EACH CHAPTER INCLUDES - Lancaster School District · Chapter 8, Lesson 10 Check My Progress 1 If Students miss Exercises… Then use this Strategic Intervention Activity… Concept

Grade 5

EACH CHAPTER INCLUDES: •Prescriptivetargetedstrategic

interventioncharts. •Studentactivitypages

alignedtotheCommonCoreStateStandards.

•Completelessonplanpageswithlessonobjectives,gettingstartedactivities,teachingsuggestions,andquestionstocheckstudentunderstanding.

Targeted Strategic Intervention

Grade 5, Chapter 9

Based on student performance on Am I Ready?, Check My Progress, and Review, use these charts to select the strategic intervention lessons found in this packet to provide remediation.

Am I Ready?

If Students miss

Exercises…

Then use this Strategic

Intervention Activity… Concept

Where is this concept in My Math?

1-7 9-A: Find the Greatest Common Factor

Simplest form 5.NF.5 Chapter 8, Lesson 3

8-14 9-B: Mixed Numbers Improper fractions Prep for 5.NF.4

Grade 4, Chapter 8, Lesson 10

Check My Progress 1

If Students miss

Exercises…




3-5 9-C: Fraction of a Whole Round fractions Prep for 5.NF.2

Chapter 9, Lesson 1

6-11 9-D: Common Denominators

Add like and unlike fractions

5.NF.1, 5.NF.2

Chapter 9, Lessons 2 and 5

12-14 9-E: Fractions in Simplest Form

Subtract like fractions 5.NF.2 Chapter 9,

Lesson 3

Check My Progress 2

If Students miss

Exercises…




5-7 9-F: Subtract Like Fractions

Subtract unlike fractions

5.NF.1, 5.NF.2

Chapter 9, Lesson 7

8-10 9-G: Estimate the Value

of Fractions Estimate sums and

differences 5.NF.2 Chapter 9, Lesson 9

Review

If Students miss

Exercises…




6-8 9-H: Fractions on a

Number Line Round fractions Prep for 5.NF.2

Chapter 9, Lesson 1

9-17 9-I: Least Common

Denominator Add fractions 5.NF.1,

5.NF.2 Chapter 9,

Lessons 2 and 5

18-23 9-J: Simplest Form and Common Denominators

Estimate and subtract fractions

5.NF.1, 5.NF.2

Chapter 9, Lessons 3 and 7

Program: SI_Chart Component: SEPDF Pass

Vendor: Laserwords Grade: 5

Name

Find the Greatest Common Factor

List the factors.

What are the factors of 12 and 18?

Factors of 12

Factors of 18

1 × 12, 2 × 6, 3 × 4

1 × 18, 2 × 9, 3 × 6

List the factors in order for each number.12 1, 2, 3, 4, 6, 1218 1, 2, 3, 6, 9, 18

Find the common factors.1, 2, 3, 6 are factors of both 12 and 18.

Find the greatest common factor (GCF).6 is the greatest common factor of both 12 and 18.

List factors.

1. List factors of 10.



Find the common factors of each pair of numbers.

4. 10 and 15 5. 15 and 20 6. 10 and 20

Find the greatest common factor for each pair of numbers.

7. 10 and 15 8. 15 and 20 9. 10 and 20

Lesson

9-A

What Can I Do?I want to find the greatest

common factor of two numbers.

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.

276_S_G5_C09_SI_119817.indd 276276_S_G5_C09_SI_119817.indd 276 12/07/12 5:41 PM12/07/12 5:41 PM

Program: SI_Chart Component: TEPDF 2nd


USING LESSON 9-A

WHAT IF THE STUDENT NEEDS HELP TO

Lesson Goal• Find the common factors and

greatest common factor (GCF) of two numbers.

What the Student Needs to Know• Find factors.

• Find the greatest number in a group of numbers.

Getting Started• Have students think of as many

pairs of numbers as they can that have the following products.

9 (1×9, 3×3)

14 (1×14, 2×7)

27 (1×27, 3×9)

What Can I Do?Read the question and the response. Then read and discuss the examples. Ask:

• How were the factors of 12 found? (Find pairs of numbers that have 12 as their product.)

• How can you find the common factors of 12 and 18? (Look for numbers that are listed as factors for both 12 and 18.)

• How can you tell 6 is the greatest common factor? (If 6 is compared to the other common factors 1, 2 and 3, 6 is the largest number.)

Try It• Ask: Can the greatest common

factors of two numbers be one of the two numbers? (Yes, for example: the greatest common factor of 6 and 24 is 6.)

• Have students share their strategy for finding the greatest common factor.

Find Factors• Have the student think of pairs

of numbers that multiply togeth-er to receive a product. Remind him or her that the numbers that are multiplied together are called factors. For example, in the number sentence 6 × 3 = 18, the factors are 6 and 3.

• Provide practice with multiplication facts the student has not yet mastered.

Find the Greatest Number in a Group of Numbers• Tell the student to draw a

number line and then locate each number on the line. Remind the student that the greatest number is the number that is farthest to the right on the number line.

• Review ordering numbers. Have students compare the digits in the greatest place first, then the digits in the next place, and so on.

Name

Find the Greatest Common Factor

List the factors.

What are the factors of 12 and 18?

Factors of 12

Factors of 18

1 × 12, 2 × 6, 3 × 4

1 × 18, 2 × 9, 3 × 6

List the factors in order for each number.12 1, 2, 3, 4, 6, 1218 1, 2, 3, 6, 9, 18

Find the common factors.1, 2, 3, 6 are factors of both 12 and 18.

Find the greatest common factor (GCF).6 is the greatest common factor of both 12 and 18.

List factors.

1. List factors of 10. 1, 2, 5, 10

2. List factors of 15. 1, 3, 5, 15

3. List factors of 20. 1, 2, 4, 5, 10, 20

Find the common factors of each pair of numbers.

4. 10 and 15 1, 5 5. 15 and 20 1, 5 6. 10 and 20 1, 2, 5, 10

Find the greatest common factor for each pair of numbers.

7. 10 and 15 5 8. 15 and 20 5 9. 10 and 20 10

Lesson

9-A

What Can I Do?I want to find the greatest

common factor of two numbers.

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.

276_S_G5_C09_SI_119817.indd 276 12/07/12 5:41 PM

277_T_G5_C09_SI_119817.indd 277277_T_G5_C09_SI_119817.indd 277 7/18/12 9:38 AM7/18/12 9:38 AM



Name

Mixed Numbers

Write a number and a fraction.

A mixed number includes a whole number and a fraction. The whole number shows the number of wholes. The fraction shows the number of remaining parts.

To write the mixed number, write the whole number and the fraction together. Write the whole number first.

This model shows 2 whole rectangles shaded. It also shows 1 __ 4 rectangle shaded.

All together, the model shows the mixed number 2 1 __ 4 .

Complete each sentence. Then write each mixed number.

1. 2.

There are wholes. There is whole.

The fraction is . The fraction is .

The mixed number is . The mixed number is .

Lesson

9-B

What Can I Do?I want to write mixed

numbers.

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.

278_279_S_G5_C09_SI_119817.indd 278278_279_S_G5_C09_SI_119817.indd 278 12/07/12 7:01 PM12/07/12 7:01 PM



Name

3. 4.

There are wholes. There are whole.

The fraction is . The fraction is .

The mixed number is . The mixed number is .

Write each mixed number.

5.

6.

7.

8.

9.

10.

11.

12.

Complete each sentence. Then write each mixed number. Lesson

9-BC

op

yrig

ht

© T

he

McG

raw

-Hil

l C

om

pa

nie

s, I

nc.


Program: SI_Chart Component: TEPDF Pass


USING LESSON 9-B


Lesson Goal• Model and write mixed numbers.

What the Student Needs to Know• Model whole numbers and

fractions.

• Understand that mixed numbers combine a whole number and a fraction.

Getting Started• Review fractions with students.

Draw a square on the board and divide it into four equal parts.

Write 3 __ 4 on the board. Ask: How can

I shade 3 __ 4 of this square? (Shade 3

out of the 4 parts.) Is 3 __ 4 more or less

than 1? (less) Is 3 __ 4 more or less than 0? (more)

• Draw a number line on the board. Label 0, 1, 2, 3, and 4. Ask: Where

do you think 2 1 __ 2 is on this number

line? (Students should indicate halfway between 2 and 3.) Where is

3 1 __ 2 ? (halfway between 3 and 4)

What Can I Do?Read the question and the response. Then read and discuss the example. Ask:

• What is a mixed number? (A mixed number is a number that includes a whole number and a fraction.) Are all mixed numbers greater than 1? (Yes) Why? (Because they all have a whole number, which is 1 or greater, plus a fraction.)

• Have students look at the model of

2 1 __ 4 . How does this model show the

whole number 2? (Two whole rectangles are shaded.) How does the model show the fraction 1 __ 4 ? (One quarter, or one fourth, of the third rectangle is shaded.)

Model Whole Numbers and Fractions• Have the student practice

modeling whole numbers. Write the fraction 4 __ 4 on the board and draw a circle divided into four parts. Ask: How can you shade this circle to show 4 __ 4 ? (Color all four parts.)

Write 4 __ 4 = 1 on the board. Explain that when you shade an entire shape, it can represent one whole number. Add another circle divided into four parts and shade all four parts. Ask: What whole number do these two circles show? (2) Repeat with other whole numbers, such as 5 __ 5 , 3 __ 3 , and 8 __ 8 .

• Review modeling fractions. Write these fractions on the

board: 1 __ 2 , 3 __ 5 , 5 __ 8 , 3 __ 10 and have

the student describe how to show each fraction. Remind the student that the numerator of a fraction tells how many parts are shaded in the whole. The denominator tells how many total parts make up the whole.

Name

Mixed Numbers

Write a number and a fraction.

A mixed number includes a whole number and a fraction. The whole number shows the number of wholes. The fraction shows the number of remaining parts.

To write the mixed number, write the whole number and the fraction together. Write the whole number first.

This model shows 2 whole rectangles shaded. It also shows 1 __ 4 rectangle shaded.

All together, the model shows the mixed number 2 1 __ 4 .

Complete each sentence. Then write each mixed number.

1. 2.

There are 3 wholes. There is 1 whole.

The fraction is 1 __ 2

. The fraction is

2 __ 3

.

The mixed number is 3 1 __

2

. The mixed number is 1 2 __

3

.

Lesson

9-B

What Can I Do?I want to write mixed

numbers.

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.

278_279_S_G5_C09_SI_119817.indd 278 12/07/12 7:01 PM

280_281_T_G5_C09_SI_119817.indd 280280_281_T_G5_C09_SI_119817.indd 280 12/07/12 7:02 PM12/07/12 7:02 PM

Lesson 9-B




Understand that Mixed Numbers Combine a Whole Number and a Fraction• Help the student visualize

mixed numbers by creating concrete models. Cut three identical squares out of construction paper. Ask: How many squares do I have? (3) Fold one square in half and cut along the fold. Discard one half and show the remaining half with the other squares. How many squares do I have now? (2 1 __ 2 ) Have the student name the parts of the mixed number. (the whole number 2 and the fraction 1 __ 2 ) Have the student create paper models to show and write other mixed numbers.

Complete the Power Practice• Encourage the student to use

fraction manipulatives to model the mixed numbers in the exercises.

• Emphasize that different models can show the same mixed number. Have the student draw four circles divided into quarters and four squares divided into quarters. Ask him or her to shade 3 1 __ 4 of the circles. Then have the student shade 3 1 __ 4 of the squares in a different way.

• Review the meaning of mixed numbers by writing these numbers

on the board: 5, 4 1 __ 2 , 6, and 3 5 __ 6 . Have

students identify the mixed

numbers (4 1 __ 2 , 3 5 __ 6 ) and explain why

they are mixed numbers.

Try It• Ask a volunteer to read each

exercise aloud and complete the sentences below the models.

• You may wish to have students use fraction manipulatives to model each mixed number in Exercises 1–4.

Power Practice• Help students answer Exercises

5–12 by following this strategy. First, count the number of wholes shown. Write that number as the first part of the mixed number. Then, look at the shape that is only partly shaded. Write the fraction that names the shaded area. Put the whole number and the fraction together to write the answer.

Name

3. 4.

There are 2 wholes. There are 4 whole.

The fraction is 5 __ 6

. The fraction is

3 __ 4

.

The mixed number is 2 5 __

6

. The mixed number is 4 3 __

4

.

Write each mixed number.

5.

2 1 __ 3

6.

3 1 __ 4

7.

1 1 __ 6

8.

4 7 __ 8

9.

1 3 __ 5

10.

3 1 __ 3

11.

3 3 __ 4

12.

1 5 __ 8

Complete each sentence. Then write each mixed number. Lesson

9-BC

op

yrig

ht

© T

he

McG

raw

-Hil

l C

om

pa

nie

s, I

nc.

278_279_S_G5_C09_SI_119817.indd 279 12/07/12 7:02 PM




Name

Fraction of a Whole

Write a fraction for the shaded part.

1. 2.

3. 4.

5. 6.

To identify the fraction of a whole, first count the number of equal parts in the whole. Then count the number of shaded parts.

numerator = number of shaded partsdenominator number of equal parts

What fraction of the rectangle is shaded?

The rectangle has 8 equal parts. 5 parts are shaded. So, 5 __ 8 of the rectangle is shaded.

_____ 8

_____

6

_____ 9

_____ 5

_____ 7

_____ 12

Lesson

9-C

What Can I Do?I want to find the fraction

of a whole.

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.




Name


7.

8.

9.

10.

11.

12.

13.

Picture This!Each player will need several sheets of graph paper and a pencil or crayon.

• Each player makes a large rectangle or square on the graph paper. The figure should have from 10 to 100 equal-sized squares.

• Each player shades a design inside his or her rectangle or square. Players can make any type of design, including letters or numbers. They must be sure to completely shade the equal-sized squares within their figures. Have them count the number of squares as they shade the figure. Then have them record the fraction of the whole that the figure takes up on a different sheet of paper.

• Players should make several designs, using larger rectangles or squares with different numbers of equal parts.

• Players may then exchange designs and write the number of equal parts each figure represents. The player who correctly identifies the most fractions wins.

Lesson

9-CC

op

yrig

ht

© T

he

McG

raw

-Hil

l C

om

pa

nie

s, I

nc.




USING LESSON 9-C


Lesson Goal• Find the fraction of a whole.

What the Student Needs to Know• Read a fraction from a diagram.

• Recognize the numerator and the denominator of a fraction.

Getting Started• Find out whether students can

draw a diagram to represent a fraction. For example, ask:

• Consider the fraction 1 __ 2 . Can you draw a diagram that shows 1 __ 2 ? (Check students’ diagrams. Some

of the diagrams may show 1 __ 2 of a

whole and some may show 1 __ 2 of a group.)

• Have volunteers copy some of their diagrams on the board. Discuss how the drawings are different and how they are similar. For example, if applicable, have students distinguish between the drawings that show 1 __ 2 of a whole

and the drawings that show 1 __ 2 of a group.

• Then have students focus on one of the drawings that shows 1 __ 2 of a whole. Ask:

• In the fraction 1 __ 2 , what part of the

fraction is the “1”? The “2”? (the numerator; the denominator)


• What if you want to write a fraction for the part of the rectangle that is not shaded? Which part of the fraction would change? Which part would not change? (The numerator would change, but the denominator would not change.)

• What is the fraction for the part of the

rectangle that is not shaded? ( 3 __ 8 )

Read a Fraction from a Diagram• Have the student trace over

and copy the diagram without shading any of the parts of the figure but including all of the lines that show how the figure is divided into equal parts. Tell the student that the number of parts in the diagram represents the denominator of the fraction.

• Then have the student use a crayon to shade the figure so that it corresponds to the original diagram. The number of parts the student shades is the numerator.

Recognize the Numerator and the Denominator of a Fraction• Have the student focus on the

meaning of the denominator by counting the number of equal parts. Suggest that the student record this number first. The numerator is written above the denominator and is the number of parts that are shaded or identified in some other characteristic of interest.

Name

Fraction of a Whole


1. 2.

3. 4.

5. 6.

To identify the fraction of a whole, first count the number of equal parts in the whole. Then count the number of shaded parts.

numerator = number of shaded partsdenominator number of equal parts

What fraction of the rectangle is shaded?

The rectangle has 8 equal parts. 5 parts are shaded. So, 5 __ 8 of the rectangle is shaded.

3

_____ 8

4 _____

6

7

_____ 9

4

_____ 5

5

_____ 7

1

_____ 12

Lesson

9-C

What Can I Do?I want to find the fraction

of a whole.

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.

282_283_S_G5_C09_SI_119817.indd 282 12/07/12 6:06 PM


Lesson 9-C




Complete the Power Practice• Discuss each incorrect answer.

Have the student explain how he or she identified each fraction. The student may not see immediately how many parts are shaded. Point out that the location of shaded parts within the figure does not affect how many are shaded.

• Have students summarize the relationship between the numerator and the denominator of a fraction. Ask:

• Which part of a fraction always tells the total number of equal parts in a whole? (the denominator)

• Which part of the fraction tells the number of equal parts that you are describing or shading with respect to the whole? (the numerator)

Try It• Have students tell whether the

numerator or the denominator is missing in each exercise. Then have students explain how to find the number to complete the fraction.

Power Practice• Have students complete the

practice items. Then review each answer.

• Encourage students to explain how they found the numerator and denominator of each fraction.

Learn with Partners & Parents• Emphasize that each figure must

be made of equal-sized parts to be able to correctly identify a fraction of a whole.

• Encourage students to look for patterns or number the squares to help them count the number of shaded parts or the total number of equal parts.

• You can enrich the activity by having students write the fractions in simplest form.

Name


5 __ 8

1 __ 4

3 ___ 10

7 ___ 12

5 ___ 12

2 __ 5

4 __ 9

7.

8.

9.

10.

11.

12.

13.

Picture This!Each player will need several sheets of graph paper and a pencil or crayon.

• Each player makes a large rectangle or square on the graph paper. The figure should have from 10 to 100 equal-sized squares.

• Each player shades a design inside his or her rectangle or square. Players can make any type of design, including letters or numbers. They must be sure to completely shade the equal-sized squares within their figures. Have them count the number of squares as they shade the figure. Then have them record the fraction of the whole that the figure takes up on a different sheet of paper.

• Players should make several designs, using larger rectangles or squares with different numbers of equal parts.

• Players may then exchange designs and write the number of equal parts each figure represents. The player who correctly identifies the most fractions wins.

Lesson

9-CC

op

yrig

ht

© T

he

McG

raw

-Hil

l C

om

pa

nie

s, I

nc.

282_283_S_G5_C09_SI_119817.indd 283 12/07/12 6:07 PM




Name

Common Denominators

Find the least common denominator.

Find a common denominator for 1 __ 6 and 3 __ 4 .

First, list the multiples of each denominator. Circle the least common multiple.

Multiply by 1 2 3 4 5 6

Multiples of 6 6 12 18 24 30 36

Multiples of 4 4 8 12 16 20 24

The least common multiple of 6 and 4 is 12.

A common denominator for 1 __ 6 and 3 __ 4 is 12.

Find the multiples of each denominator. Then, find the least common denominator for each pair of fractions.

1. 2 __ 3

and 1 __ 2

2. 1 __ 9

and 5 __ 6

Multiples of 3 Multiples of 9

Multiples of 2 Multiples of 6

The least common The least common denominator is . denominator is .

Find the multiples of each denominator.Then circle the number that is a common denominator for the two fractions.

3. 1 __ 6

and 2 __ 3

2 3 4 5 6

4. 3 __ 4

and 1 __ 3

4 6 8 12 14

5. 4 __ 5

and 1 __ 2

4 5 10 15 25

6. 1 __ 2

and 5 __ 8

10 8 6 4 2

Lesson

9-D

What Can I Do?I want to find a

common denominator for two fractions.

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.




USING LESSON 9-D


Lesson Goal• Find the common denominator

for two fractions.

What the Student Needs to Know• Find the common multiples for

two numbers.

Getting StartedAsk students to write equivalent fractions for each fraction.

• 1 __ 6 (example: 2 ___ 12 )

• 3 __ 4 (example: 9 ___ 12 )

• 2 __ 3 (example: 4 __ 6 )

• 1 __ 2 (example: 3 __ 6 )

• 2 __ 9 (example: 4 ___ 18 )

• 1 __ 5 (example: 3 ___ 15 )


• What is another common

denominator for 1 __ 6 and 3 __ 4 ? (24)

• What is the least common

denominator for 1 __ 6 and 3 __ 4 ? (12)

Try It• Tell students that the least

common denominator for a pair of fractions is the least common multiple of the two denominators.

• Have students complete the exercises. Then ask volunteers to explain how they found the leastcommon denominator for Exercises 1–2.


practice. Then review each answer.

• Ask students to share their methods for choosing the common denominator for the two fractions in each exercise.

Find the Common Multiples for Two Numbers• Remind the student that he or

she can use a number line or skip counting to find multiples of each of the two numbers. Tell him or her to write down the multiples as they count.

• The student should recall that they can find multiples by finding the product of a number and each of the digits 1, 2, 3, 4, and so on. It may help the student to list the factors and the products in a table. Then circle all the common multiples.


Have the student circle the denominators. Explain that it is the denominators for which he or she needs to find common multiples.

• Have the student find the multiples for each denominator and circle the least common multiple.

Name

Common Denominators

Find the least common denominator.

Find a common denominator for 1 __ 6 and 3 __ 4 .

First, list the multiples of each denominator. Circle the least common multiple.

Multiply by 1 2 3 4 5 6

Multiples of 6 6 12 18 24 30 36

Multiples of 4 4 8 12 16 20 24

The least common multiple of 6 and 4 is 12.

A common denominator for 1 __ 6 and 3 __ 4 is 12.

Find the multiples of each denominator. Then, find the least common denominator for each pair of fractions.

1. 2 __ 3

and 1 __ 2

2. 1 __ 9

and 5 __ 6

Multiples of 3 3, 6, 9, 12 Multiples of 9 9, 18, 27, 36

Multiples of 2 2, 4, 6, 8 Multiples of 6 6, 12, 18, 24

The least common The least common denominator is 6 . denominator is 18 .

Find the multiples of each denominator.Then circle the number that is a common denominator for the two fractions.

3. 1 __ 6

and 2 __ 3

2 3 4 5 6

4. 3 __ 4

and 1 __ 3

4 6 8 12 14

5. 4 __ 5

and 1 __ 2

4 5 10 15 25

6. 1 __ 2

and 5 __ 8

10 8 6 4 2

Lesson

9-D

What Can I Do?I want to find a

common denominator for two fractions.

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.

286_S_G5_C09_SI_119817.indd 286 12/07/12 6:12 PM

287_T_G5_C09_SI_119817.indd 287287_T_G5_C09_SI_119817.indd 287 12/07/12 6:14 PM12/07/12 6:14 PM

Program: SI_Chart Component: SEPDF 2nd


Name

Fractions in Simplest Form

Use the GCF to write each fraction in simplest form.

You can write a fraction in simplest form by dividing the numerator and denominator by a common factor.

30 ___ 36 Common factors of 30 and 36

are 1, 2, 3, and 6.

30 ÷ 3 ______ 36 ÷ 3 = 10 ___ 12 = 10 ÷ 2 ______ 12 ÷ 2 =

5 __ 6

Not in simplest form. Simplest form.

You can find the simplest form of a fraction in one step by using the greatest common factor (GCF). The GCF of 30 and 36 is 6.

30 ÷ 6 ______ 36 ÷ 6 = 5 __ 6

Write each fraction in simplest form.

1. 18 ___ 27 = 18 ÷ 9 ______ 27 ÷ 9 =

3. 9 ___ 12 = 9 ÷ 3 ______ 12 ÷ 3 =

2. 12 ___ 48 = 12 ÷ 12 _______ 48 ÷ 12 =

4. 6 ___ 10 = 6 ÷ 2 ______ 10 ÷ 2 =

5. 16 ___ 20 = 16 ÷ 4 ______ 20 ÷ 4 =

7. 12 ___ 14 = 12 ÷ 2 ______ 14 ÷ 2 =

9. 20 ___ 35 = 20 ÷ 5 ______ 35 ÷ 5 =

11. 12 ___ 30 = 12 ÷ 6 ______ 30 ÷ 6 =

6. 9 ___ 24 = 9 ÷ 3 ______ 24 ÷ 3 =

8. 10 ___ 15 = 10 ÷ 5 ______ 15 ÷ 5 =

10. 12 ___ 20 = 12 ÷ 4 ______ 20 ÷ 4 =

12. 9 ___ 21 = 9 ÷ 3 ______ 21 ÷ 3 =

Lesson

9-E

What Can I Do?I want to write a fraction

in simplest form.

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.

288_S_G5_C09_SI_119817.indd 288288_S_G5_C09_SI_119817.indd 288 7/18/12 10:11 AM7/18/12 10:11 AM

Program: SI_Chart Component: TEPDF 2nd


USING LESSON 9-E


Lesson Goal• Write a fraction in simplest form.

What the Student Needs to Know• Recognize a fraction in simplest

form.

• List common factors of pairs of numbers.

Getting StartedFind out what students know about factors. Ask:

• What are the factors of 8? (1, 2, 4, 8)

• How do you find the factors of a number? (Possible answer: When you divide a whole number by one of its factors, the quotient will not have a remainder.)


• How can you find the common factors and the GCF of a pair of numbers? (Possible answer: List the factors of both numbers. Then write the factors that are on both lists. The GCF is the greatest number that appears on the lists for both factors.)

• How can you recognize when a fraction is in simplest form? (Possible answer: When the GCF of the numerator and the denominator is 1.)

• Why do you divide the numerator and the denominator by the same number to write the fraction in simplest form? (To find the equivalent fraction.)

Try It• Have students verify that the

divisors in Exercises 1–4 are the GCFs for each fraction. Have them list the factors, the common factors, and the GCF for the numerator and denominator of each fraction.


practice items. Then review each answer.

Recognize a Fraction in Simplest Form• Provide the student with a list

of fractions. Have the student use a checklist showing the numbers 2, 3, 5, and 6 to decide if the numerator and the denominator can be divided by any of those numbers. If there are two checks in a column (one for the numerator and one for the denominator) the fraction is not in simplest form.

List Common Factors of Pairs of Numbers• Have the student list all of the

factors of each number sepa-rately. Then have the student compare the numbers in both lists to find the factors common in both numbers.


Have the student show each step used to simplify the fraction.

Name

Fractions in Simplest Form

Use the GCF to write each fraction in simplest form.

You can write a fraction in simplest form by dividing the numerator and denominator by a common factor.

30 ___ 36 Common factors of 30 and 36

are 1, 2, 3, and 6.

30 ÷ 3 ______ 36 ÷ 3 = 10 ___ 12 = 10 ÷ 2 ______ 12 ÷ 2 =

5 __ 6

Not in simplest form. Simplest form.

You can find the simplest form of a fraction in one step by using the greatest common factor (GCF). The GCF of 30 and 36 is 6.

30 ÷ 6 ______ 36 ÷ 6 = 5 __ 6


1. 18 ___ 27 = 18 ÷ 9 ______ 27 ÷ 9 =

2 __ 3

3. 9 ___ 12 = 9 ÷ 3 ______ 12 ÷ 3 =

3 __ 4

2. 12 ___ 48 = 12 ÷ 12 _______ 48 ÷ 12 =

1 __ 4

4. 6 ___ 10 = 6 ÷ 2 ______ 10 ÷ 2 =

3 __ 5

5. 16 ___ 20 = 16 ÷ 4 ______ 20 ÷ 4 =

4 __ 5

7. 12 ___ 14 = 12 ÷ 2 ______ 14 ÷ 2 =

6 __ 7

9. 20 ___ 35 = 20 ÷ 5 ______ 35 ÷ 5 =

4 __ 7

11. 12 ___ 30 = 12 ÷ 6 ______ 30 ÷ 6 =

2 __ 5

6. 9 ___ 24 = 9 ÷ 3 ______ 24 ÷ 3 =

3 __ 8

8. 10 ___ 15 = 10 ÷ 5 ______ 15 ÷ 5 =

2 __ 3

10. 12 ___ 20 = 12 ÷ 4 ______ 20 ÷ 4 =

3 __ 5

12. 9 ___ 21 = 9 ÷ 3 ______ 21 ÷ 3 =

3 __ 7

Lesson

9-E

What Can I Do?I want to write a fraction

in simplest form.

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.

288_S_G5_C09_SI_119817.indd 288 7/18/12 10:11 AM

289_T_G5_C09_SI_119817.indd 289289_T_G5_C09_SI_119817.indd 289 7/18/12 10:13 AM7/18/12 10:13 AM



Name

1. 3 __ 4

- 1 __ 4 = 2. 5 __ 7

- 2 __ 7

=

3. 4 __ 6

- 2 __ 6

= 4. 9 ___ 10

- 2 ___ 10

=

Circle the simplest form of the correct answer.

5. 6 ___ 11

- 3 ___ 11

= 3 ___ 11

3 6. 9 ___ 12

- 1 ___ 12

= 2 __ 3

8 ___ 12

7. 8 __ 9

- 2 __ 9

= 6 __ 9

2 __ 3

8. 2 __ 3

- 1 __ 3

= 1 1 __ 3

Subtract. Write each difference in simplest form.

9. 6 ___ 10

- 2 ___ 10

= 10. 6 __ 8

- 1 __ 8

=

11. 3 __ 5

- 2 __ 5

= 12. 13 ___ 14

- 2 ___ 14

=

13. 9 ___ 12

- 6 ___ 12

= 14. 80 ____ 100

- 25 ____ 100

=

15. 11 ___ 12

- 6 ___ 12

= 16. 7 __ 9

- 1 __ 9

=

17. 5 __ 6

- 3 __ 6

= 18. 8 ___ 12

- 3 ___ 12

=

Subtract Like FractionsUse drawings to subtract. Write each difference in simplest form.

Lesson

9-FC

op

yrig

ht

© T

he

McG

raw

-Hil

l C

om

pa

nie

s, I

nc.

290_S_G5_C09_SI_119817.indd 290290_S_G5_C09_SI_119817.indd 290 7/17/12 11:20 AM7/17/12 11:20 AM



USING LESSON 9-F


Lesson Goal• Subtract fractions with common

denominators.

What the Student Needs to Know• Subtract like fractions.

Getting Started• Write the following equation on

the board: 5 __ 8 - 3 __ 8

• Do the fractions have common denominators? (Yes) What is the common denominator? (8)

• Is the fraction 5 __ 8 written in simplest form? (Yes)

• Is the fraction 3 __ 8 written in simplest form? (Yes)

• Provide additional examples of identifying common denominators when subtracting fractions.

TeachRead and discuss Exercise 1 at the top of the page.

• How many parts of the square do we

need to shade to show 3 __ 4 ? (3 parts)

• How many parts of the square do we need to cross out to show we are

taking away 1 __ 4 ? (1 part)

• How many shaded parts are not crossed out? (2) What fraction

represents this shaded part? ( 2 __ 4 )

• Let’s check to make sure the fraction is in simplest form.

• What are the factors of 2? (1, 2) What are the factors of 4? (1, 2, 4)

• What is the greatest factor the numbers have in common? (2)

• We need to divide the numerator and denominator by 2 to find the fraction in simplest form. What’s 2 ÷ 2? (1) What’s 4 ÷ 2? (2) What is 2 __ 4

in simplest form? ( 1 __ 2 )

• What is 3 __ 4 - 1 __ 4 ? ( 1 __ 2 )

Practice• Read the directions and have

students complete Exercises 2 through 18. Check their work.

Subtract Like Fractions• For this activity, the student will

use drawings to model subtracting like fractions.

• The students will start by modeling the number sentence 7 __ 8 - 1 __ 8 .

• Have him or her draw a picture of 8 squares.

• How many squares should be shaded to represent 7 __ 8 ? (7)

• How many squares should be crossed out to show we are taking away 1 __ 8 ? (1)

• How many shaded parts are not crossed out? (6)

• What fraction represents the shaded part? ( 6 __ 8 )

• Let’s check to make sure the fraction is in simplest form.

• What are the factors of 6? (1, 2, 3, 6) What are the factors of 8? (1, 2, 4, 8)

• What is the greatest factor the numbers have in common? (2)

• Divide the numerator and denominator by 2 to find the frac-tion in simplest form.

• What’s 6 ÷ 2? (3) What’s 8 ÷ 2? (4) What is 6 __ 8 in simplest form? ( 3 __ 4 )

• Provide additional examples for the student to draw or use manipluatives to practice subtracting fractions with common denominators.

Name

1. 3 __ 4

- 1 __ 4 = 2. 5 __ 7

- 2 __ 7

=

3. 4 __ 6

- 2 __ 6

= 4. 9 ___ 10

- 2 ___ 10

=

Circle the simplest form of the correct answer.

5. 6 ___ 11

- 3 ___ 11

= 3 ___ 11

3 6. 9 ___ 12

- 1 ___ 12

= 2 __ 3

8 ___ 12

7. 8 __ 9

- 2 __ 9

= 6 __ 9

2 __ 3

8. 2 __ 3

- 1 __ 3

= 1 1 __ 3

Subtract. Write each difference in simplest form.

9. 6 ___ 10

- 2 ___ 10

= 10. 6 __ 8

- 1 __ 8

=

11. 3 __ 5

- 2 __ 5

= 12. 13 ___ 14

- 2 ___ 14

=

13. 9 ___ 12

- 6 ___ 12

= 14. 80 ____ 100

- 25 ____ 100

=

15. 11 ___ 12

- 6 ___ 12

= 16. 7 __ 9

- 1 __ 9

=

17. 5 __ 6

- 3 __ 6

= 18. 8 ___ 12

- 3 ___ 12

=

Subtract Like FractionsUse drawings to subtract. Write each difference in simplest form.

1 __ 5

5 ___ 12

5 __ 8

5 ___ 12

2 __ 4

= 1 __ 2

3 __ 7

7 ___ 10

2 __ 6

= 1 __ 3

4 ___ 10

= 2 __ 5

3 ___ 12

= 1 __ 4

11 ___ 14

6 __ 9

= 2 __ 3

55 ____ 100

= 11 ___ 20

2 __ 6

= 1 __ 3

Lesson

9-F

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.

290_S_G5_C09_SI_119817.indd 290 7/17/12 11:20 AM


Name

Estimate the Value of Fractions

Estimate the value of each fraction as 0, 1 __ 2 , or 1. Shade fraction models to help you.

1. 1 __ 8

2. 4 __ 5

3. 3 ___ 20

4. 5 __ 9

5. 4 __ 7

6. 7 ___ 12

Use a number line to estimate the value of each fraction. Label the number line and round to 0, 1 __ 2 , or 1.

7. 1 __ 9

8. 5 __ 6

0 1 0 1

9. 6 ___ 10

10. 2 __ 5

0 1 0 1

11. 1 __ 6

12. 8 __ 9

0 1 0 1



Lesson

9-G

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.




USING LESSON 9-G


Lesson Goal• Round fractions to 0, 1 __ 2 , or 1.

What the Student Needs to Know• Plot points on a number line.

• Round fractions by comparing with models.

Getting Started• Write the fraction 3 __ 7 on the board.

• Ask student volunteers to identify the numerator (3) and denominator (7) in the fraction.

• Draw a rectangular model divided into seven equal sections.

• Why is the model divided into seven equal sections for the

fraction 3 __ 7 ? (The model is divided into 7 sections because the

denominator of 3 __ 7 is 7.)

• If we used the rectangular model, how many sections should we shade to represent the fraction 3 __ 7 ? (Shade 3 sections because the numerator is 3.)

• Continue to model additional fractions as needed.

Teach Read and discuss Exercise 1 at the top of the page.

• How many equal sections is the model divided into? (8)

• How many sections do we need to shade to show 1 __ 8 ? (1 section)

• With one out of eight squares

shaded, is the fraction 1 __ 8 closer to 0,

1 __ 2 , or 1? ( 1 __ 8 is closer to 0)

• How do you know 1 __ 8 is closer to 0 and not 1 __ 2 or 1? (The fractions 1 __ 8

and 2 __ 8 are closer to zero, the

fractions 3 __ 8 and 5 __ 8 are closer to one half, and the fractions 6 __ 8 and 7 __ 8 are

closer to one.)

Practice• Read the directions as students

complete Exercises 2 through 12.

• Check student work.

Plot Points on a Number Line• Make sure the student

understands how to choose the beginning and end points of the number line.

• Help the student determine the number of marks on the number line based on the denominator.

• Remind him or her to label the fractions on the number line and to count from left to right when plotting points.

Round Fractions by Comparing with Models• Tell the student to draw a model of 5 __ 8 as a rectangle that

is divided into eighths and shade 5 parts.

• Then ask him or her to make another model to represent 1 __ 2 . This rectangle should be the same size as the first rectangle, but divided into two.

• After the student shades 1 part, have him or her label the left end of the model 0 and the right end of the model 1. Ask the student to compare the models. ( 5 __ 8 is closer to 1 __ 2 )

• Have the student compare other fractions to the 1 __ 2 model.

Name

Estimate the Value of Fractions

Estimate the value of each fraction as 0, 1 __ 2 , or 1. Shade fraction models to help you.

1. 1 __ 8

0 2. 4 __ 5

1

3. 3 ___ 20

0 4. 5 __ 9

1 __ 2

5. 4 __ 7

1 __ 2

6. 7 ___ 12

1 __ 2

Use a number line to estimate the value of each fraction. Label the number line and round to 0, 1 __ 2 , or 1.

7. 1 __ 9

0 8. 5 __ 6

1

0 1 0 1

9. 6 ___ 10

1 __ 2

10. 2 __ 5

1 __ 2

0 112

0 1

11. 1 __ 6

0 12. 8 __ 9

1

0 1 0 1

Lesson

9-G

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.

292_S_G5_C09_SI_119817.indd 292 12/07/12 6:29 PM


Name

Fractions on a Number Line

Write each numerator on the number line. Start at zero and draw hops to reach the fraction. Circle the fraction.

1. 1 __ 5

2. 3 __ 4

0 or 15 5 5 5 5

0or 14 4 4 4

3. 4 __ 7

0

7 7 7or 1

7 7 7 7

4. 4 __ 6

0

6 6 6 6 6 6or 1

5. 2 __ 8

0

8 8 8 8 8 8 8or 1

8



Lesson

9-H

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.




USING LESSON 9-H


Lesson Goal• Identify fractions on a number line.

What the Student Needs to Know• Understand fractions.

• Count fractions on a number line.

Getting Started• Show students a ruler or yardstick.

Tell them it can be used as anumber line.

• Have students view the whole numbers on the ruler/yardstick and how the distance from one end of the ruler to the other is divided into equal parts.

Teach Read and discuss Exercise 1 at the top of the page.

• On the board, draw a number line with six tick marks starting at 0 and

spaced equally from 1 __ 5 to 5 __ 5 . Write a zero (0) at the first tick mark.

• Point to the remaining tick marks and explain to students that every tick mark represents a fraction.

• Remind students that a fraction is part of a whole. After zero, label

the first fraction tick mark 1 __ 5 . Tell students that this tick mark is the

first part of the whole.

• Point to the second fraction tick mark. Say: “This is the second part of the whole. Label it 2 __ 5 .” Helpstudents label the remainingfraction tick marks.

• What fraction of the rectangularmodel is shaded? ( 1 __ 5 )

• Start at zero and hop until you reach 1 __ 5 . How many hops did you make? (1) What fraction should we

circle? ( 1 __ 5 )Practice• Read the directions as students


• Check student work.

Understand Fractions• Make sure the student

understands that the numerator refers to the total amount of parts being used and the denominator refers to the total number of parts.

• Have students work in small groups to take a walk around the school grounds.

• Tell students to identify three representations of fractions.(Ex: types of trees, flowers or bushes, stones or pebbles, leaves, and colors of birds.)

• Instruct each group to write their examples down. For instance, they might write, “three of the five flowers are red.”

• Have each group present their fraction observations to the class. Students should describe the part of the whole or set.

Count Fractions on a Number Line• Display a number line from

0 to 20 and count each number.

• Remind the student to count one number at a time.

• Display a number line divided into fifths.

• Emphasize the similarity between counting whole numbers and fractions: 1, 2, 3

and 1 __ 5 , 2 __ 5 , 3 __ 5 .

Name

Fractions on a Number Line

Write each numerator on the number line. Start at zero and draw hops to reach the fraction. Circle the fraction.

1. 1 __ 5

2. 3 __ 4

0 or 115

25

35

45

55

0or 11

424

34

44

3. 4 __ 7

0 1

727

77

or 137

47

57

67

4. 4 __ 6

0 1

626

36

46

56

66

or 1

5. 2 __ 8

0 1

828

38

48

58

68

78

or 188

Lesson

9-H

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.

294_S_G5_C09_SI_119817.indd 294 12/07/12 6:31 PM




Name

Least Common Denominator

Find the least common multiple (LCM) ofthe denominators in the fractions 2 __

3 and 1 __

5 .

The denominators are 3 and 5.

Make a list of the multiples of each denominator.

2 __ 3

3 6 9 12 15 18 21 24

1 __ 5

5 10 15 20 25 30 35 40

× 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8

Circle the least common multiple that appears on both lists.

Use the LCM ‘15’ as the least common denominator.

So, 2 __ 3

= 10 ___ 15

and

1 __ 5

= 3 ___ 15

.

Use the least common multiple to find the least common denominator (LCD) for each pair or group of fractions.

1. 1 __ 3

: 3, 6, 2. 3 __

5 : 5, 10,

1 __ 2

: 2, 4, 1 __

4 : 4, 8,

LCD: LCD:

3. 3 __ 8

: 4. 5 __

6 :

3 __ 4

: 1 __

3 :

LCD: LCD:

Lesson

9-I

What Can I Do?I want to find the least common denominator of

two fractions.

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.




Name

5. 3 __ 4

and 5 ___ 12

6. 1 __ 2

and 3 __ 4

7. 1 __ 2

and 3 __ 7

8. 1 __ 2

and 4 __ 5

9. 5 ___ 16

and 3 __ 8

10. 1 ___ 10

and 3 __ 4

11. 9 ___ 10

and 2 __ 5

12. 5 __ 9

and 3 __ 4

13. 1 __ 3

and 6 __ 7

14. 3 __ 8

and 7 ___ 12

15. 1 __ 5

and 5 __ 8

16. 2 __ 3

and 1 __ 6

17. 3 ___ 16

and 5 __ 6

18. 8 ___ 15

and 2 __ 3

19. 2 __ 5

and 3 __ 7

20. 7 ___ 15

and 2 __ 5

Use a separate paper to make a list of the multiples of each

denominator. Find the least common denominator (LCD) for each pair of fractions.

Lesson

9-IC

op

yrig

ht

© T

he

McG

raw

-Hil

l C

om

pa

nie

s, I

nc.




USING LESSON 9-I


Lesson Goal• Find the least common

denominator for a pair of fractions.

What the Student Needs to Know• Identify the denominator of

a fraction.

• Find the least common multiple for a pair of numbers.

Getting StartedAsk students how to find the least common multiple for a pair of numbers. For example, ask:

• How would you find the least common multiple (LCM) for 3 and 5? (List the multiples of 3 and the multiples of 5. Find the multiples that are common to both 3 and 5. Find the least commonmultiple.)

• What is the LCM of 3 and 5? (15)


• What are the denominators of the

fractions 2 __ 3

and 1 __ 5

? (3 and 5)

• What are the first 8 multiples of 3? (3, 6, 9, 12, 15, 18, 21, 24)

• What are the first 8 multiples of 5? (5, 10, 15, 20, 25, 30, 35, 40)

• What multiple is common to both 3 and 5? (15)

• Is 15 the least common multiple of 3 and 5? (Yes.)

Identify the Denominator of a Fraction• Have the student give an

example of a fraction and describe the meaning of the numerator and the denominator. The student should understand that the denominator tells the total number of equal parts and the numerator tells the number of parts in the group that are specified in some way.

• Have the student identify the denominator of each fraction in the Power Practice.

Find the Least Common Multiple for a Pair of Numbers• Have the student complete a

table of multiplication facts.

• Have the student list the first 8 multiples of the numbers from 2 through 10, and for 12, 15, and 16. Remind the student that he or she can use repeated addition to find the multiples of larger numbers.

Name

Least Common Denominator

Find the least common multiple (LCM) ofthe denominators in the fractions 2 __

3 and 1 __

5 .

The denominators are 3 and 5.

Make a list of the multiples of each denominator.

2 __ 3

3 6 9 12 15 18 21 24

1 __ 5

5 10 15 20 25 30 35 40

× 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8

Circle the least common multiple that appears on both lists.

Use the LCM ‘15’ as the least common denominator.

So, 2 __ 3

= 10 ___ 15

and

1 __ 5

= 3 ___ 15

.

Use the least common multiple to find the least common denominator (LCD) for each pair or group of fractions.

1. 1 __ 3

: 3, 6, 9, 12, 15, 18, 21, 24 2. 3 __

5 : 5, 10, 15, 20, 25, 30, 35, 40

1 __ 2

: 2, 4, 6, 8, 10, 12, 14, 16 1 __

4 : 4, 8, 12, 16, 20, 24, 28, 32

LCD: 6 LCD: 20

3. 3 __ 8

: 8, 16, 24, 32, 40, 48, 56, 64 4. 5 __

6 : 6, 12, 18, 24, 30, 36, 42, 48

3 __ 4

: 4, 8, 12, 16, 20, 24, 28, 32 1 __

3 : 3, 6, 9, 12, 15, 18, 21, 24

LCD: 8 LCD: 6

Lesson

9-I

What Can I Do?I want to find the least common denominator of

two fractions.

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.

296_297_S_G5_C09_SI_119817.indd 296 12/07/12 6:38 PM


Lesson 9-I




Complete the Power Practice• Discuss each incorrect

answer. Have the student list the multiples of each denominator. Have the student circle the common multiples that appear in each list. Have the student identify the least common denominator.

Try It• For Exercises 1 through 4, have

students finish listing the first 8 multiples of each denominator. Then have students circle the common multiples and identify the least common multiple. The least common multiple will be the denominator for each pair.


practice items. Then review each answer. Be sure that students have found the least common denominator.

Name

5. 3 __ 4

and 5 ___ 12

12 6. 1 __ 2

and 3 __ 4

4

7. 1 __ 2

and 3 __ 7

14 8. 1 __ 2

and 4 __ 5

10

9. 5 ___ 16

and 3 __ 8

16 10. 1 ___ 10

and 3 __ 4

20

11. 9 ___ 10

and 2 __ 5

10 12. 5 __ 9

and 3 __ 4

36

13. 1 __ 3

and 6 __ 7

21 14. 3 __ 8

and 7 ___ 12

24

15. 1 __ 5

and 5 __ 8

40 16. 2 __ 3

and 1 __ 6

6

17. 3 ___ 16

and 5 __ 6

48 18. 8 ___ 15

and 2 __ 3

15

19. 2 __ 5

and 3 __ 7

35 20. 7 ___ 15

and 2 __ 5

15

Use a separate paper to make a list of the multiples of each

denominator. Find the least common denominator (LCD) for each pair of fractions.

Lesson

9-IC

op

yrig

ht

© T

he

McG

raw

-Hil

l C

om

pa

nie

s, I

nc.

296_297_S_G5_C09_SI_119817.indd 297 12/07/12 6:38 PM


Name

Definition Review

A fraction is in simplest form when the numerator and denominator have no common factor greater than 1.

Fractions that have the same bottom number have common denominators.


1. 4 __ 8

= 4 ÷ 4 _____ 8 ÷ 4

= 2. 3 __ 6

= 3 ÷ 3 _____ 6 ÷ 3

=

3. 2 ___ 16

= 2 ÷ 2 _______ 16 ÷ 2

= 4. 4 ___ 10

= 4 ÷ 2 _______ 10 ÷ 2

=

5. 6 __ 9

= 6 ÷ 3 _____ 9 ÷ 3

= 6. 4 ___ 12

= 4 ÷ 4 _______ 12 ÷ 4

=

7. 9 ___ 12

= 9 ÷ 3 _______

12 ÷ 3 = 8. 6 ___

10 = 6 ÷ 2 _______

10 ÷ 2 =

Write yes or no to tell if each pair of fractions have common denominators.

9. 2 __ 5

and 5 ___ 10

10. 1 __ 6

and 2 ___ 12

11. 3 __ 8

and 5 __ 8

12. 1 __ 9

and 5 __ 9

13. 4 ____ 100

and 4 ___ 10

14. 4 __ 8

and 2 __ 8

15. 1 ___ 10

and 2 ___ 10

16. 1 __ 8

and 1 ___ 10

17. 1 ___ 12

and 2 ___ 12

18. 1 __ 3

and 2 __ 3

Simplest Form and Common Denominators



Lesson

9-J

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.




USING LESSON 9-J


Lesson Goal• Write fractions in simplest form.

• Identify common denominators.

What the Student Needs to Know• Understand the steps to write

fractions in simplest form.

Getting Started• Let’s show our work to write 24 _

40 in

simplest form.

• First, let’s list all the factors of 24 on the board. (1 × 24, 2 × 12, 3 × 8, and 4 × 6) Put the factors in order from least to greatest. (1, 2, 3, 4, 6, 8, 12, 24)

• Now, let’s list all the factors of 40 on the board. (1 × 40, 2 × 20, 4 × 10, and 5 × 8) Put the factors in order from least to greatest. (1, 2, 4, 5, 8, 10, 20, 40)

• What numbers do 24 and 40 have in common? (Circle the numbers 1, 2, 4, 8)

• Out of those numbers 1, 2, 4, and 8, what number is the greatest common factor? (8)

• Divide the numerator and

denominator of 24 _ 40

by 8.

• The fraction 24 _ 40

in simplest

form is 3 _ 5

.

TeachRead and discuss Exercise 1 at the top of the page.

• Since 4 is the greatest common factor, it will evenly divide into the numerator and denominator.

• Divide the numerator by 4. What is 4 ÷ 4? (1) Divide the denominator by 4. What is 8 ÷ 4? (2)

• What is 4 _ 8

in simplest form? ( 1 _ 2

)Practice• Read the directions as students


Understand the Steps to Write Fractions in Simplest Form• Work with the student to create

a poster to summarize the steps for simplifying fractions.

• Make sure the student includes the following points:

Simplify a Fraction with the Greatest Common Factor

1. Write the factors of the numerator.

2. Write the factors of the denominator.

3. Find the common factors of the numerator and denominator.

4. From that list, find the greatest common factor (GCF).

5. Divide the numerator and denominator by the GCF.

Name

Definition Review

A fraction is in simplest form when the numerator and denominator have no common factor greater than 1.

Fractions that have the same bottom number have common denominators.


1. 4 __ 8

= 4 ÷ 4 _____ 8 ÷ 4

= 1 __ 2

2. 3 __

6 = 3 ÷ 3 _____

6 ÷ 3 =

1 __ 2

3. 2 ___ 16

= 2 ÷ 2 _______ 16 ÷ 2

= 1 __ 8

4. 4 ___

10 = 4 ÷ 2 _______

10 ÷ 2 =

2 __ 5

5. 6 __ 9

= 6 ÷ 3 _____ 9 ÷ 3

= 2 __ 3

6. 4 ___

12 = 4 ÷ 4 _______

12 ÷ 4 =

1 __ 3

7. 9 ___ 12

= 9 ÷ 3 _______

12 ÷ 3 =

3 __ 4

8. 6 ___

10 = 6 ÷ 2 _______

10 ÷ 2 =

3 __ 5

Write yes or no to tell if each pair of fractions have common denominators.

9. 2 __ 5

and 5 ___ 10

no 10. 1 __ 6

and 2 ___ 12

no

11. 3 __ 8

and 5 __ 8

yes 12. 1 __ 9

and 5 __ 9

yes

13. 4 ____ 100

and 4 ___ 10

no 14. 4 __ 8

and 2 __ 8

yes

15. 1 ___ 10

and 2 ___ 10

yes 16. 1 __ 8

and 1 ___ 10

no

17. 1 ___ 12

and 2 ___ 12

yes 18. 1 __ 3

and 2 __ 3

yes

Simplest Form and Common Denominators

Lesson

9-J

Co

pyr

igh

t ©

Th

e M

cGra

w-H

ill

Co

mp

an

ies,

In

c.

300_S_G5_C09_SI_119817.indd 300 12/07/12 6:50 PM


Documents

EACH CHAPTER INCLUDES - Lancaster School District · Chapter 8, Lesson 10 Check My Progress 1 If Students miss Exercises… Then use this Strategic Intervention Activity… Concept