 1 1 1 16 16 16 16 16 16 16 16 16 16 16 16 16

1 6 1 7 1 8 1 1 9 9 1 1 10 10 1 1 12 12 1 1 1 16 16 16

6 8 2 3 4 5 4 , 6 , 8 , 10 , 12 , 16

Using the Fraction-Stick Chart, list all the 1 fractions that are equivalent to . 2

a.

2

1 2

1 3 1 4

1 1 1 1 1 6 6 6 6 6 1 1 1 1 1 1 7 7 7 7 7 7 1 1 1 1 1 1 1 8 8 8 8 8 8 8 1 1 1 1 1 1 1 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 12 1 1 1 1 1 1 1 1 1 1 1 1 1 16 16 16 16 16 16 16 16 16 16 16 16 16

1.

1 2 1 3

1 4 1 5

134

1

What pattern do you notice in the numerators for these fractions?

Numerators increase by 1 until the last one, which increases by 2.

ELL SUPPORT

▶ Building a Math Word Bank

SMALL-GROUP ACTIVITY

b.

What pattern do you notice in the denominators for these fractions?

c.

Denominators increase by 2 until the last one, which increases by 4. Are the patterns complete? No

d.

What fraction is missing that would make the pattern complete?

15–30 Min

(Differentiation Handbook, p. 142) 2.

To provide language support for fractions, have students use the Word Bank Template found on Differentiation Handbook, page 142. They write the term equivalent fraction, draw pictures related to the term, and write other related words. See the Differentiation Handbook for more information.

7 14

1 3

Using the Fraction-Stick Chart, list all the fractions that are equivalent to .

2 6

a.

b.

3

, 9,

4 12

What pattern do you notice in these fractions?

Numerators increase by 1 and denominators increase by 3. 5 6 7 1 Use this pattern to find the next 3 fractions that are equivalent to . 15 , 18 , 21 3

Math Masters, p. 130

Lesson 5 3

EM3cuG5TLG1_303-307_U05L03.indd 307

307

12/4/10 7:59 AM

View more...
Objectives To review equivalent fractions; and to provide experience with comparing and ordering fractions. e www.everydaymathonline.com

ePresentations

eToolkit

Algorithms Practice

EM Facts Workshop Game™

Teaching the Lesson

Assessment Management

Common Core State Standards

Ongoing Learning & Practice

Key Concepts and Skills

1 2 4 3

• Find equivalent fractions using a length model. [Number and Numeration Goal 5] • Compare fractions to the benchmarks 0, and 1. [Number and Numeration Goal 6] • Order fractions from least to greatest.

Family Letters

1 _ 2,

[Number and Numeration Goal 6]

• Solve fraction number stories using a number-line model. [Operations and Computation Goal 4]

• Use fraction sticks to add fractions.

Playing Fraction Top-It Student Reference Book, p. 316 Fraction Cards (Math Journal 2, Activity Sheets 5–7) Students practice comparing fractions by playing Fraction Top-It.

Math Boxes 5 3

Math Journal 1, p. 133 Students practice and maintain skills through Math Box problems.

Study Link 5 3

[Operations and Computation Goal 4]

Key Activities Students use the Fraction-Stick Chart to find equivalent fractions and compare fractions to the benchmarks 0, _12 , 1, and 1_12 . They use the fraction-stick model to compare pairs of fractions, find equivalent fractions, and continue their exploration of fraction addition.

Math Masters, p. 131 Students practice and maintain skills through Study Link activities.

Curriculum Focal Points

Interactive Teacher’s Lesson Guide

Differentiation Options READINESS

Making Fraction Strips 6 strips of colored paper, each 2" by 8_12 " Students use a length model to explore comparing and ordering fractions by making fraction strips. ENRICHMENT

Exploring a Fraction-Stick Chart Math Masters, p. 130 Students explore relationships between the numerators and denominators of equivalent fractions. ELL SUPPORT

Building a Math Word Bank Differentiation Handbook, p. 142 Students add the term equivalent fractions to their Math Word Banks.

Ongoing Assessment: Recognizing Student Achievement Use journal page 129. [Number and Numeration Goal 6]

Ongoing Assessment: Informing Instruction See page 305. Key Vocabulary benchmark fraction stick equivalent fractions

Materials Math Journal 1, pp. 129–132 Study Link 52 transparency of Math Masters, p. 137 slate Geometry Template straightedge (optional)

Advance Preparation For Part 1, make a transparency of the chart on Math Masters, page 137. For the optional Readiness activity in Part 3, each student will need 6 strips of colored paper, each 2" by 8_12 ". These can be prepared ahead of time or during the activity.

Teacher’s Reference Manual, Grades 4–6 pp. 38, 44, 45, 60–74, 88, 89 302

Unit 5

Fractions, Decimals, and Percents

302_EMCS_T_TLG1_G5_U05_L03_576825.indd 302

2/14/11 1:20 PM

Getting Started Mental Math and Reflexes

Math Message Use the benchmarks 0, _ , 2 and 1 to answer Problems 1–5 on journal page 129. 1

Have students use the rulers on their Geometry Templates. Find 2_ inches on a ruler. How many half-inches is that? 5 2 1

Find 6 cm on a ruler. How many _ cm is that? 12 2 1

Study Link 5 2 Follow-Up

Find 2_ inches on a ruler. How many quarter-inches is that? 10 8 4

Find 3_ cm on a ruler. How many _ cm is that? 7 2 2 1

1

1 1 1 _ inch is what fraction of 2_ inches? _

Allow students five minutes to compare answers and correct any errors. Have volunteers share their mixed-number problems.

5 2 2 3 3 1 _ _ _ inch is what fraction of 2 inches? 4 2 10

1 Teaching the Lesson ▶ Math Message Follow-Up

WHOLE-CLASS DISCUSSION

(Math Journal 1, p. 129)

Remind students that a benchmark is a well-known count or measure that can serve as a reference point when estimating. 1 When working with fractions, the benchmarks 0, _ , and 1 are often 2 used. Discuss how students applied their knowledge of numerators, denominators, and benchmarks to tell if each measurement is 1 closest to 0, _ , or 1. 2

Ongoing Assessment: Recognizing Student Achievement

Journal Page 129 Problem 5

Student Page Date

Time

LESSON

Use journal page 129, Problem 5 to assess students’ understanding of the structure of fractions. Students are making adequate progress if their explanations correctly represent the relationship between the numerator and denominator and 1 the use of benchmarks such as 0, _ 2 , and 1. [Number and Numeration Goal 6]

Comparing and Ordering Fractions

53

Math Message 1 Decide whether each of these measurements is closer to the benchmark 0, _ 2 , or 1 inch. Circle the closest benchmark. 1 _ 1. 8

inch is closest to . . .

15 inch 2. _ 16 5 3. _ 8

is closest to . . .

inch is closest to . . .

3 inch is closest to . . . 4. _ 8

▶ Ordering Fractions

PARTNER ACTIVITY

(Math Journal 1, p. 129)

5.

0 inches.

1 _ 2 inch.

1 inch.

0 inches.

1 _ 2 inch.

1 inch.

0 inches.

1 _ 2 inch.

1 inch.

0 inches.

1 _ 2 inch.

1 inch.

Explain your solution for Problem 4.

3 1 _ Sample answer: I know that _ 8 is only 8 away 3 4 1 1 _ _ _ from , which is . So must be closest to _ . 8

2

8

2

Ordering Fractions

On the board or a transparency, draw 4 horizontal lines in a row to order the fractions from Problems 1–4 of the journal page. Volunteers explain which of the Math Message fractions is least 1 is the least because it is the closest to 0; and which is greatest. _ 8 15 is the greatest because it is closest to 1. Write these fractions _ 16 5 and _ 3 are on the first and last lines, respectively. Ask: Since _ 8 8 1 , how do we decide where to write them? Both equally close to _ 2 fractions are eighths, and 5 is more than 3, which means that 3 is the smaller fraction so it is closer to 0. _ 8

For each problem below, write the fractions in order from least to greatest. 6 _ 3 _ 5 _ 8 _ 6. 8 , 8 , 8 , 8 2 _ 2 _ 2 _ 2 _ 7. 7 , 9 , 5 , 12 3 2 _ 1 _ 1 _ _ 8. 3 , 4 , 3 , 4 3 _ 9 _ 4 _ 1 _ 9. 5 , 10 , 20 , 25 3 _ 5 1 _ 7 _ _ 10. 7 , 10 , 8 , 7 5 _ 9 2 _ 1 _ _ 11. 9 , 5 , 6 , 10 3 _ 4 _ 4 _ 4 _ 12. 8 , 7 , 5 , 9

3 _

8 2 _ 12 1 _ 4 1 _ 25 1 _ 10 1 _ 6 4 _ 9

5 _

, , , , , , ,

8 2 _ 9 1 _ 3 4 _ 10 3 _ 7 2 _ 5 4 _ 8

6 _

, , , , , , ,

8 2 _ 7 2 _ 3 9 _ 20 5 _ 7 5 _ 9 4 _ 7

8 _

, , , , , , ,

8

2 _ 5

3 _ 4

3 _ 5

7 _ 8

9 _ 10 3 _ 5

Math Journal 1, p. 129 EM3MJ1_G5_U05_121-163.indd 129

1/20/11 8:34 AM

Lesson 5 3

303-307_EMCS_T_TLG1_G5_U05_L03_576825.indd 303

303

2/14/11 1:26 PM

Student Page Date

Time

LESSON

Fraction-Stick Chart

53 䉬

0 1 4

1 8

1 10 1 12 1 16

9

—

7

6

2 3

—

4

9

—

8

12

12

3 4

14 8

—

1 2 1 3 1 1 4 4 1 1 5 5 1 1 1 6 6 6 1 1 1 7 7 7 1 1 1 8 8 8 1 1 1 1 9 9 9 9 1 1 1 1 10 10 10 10 1 1 1 1 1 12 12 12 12 12 1 1 1 1 1 1 1 16 16 16 16 16 16 16

—

6

4

2 1. 3

8

12

1

2 4

1

—

16

Examples:

4 7

or 8 ?

4 or 5 ?

6.

3.

2 Which is 5 closest to:

Which is closer to 1 2:

1 0 or 2 or 1?

1 3 or 1 5 ?

3 4

Which is larger:

4 7

Ask students to describe the fractions in Problem 6. The denominators are the same. So we know that all the unit fractions are the same size. Only the number of pieces (the numerators) need to be compared.

1 3

2.

Which is larger:

7 12

1 9 1 10

5.

Which is larger:

13 or 3 ? 12. Which is 8 closest to:

1 16

8.

Which is larger:

1 4

1 12

1 5

1 6 1 7 1 8 1 9 1 10 1 12 1 16

1 16

1 1

3

1 4

1 8

1

143

1 3

1 9 1 10

1 16

1 4

1 12

1

1 5

2

1 6 1 7 1 8 1 9 1 10 1 12 1 16

1 16

1

2

0 or 2 or 1?

1 2 1 3 1 4 1 1 5 5 1 1 6 6 1 1 1 7 7 7 1 1 1 8 8 8 1 1 1 9 9 9 1 1 1 10 10 10 1 1 1 1 12 12 12 12 1 1 1 1 1 16 16 16 16 16

142

1 10 1 12 1 16

5

1

3 1 4 or 6 ? 9. Which is 1 6 closest to: 0 or 2 or 1?

4

1 2 1 3 1 1 4 4 1 1 5 5 1 1 1 6 6 6 1 1 1 7 7 7 1 1 1 8 8 8 1 1 1 1 9 9 9 9 1 1 1 1 10 10 10 10 1 1 1 1 1 12 12 12 12 12 1 1 1 1 1 1 1 16 16 16 16 16 16 16

2

11.

1 2 1 3 1 4 1 1 5 5 1 1 6 6 1 1 1 7 7 7 1 1 1 8 8 8 1 1 1 9 9 9 1 1 1 10 10 10 1 1 1 1 12 12 12 12 1 1 1 1 1 16 16 16 16 16

—

12

12

2 3

—

8

3 4

16

28

12

11 6

—

22

14

3

Fill in the blanks. Circle the correct answer.

—

6

5

3 4. 4

4

—

5

8

—

3

15

20 7. 16

10.

Explain that examining numerators and denominators is the first step when comparing and ordering fractions. Refer students to journal page 129.

Math Journal 1, p. 130

Ask students to describe the fractions in Problem 7. The numerators are the same. Now what do we know? There are the same number of pieces for each fraction. So only the size of the pieces (the denominators) needs to be compared. Remind students that the smaller the denominator is, the larger the piece is. Ask students to describe the fractions in Problem 8. There are two different denominators; there are two unit fractions. First 1 and _ 1 . The smaller denominator is compare the unit fractions _ 3 4 the larger fraction. The remaining fractions are within one 3 is _ 1 away from 1, and _ 2 is _ 1 away from 1. piece of 1—that is, _ 4 4 3 3 1 is greater than _ 1 , that makes _ 2 farther away from 1. Since _ 3

4

3

Ask partners to complete the problems on the journal page. When most students are finished, discuss their strategies for Problems 9–12, including the following: 1 . That leaves the other three Problem 9: The least fraction is _ 25

to compare. Change each to an equivalent fraction with a denominator of 20. Problem 10: One of these fractions is close to 0, one is close to 1. 1, and the other two are close to _ 2 1 is to see if the Problem 11: One way to compare a fraction to _ 2 1 _ numerator is more or less than 2 of the denominator. Two of 1 . Their order is determined the fractions are greater than _ 2 5 9 1 _ _ _ because 9 is close to 2 and 10 is close to 1. Of the two fractions 1 , the denominators are close to each other, that are less than _

Student Page Date

Time

LESSON

Adding with Fraction Sticks

5 3 䉬

1.

2.

2 halves

8 eighths

4 quarters

16 sixteenths

and one numerator is 2 times the numerator of the other. 1 (the numerator is _ 1 of the Problem 12: One fraction equals _ 2 2 1 , and _ 4 is less than _ 1. denominator). The others are close to _ 2

Use the fraction sticks to find equivalent fractions.

2

a. 1 8

—

d. 1 2

—

b.

16

2

4

4 —

8

6 —

8

12 16

8

3 4

e.

—

16

2 —

2

6

c.

—

4 4

—

8

8 —

8

3 4

1 2 8 8

3 8

2 4

1 4

9 1 6

12 , 16

or

3 4

5 8 1 6 16

14 , 16

or

7 8

a.

3 16

b.

1 c. 16

16

16 —

16

3 4

5

1 2

1 4

b.

1 2

3 8

c.

5 8

1 4

d.

1 4

7

2

WHOLE-CLASS ACTIVITY

Fraction-Stick Chart

3 4 7 8 7 8

8 1 6

2

7

▶ Introducing the

Use the fraction sticks to add fractions with different denominators. a.

9

1 but only by _ 1 of a piece The other two are greater than _ 2 2 3 is _ 4 1 1 , and _ 1 of _ _ each—that is, 7 is 2 of a seventh greater than _ 2 5 2 1 . Because fifths are greater than sevenths, a fifth greater than _ 2 3 is greater than _ 4. _

12 —

Use the fraction sticks to add fractions with the same denominator. Example:

3.

2

1

A whole stick is worth 1.

(Math Journal 1, p. 130; Math Masters, p. 137)

20 16 ,

4

1

116, or 14

Use a transparency of the chart from Math Masters, page 137 to demonstrate how to use the Fraction-Stick Chart.

Math Journal 1, p. 131

304

Unit 5

Fractions, Decimals, and Percents

EM3cuG5TLG1_303-307_U05L03.indd 304

12/4/10 7:59 AM

1. Skip-Counting with Fractions Please refer students to journal page 130. Explain that a fraction stick is a model for the whole, or the ONE, that shows unit fractions for the interval between 0 and 1. Each row of the Fraction-Stick Chart combines 2 fraction sticks to show the interval from 0 to 2, divided into unit fractions for a particular denominator.

NOTE A fraction stick is a narrow rectangle divided into pieces that represents fractions. Sometimes it is helpful to make physical fraction sticks, as in Part 3 of this lesson.

Example: The third row shows two sticks, each divided into 1 . The pieces thirds. There are 6 pieces in this row, each labeled _ 3 can be used to count by thirds.

2. Finding Equivalent Fractions The Fraction-Stick Chart on Math Masters, page 137 can be used to find equivalent fractions. Survey the class for examples of pairs of fractions that name the same part of a whole. Emphasize that these are equivalent fractions and list the examples on the 3 is equivalent to _ 1. board. For example, _ 6 2 2. Example: Find equivalent fractions for _

1 3

1 3

1 3

0 3

1 3

1 3

2 3

1 3

3 3

1 3

4 3

5 3

6 3

The third row of the Fraction-Stick Chart

3

Step 1: The denominator is 3, so use the thirds stick to locate the 2 . Count the pieces from left to right. The right edge of the fraction _ 3 2. second piece is _ 3 2 , that is, along the Step 2: Place one edge of a straightedge at _ 3 1 piece. The straightedge should be right edge of the second _ 3

parallel to the sides of the Fraction-Stick Chart. Now look for other fraction sticks on the chart along the straightedge. On the sixths stick, the straightedge touches the right edge of a piece. Count the sixths-stick pieces from left to right. The 4 . So _ 4 is straightedge is at the end of the fourth piece, which is _ 6 6 2 _ equivalent to 3 .

Ongoing Assessment: Informing Instruction Watch for students who confuse the fraction labels with the actual end of the fraction stick. Remind students that the labels are in the center of a portion, not at its end. Have students draw a light pencil line along the straightedge and use the line instead of the straightedge to identify equivalent portions.

On the ninths stick, the straightedge touches the end of the sixth 6 . So _ 6 =_ 2. piece, which is _ 9 9 3 On the twelfths stick, the straightedge touches the end of the 8 . So _ 8 =_ 6 , and _ 8 2 . The fractions _ 2, _ 4, _ eighth piece, which is _ 12 12 3 3 6 9 12 are equivalent. They name the same distance on the FractionStick Chart.

0

1 4

On the other sticks, the straightedge cuts through some of the 2 cannot be written as an equivalent fraction using the pieces, so _ 3 denominator on those sticks.

1 1 2 1 3

3. Comparing Fractions The Fraction-Stick Chart on Math Masters, page 137 can be used 3 . (See margin.) 4 and _ to compare fractions, for example, compare _ 9 8 Step 1: The denominator of the first fraction is 9, so use the 4 . Count the pieces from left to right. The ninths stick to locate _ 9 4 . Place the straightedge along right edge of the fourth piece is _ 9 this edge.

2 4

1 3

1 4 1 5

eighths ninths

1 4 1 5

1 5

1 1 1 6 6 6 1 1 1 7 7 7 1 1 1 8 8 8 1 1 1 1 9 9 9 9 1 1 1 1 10 10 10 10 1 1 1 1 1 12 12 12 12 12 1 1 1 1 1 1 1 16 16 16 16 16 16 16

1 7 1 8 1 9 1 10 1 12 1 16

Lesson 5 3

EM3cuG5TLG1_303-307_U05L03.indd 305

305

12/4/10 7:59 AM

Student Page Date

3 (the right edge of the third piece on the eighths Step 2: Locate _ 8 3 is to the left of _ 4 , it is less than _ 4 . Conversely, _ 4 is stick). Since _ 8 9 9 9 3 3 _ _ to the right of 8 , so it is greater than 8 . Ask partners to complete journal page 130. Ask volunteers to explain their solutions.

Time

LESSON

Fraction Number Stories

5 3 䉬

Shade the fraction sticks to help you solve these fraction number stories. Write a number model for each story. 1.

2.

3.

5

ᎏ7ᎏ 8 1 ᎏᎏ ⫽ ᎏ7ᎏ 4 8

a.

How much flour did he use in all?

b.

Number model:

ᎏ5ᎏ 8

⫹

cup

1

Sheryl’s puppy weighed 1ᎏ2ᎏ pounds when it was born. After two weeks, 3 the puppy had gained ᎏ8ᎏ pounds. a.

How much did the puppy weigh after two weeks?

b.

Number model:

1ᎏ12ᎏ ⫹

ᎏ3ᎏ 8

⫽ 1ᎏ78ᎏ

1ᎏ78ᎏ

▶ Adding with Fraction Sticks

pounds

5 8

⫹ ᎏᎏ =

1ᎏ38ᎏ

The five fraction sticks at the top of journal page 131 provide a length model for fraction work. Note that the denominators are restricted to 1, 2, 4, 8, and 16. This model will be used to formally introduce the addition of fractions. All these problems can be solved visually. The correct amount of shading for any fraction can be decided by using the appropriate fraction stick at the top of the page.

Answers vary.

Number story:

b.

Make up your own fraction number story. Draw and shade fraction sticks to solve it. Write a number model for your story.

Answers vary. a.

Number story:

b.

Number model:

c.

Solution:

PARTNER ACTIVITY

(Math Journal 1, p. 131)

Shade the fraction sticks to solve the number model. Then write a fraction number story that fits the number model. 3 a. ᎏᎏ 4

4.

1

Chris made pizza dough with ᎏ8ᎏ cup of white flour and ᎏ4ᎏ cup of whole wheat flour.

▶ Solving Fraction Number Stories

Math Journal 1, p. 132

(Math Journal 1, p. 132)

INDEPENDENT ACTIVITY PROBLEM PRO PR P RO R OB BLE BL L LE LEM EM SO S SOLVING OL O LV VIN IIN NG

Students solve the fraction number stories on journal page 132. Circulate and assist. Encourage students to use the benchmarks 1 , and 1 when explaining their solutions and assessing the 0, _ 2 reasonableness of answers. Discuss the answers and write the strategies on the board.

2 Ongoing Learning & Practice ▶ Playing Fraction Top-It

Student Page Date

Math Boxes

53 䉬

1.

(Student Reference Book, p. 316; Math Journal 2, Activity Sheets 5–7)

Time

LESSON

Write a 10-digit numeral that has 9 3 5 7 1 6

in in in in in in

2.

the tens place, the millions place, the billions place, the hundred-millions place, the thousands place, and all other places.

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

4ᎏ14ᎏ 8 2ᎏ12ᎏ

17 a. ᎏᎏ ⫽ 4 24 b. ᎏᎏ 3

5, 7 6 3, 6 6 1, 6 9 6

Write the numeral in words.

Five billion, seven hundred sixty-three million, six hundred sixty-one thousand, six hundred ninety-six

⫽

5 c. ᎏᎏ 2

⫽

9 d. ᎏᎏ 8

⫽

32 e. ᎏᎏ 5

1ᎏ18ᎏ 6ᎏ25ᎏ

⫽

what fraction of the students traveled within their state?

b.

what fraction traveled to Europe?

c.

62 63

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 5-1. The skill in Problem 5 previews Unit 6 content.

Vacation Travel 11 ᎏ ᎏ 32 ᎏ4ᎏ 32

, or

what fraction traveled to Canada or Mexico?

ᎏ8ᎏ 32

, or

within state 11

ᎏ1ᎏ 8

Canada or Mexico 8

stayed home 3

another state 6 Europe 4

ᎏ1ᎏ 4

59 125

4.

Divide.

5.

a.

21冄4 苶9 苶3 苶∑

23 R10

b.

35冄6 苶2 苶3 苶∑

17 R28

INDEPENDENT ACTIVITY

(Math Journal 1, p. 133)

Where 32 students vacationed, ... a.

Students practice comparing fractions by playing Fraction Top-It. Students use the Fraction Cards that were stored in Lesson 5-1.

▶ Math Boxes 5 3

4

3.

PARTNER ACTIVITY

22–24

Find the following landmarks for this set of numbers: 929, 842, 986, 978, 869, 732, 898, 986, 900, 899, 986, 920, 842 a.

Minimum:

b.

Maximum:

c.

Mode:

d.

Range:

e.

Median:

732 986 986 254 900

Writing/Reasoning Have students write a response to the following: Explain how you converted the fractions to mixed numbers in Problem 2. Sample answer: For the whole number part, I found how many groups of the denominator were in the numerator. The fraction part was what was left.

119

Math Journal 1, p. 133

306

Unit 5

Fractions, Decimals, and Percents

EM3cuG5TLG1_303-307_U05L03.indd 306

1/20/11 11:59 AM

Study Link Master

▶ Study Link 5 3

INDEPENDENT ACTIVITY

(Math Masters, p. 131)

Name

Date

STUDY LINK

Time

Fraction-Stick Problems

53 䉬

Shade the fraction sticks to help you find equivalent fractions. 59

Home Connection Students find equivalent fractions, add fractions, and solve fraction number stories using fraction sticks.

3 Differentiation Options

4

1 1. 2

— 8

3 2. 4

— 16

12

1

4

2 8

— 16

—

3.

4

Shade the fraction sticks to help you solve the addition problems. 1 4. 4

1 5. 2

1 6. 2

4 1 4 6 3 8 4 5 1 1 4 4

3 4 2 8 3 4

Shade the fraction sticks to help you solve the fraction number stories. 3

3

Joe was baking a cake. He added cup of white sugar and cup of brown 4 8 sugar. How much sugar did he use in all?

7.

9 , 8

118 cups

or

(unit)

READINESS

▶ Making Fraction Strips

SMALL-GROUP ACTIVITY

On the back of this page, write a number story using fractions. Then write a number model to show how you solved it.

8.

Practice

15–30 Min

To explore comparing and ordering fractions using a length model, have students make fraction strips. Students cut 6 strips of paper, 1 " and then fold and label them to represent halves, each 2" by 8_ 2 thirds, fourths, fifths, sixths, and eighths. (See margin.)

297

3冄苶8 苶9 苶1 苶

9.

74 R3

12冄苶8 苶9 苶1 苶→

11.

→

10.

6冄苶8 苶9 苶1 苶

12.

24冄苶8 苶9 苶1 苶 →

148 R3 37 R3

Math Masters, p. 131

To fold into thirds, fold one end in so the doubled parts and the single part are the same size. To fold into sixths, fold a strip into thirds and then in half. For fifths, fold the two outside edges of the strip in toward the middle but not together. Fold them so the doubled parts and the space between them look like three equal parts. Now fold the doubled parts back the other way at the point where the folded ends first came down.

When folded into thirds, the edge of the folded end divides the rest into halves.

Have students label the fractions on the folds. As they finish, ask students to fold two strips so only the unit fraction shows and then 1 is less than _ 1. make a comparison statement. For example, _ 5 3

When folded into fifths, the two folded ends are equal in size to the space in the middle.

ENRICHMENT

▶ Exploring a Fraction-Stick Chart

PARTNER ACTIVITY 15–30 Min

Teaching Master Name

Date

LESSON

Time

Fraction-Stick Chart

53 䉬

1 4

0

2 4

3 4

124

114

1

1 1 2

(Math Masters, p. 130)

1 2

1 3

1 3

1 4 1 5

To apply students’ understanding of fractions, have them explore the relationships between the numerators and denominators of equivalent fractions. When they finish, have them share one of their discoveries.

1 4 1 5

1 5

1 3

1 4 1 5

1 6 1 7 1 8 1 1 9 9 1 1 10 10 1 1 12 12 1 1 1 16 16 16

1 3

1 4

1 5

1 5

1 4

1 4

1 5

1 5

1 5

1 1 1 1 1 6 6 6 6 6 1 1 1 1 1 1 7 7 7 7 7 7 1 1 1 1 1 1 1 8 8 8 8 8 8 8 1 1 1 1 1 1 1 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 12 1 1 1 1 1 1 1 1 1 1 1 1 1 16 16 16 16 16 16 16 16 16 16 16 16 16

1 6 1 7 1 8 1 1 9 9 1 1 10 10 1 1 12 12 1 1 1 16 16 16

6 8 2 3 4 5 4 , 6 , 8 , 10 , 12 , 16

Using the Fraction-Stick Chart, list all the 1 fractions that are equivalent to . 2

a.

2

1 2

1 3 1 4

1 1 1 1 1 6 6 6 6 6 1 1 1 1 1 1 7 7 7 7 7 7 1 1 1 1 1 1 1 8 8 8 8 8 8 8 1 1 1 1 1 1 1 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 12 1 1 1 1 1 1 1 1 1 1 1 1 1 16 16 16 16 16 16 16 16 16 16 16 16 16

1.

1 2 1 3

1 4 1 5

134

1

What pattern do you notice in the numerators for these fractions?

Numerators increase by 1 until the last one, which increases by 2.

ELL SUPPORT

▶ Building a Math Word Bank

SMALL-GROUP ACTIVITY

b.

What pattern do you notice in the denominators for these fractions?

c.

Denominators increase by 2 until the last one, which increases by 4. Are the patterns complete? No

d.

What fraction is missing that would make the pattern complete?

15–30 Min

(Differentiation Handbook, p. 142) 2.

To provide language support for fractions, have students use the Word Bank Template found on Differentiation Handbook, page 142. They write the term equivalent fraction, draw pictures related to the term, and write other related words. See the Differentiation Handbook for more information.

7 14

1 3

Using the Fraction-Stick Chart, list all the fractions that are equivalent to .

2 6

a.

b.

3

, 9,

4 12

What pattern do you notice in these fractions?

Numerators increase by 1 and denominators increase by 3. 5 6 7 1 Use this pattern to find the next 3 fractions that are equivalent to . 15 , 18 , 21 3

Math Masters, p. 130

Lesson 5 3

EM3cuG5TLG1_303-307_U05L03.indd 307

307

12/4/10 7:59 AM