lesson 10 multiplying fractions by a fraction equal to 1 · steps for making equivalent fractions...

Unit 1 • Lesson 10 81

Unit1•Lesson10 27

Name Date

Uni

t 1

SkillsMaintenanceMultiplicationFacts

Activity1

Solvethemultiplicationfacts.

1. 2 · 8 16

2. 3 · 9 27

3. 4 · 3 12

4. 4 · 7 28

5. 5 · 6 30

6. 9 · 8 72

7. 6 · 8 48

8. 4 · 9 36

9. 8 · 8 64

Lesson10 SkillsMaintenance

Skills MaintenanceMultiplication Facts(Interactive Text, page 27)

Activity 1

Students solve basic multiplication facts. This prepares them for the multiplication they do in the Building Number Concepts section.

Skills MaintenanceMultiplication Facts

Building Number Concepts: Multiplying Fractions by a Fraction Equal to 1

In this lesson, we move away from fraction bars for finding common denominators and look at the traditional way of multiplying the numerator and denominator by the same number. Students learn that when we multiply the numerator and the denominator by the same number, it is like multiplying by 1. Also when the numerator and the denominator of a fraction are the same, the fraction is equal to

1 (e.g., 22 = 1, 33 = 1, 44 = 1).

ObjectiveStudents will find common denominators by multiplying fractions by a fraction equal to 1.

Monitoring Progress: Quiz 2

Distribute the quiz, and remind students that the questions involve material covered over the previous lessons in the unit.

HomeworkStudents fill in the missing parts of fractions that equal 1. Next students write the fraction equal to 1 that they need to multiply by in order to get the equivalent fraction. Then students write the equivalent fraction. In Distributed Practice, students continue practicing whole-number operations to help them gain proficiency.

Lesson Planner

Multiplying Fractions by a Fraction Equal to 1Monitoring Progress: Quiz 2

Lesson 10

82 Unit 1 • Lesson 10

Lesson 10


How do we make an equivalent fraction by multiplying by 1?

Any fraction with the same numerator and denominator is equal to one. The fractions below are all equal to 1.

33 = 1 65

65 = 144 = 119

19 = 1

Let’s see how we change the fraction 35 into tenths. The key idea is to

multiply by a fraction equal to 1.

Steps for Making Equivalent Fractions

STEP 1We start with the denominator. We need to find the number that we multiply by 5 to get 10. We know that 5 · 2 = 10.

STEP 2Now we make the fraction in the middle equal to 1. If the denominator is 2, then the numerator must also be 2. Now we have a fraction equal to 1.

STEP 3We make the new fraction by multiplying the numerators and denominators.

35 · = 10

35 · 22 = 10

35 · 22 = 6

10

Multiplying Fractions by a Fraction Equal to 1

Multiplying Fractions by a Fraction Equal to 1Monitoring Progress: Quiz 2

Lesson 10

To find an equivalent fraction, we multiply by a fraction equal to 1.

STEP 2• Make the fraction equal to 1 by finding a

fraction with the same numerator and denominator. Show a 2 in the numerator: 22 .

STEP 3• Multiply the numerators: 3 · 2 = 6, so 35 · 22 =

61 0 . The fraction 6

10 is the equivalent to 35.

DiscussCall students’ attention to the Power Concept, and explain that it will be helpful when completing the activities.

Building Number Concepts: Multiplying Fractions by a Fraction Equal to 1

How do we make an equivalent fraction by multiplying by 1?(Student Text, pages 48–49)

DemonstrateEngagement Strategy: Teacher ModelingDemonstrate how to find equivalent fractions in one of the following ways:

: Use the mBook Teacher Edition for Student Text, page 48.

Overhead Projector: Copy the circles, and modify as discussed.

Board: Draw the circles, and modify as discussed.

• Remind students that we can use shapes to look at fractions. Display a circle. Divide

the circle into thirds and shade 33 .

• Help students notice that there are three shaded parts and three total parts. When the numerator and the denominator are the same number, the fraction is equal to 1.

• Walk through the other examples: 1919, 44,

6565. Show each circle, shade the parts, and

point out each numerator and denominator to show that the fraction is equal to 1.

• Tell students we want to change 35 to tenths.

STEP 1• Find the number we multiply 5 by to get 10:

5 × 2 = 10. Show 2 in the denominator.

To find an equivalent fraction, we multiply by a fraction equal to 1.

48



Lesson 10

We get the same answer when we use fraction bars. Let’s use this method.

Fifths

Tenths

35 = 6

10

Fraction bars are difficult to use for larger numbers because it is hard to see the fair shares. When we multiply by a fraction equal to 1, we can find an equivalent fraction more easily.

Example 1

Make equivalent fractions using fractions equal to 1.

710 · 33 = 21

30 14 · 33 = 3

12 722 · 44 = 28

88 38 · 22 = 6

16

710 = 21

30 14 = 3

12 722 = 28

88 38 = 6

16

Reinforce UnderstandingUse the mBook Study Guide to review lesson concepts.

Monitoring ProgressQuiz 2

Apply SkillsTurn to Interactive Text, page 28.

Demonstrate• Next have students look at the top of page

49 of the Student Text where we use

fraction bars to show that 35 and 61 0 are

equivalent fractions. Help students notice

that the bars line up at 35 and 610. This

means they are equivalent fractions.

• Make sure students see that we get the same result. Explain to students that it is important to move toward this method because denominators can get very large. Imagine drawing a fraction with a denominator of 100, or imagine folding a paper 100 times.

• Tell students that we need a more efficient method. We need to get faster at finding equivalent fractions and move away from using fraction bars and folding paper.

• Now turn students’ attention to the fractions in Example 1 . Walk through each of the fractions, pointing out each part of the process as we multiply by a fraction equal to 1.

• If necessary, show students a visual representation of the equivalent fractions. This can be a fraction bar, a circle, or another visual representation. Invite student volunteers to explain the steps they took to find the equivalent fraction.

Check for UnderstandingEngagement Strategy: Look About

Ask students to use the strategy of multiplying a fraction by a fraction equal to 1 to find the

equivalent fraction of 34 in twelfths. Tell students

to write their solution in large writing on a piece of paper or a dry erase board. Have students hold up their solutions and encourage students to look about if they need help.

Ask:

Which number do you multiply 4 by to get 12? (3)

What number do we multiply the numerator by to get the numerator of the equivalent fraction? (3)

What is the fraction equal to 1 in this case? Q33RWhat is the equivalent fraction? Q 9

12 R

49


Lesson 10

28 Unit1•Lesson10

Name Date

ApplySkillsMultiplyingFractionsbyaFractionEqualto1

Activity1

Fillinthemissingnumberstomakeequivalentfractions.

1. 710 · 33 = 21

30 2. 48 · 22 = 8

16 3. 59 · 33 = 15

27

4. 24 · 22 = 48 5. 7

10 · 44 = 2840 6. 2

5 · 22 = 410

Activity2

Usefractionbarstoshowequivalentfractions.Dividethefractionbarandshadeit.

1. 25 = 10

25

10

2. 13 = 9

13

9

3. 34 = 12

34

12

4. 34 = 8

34

8

4

4

3

3

9

9

6

6

Lesson10 ApplySkills

Apply Skills(Interactive Text, page 28)

Have students turn to Interactive Text, page 28, to practice these concepts.

Activity 1

Students fill in the missing fraction equal to 1 and determine the numerator for the equivalent fraction.

Activity 2

Students show equivalent fractions using fraction bars.

Monitor students’ work as they complete these activities.

Watch for:

• Can students identify the fraction equal to 1 needed to get the equivalent fraction?

• Can students divide the second fraction bar in the correct number of parts?

• Can students identify the area of the second fraction bar that needs to be shaded?

• Can students identify the equivalent fraction from the shaded fraction bar?

Reinforce Understanding Remind students that they can review lesson concepts by accessing the online mBook Study Guide.


Monitoring Progress: Quiz 2

Assess Quiz 2

• Administer Quiz 2 Form A in the Assessment Book, pages 11–13. (If necessary, retest students with Quiz 2 Form B from the mBook Teacher Edition following differentiation.)

StudentsAssess Differentiate

Day 1 Day 2

All Quiz 2 Form A

Scored80% or above

Extension

Scored Below 80%

Reinforcement

Differentiate• Review Quiz 2 Form A with class.

• Identify students for Extension or Reinforcement.

Extension For those students who score 80 percent or better, provide the On Track! Activities from Unit 1, Lessons 6–10, from the mBook Teacher Edition.

Reinforcement For those students who score below 80 percent, provide additional support in one of the following ways:

■ Have students access the online tutorial provided in the mBook Study Guide.

■ Have students complete the Interactive Reinforcement Exercises for Unit 1, Lessons 5–9, in the mBook Study Guide.

■ Provide teacher-directed reteaching of unit concepts.

Name Date

Uni

t 1

Unit1•Quiz2•FormA 11

Monitoring ProgressFractions

Part 1

Tell if the fractions are (a) greater than 1, (b) less than 1, or (c) equal to 1.

1. 58 b 2. 12

10 a 3. 105 a

4. 45 b 5. 13

13 c 6. 78 b

Part 2

Estimate the fractional parts using benchmarks. Circle the correct answer below the bar.

1.

14 1

2 23 3

4 114 11

2

2.

14 1

2 23 3

4 114 11

2

3.

14 1

2 23 3

4 114 11

2

Part 3

Write the fraction shown by the shapes.

1.

Write the fraction here. 54

2.


3.


4.


Unit 1 Quiz2•FormA

12 Unit1•Quiz2•FormA

Part 4

Make equivalent fractions by shading the fraction bars.

1. Make fraction bars equal to 12.





Form A


Lesson 10

©2010 Sopris West Educational Services. All rights reserved.

Final Pages

Unit1•Quiz2•FormB 1

Name Date

MonitoringProgressFractions

Part1

Tellifthefractionsare(a)greaterthan1,(b)lessthan1,or(c)equalto1.

1. 54 a 2. 8

10 b 3. 1515 c

4. 35 b 5. 14

13 a 6. 18 b

Part2

Estimatethefractionalpartsusingbenchmarks.Circlethecorrectanswerbelowthebar.

1.

14 1

3 12 2

3 34 11

4 112

2.

14 1

3 12 3

4 1 114 11

2

3.

14 1

3 12 3

4 1 114 11

2

Part3

Writethefractionshownbytheshapes.

1.


2.


3.


4.


Unit 1 Quiz2•FormB

Name Date

Uni

t 1

Unit1•Quiz2•FormA 13

Monitoring ProgressWorking With Data

Part 5

Sarah and her brother are doing a science experiment in the kitchen. They are trying to see how long it takes before cold liquid boils. They put a thermometer into the pot of water, and they write down the temperature every minute. Use the data in the table to make a line graph. Be sure to label your graph.

Temperature1 minute 50 degrees

2 minutes 80 degrees




Time in Minutes

Deg

rees

0

100

150

200

250

1 2 3 4 5

50

Length of Time Before Cold Liquid Boils



Final Pages


Name Date

Part4

Makeequivalentfractionsbyshadingthefractionbars.






Form B


Final Pages


Name Date

MonitoringProgressWorkingWithData

Part5

Sarahandherbrotheraredoingascienceexperimentinthekitchen.Theyaretryingtoseehowlongittakesbeforecoldliquidboils.Theyputathermometerintothepotofwater,andtheywritedownthetemperatureeveryminute.Usethedatainthetabletomakealinegraph.Besuretolabelyourgraph.

Temperature1 minute 70 degrees





TimeinMinutes

Deg

rees

0

100

150

200

250

1 2 3 4 5

50

LengthofTimeBeforeColdLiquidBoils




Lesson 10

Activity 1

Fill in the missing number to show that fractions with the same numerator and denominator are equal to 1.

1. 3? = 1 3 2. 4

4 = ? 1

3. ?5 = 1 5 4. 10

? = 1 10

5. 100100 = ? 1 6. ?

20 = 1 20

Activity 2

Write the fraction equal to 1 that you need to multiply by in each problem. Then tell the equivalent fraction.

1. 23 · ?

? = ?6 22 and 46

2. 14 · ?

? = ?12

33 and 3

123. 4

9 · ?? = ?

18 22 and 818

4. 16 · ?

? = ?24 44 and 4

245. 1

2 · ?? = ?

4 22 and 246. 3

4 · ?? = ?

8 22 and 687. 3

5 · ?? = ?

15 33 and 915

8. 24 · ?

? = ?16 44 and 8

16

Activity 3 • Distributed Practice

Solve.

1. 3,001 2,147

854

2. 5,889+ 9796,868

3. 37 42

1,554

4. 500 4

2,000

5. 8q349 43 R5

Model 35 · ?? = ?

10

Answer: 22 and 610

Homework

Homework

Go over the instructions on page 50 of the Student Text for each part of the homework.

Activity 1

Students fill in the missing parts of fractions that equal 1. Remind students that a fraction with the same numerator and denominator is a fraction equal to 1.

Activity 2

Students are to write the fraction equal to 1 that they need to multiply by to get the equivalent fraction.

Activity 3 • Distributed Practice

Students continue practicing whole- number operations.

50

lesson 10 multiplying fractions by a fraction equal to 1 · steps for making equivalent fractions...

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