For the student For the teacher

Teacher Edition

Math on the Spot Video Tutor Online Assessment

System

Soar to Success Math Online Intervention

iTools Virtual Manipulatives

Digital ManagementCenter organizes program resources by TEKS!

Interactive Student Edition provides students

with an interactive learning environment!

Resources

e

Texas Essential Knowledge and Skills

Number and Operations—3.3.A Represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines.

MATHEMATICAL PROCESSES3.1.D Communicate mathematical ideas and reasoning3.1.F Analyze mathematical relationships

Are You Ready?Access Prior KnowledgeUse the Are You Ready? 2.3 in the Assessment Guide to assess students’ understanding of the prerequisite skills for this lesson.

Vocabularynumerator, denominator

Go to Multimedia eGlossary at thinkcentral.com

2.3 Fractions of a Whole How does a fraction name part of a whole? Essential Question?

Lesson OpenerMaking ConnectionsInvite students to talk about fractions. Ask students the following questions.

What does the word whole mean? (all of the parts of one shape or group) What do we call parts that have exactly the same size? (equal parts) What is a fraction? (a number that names part of a whole or part of a group) What is a unit fraction? (a fraction that names one equal part of a whole)

Using the Digital LessonAsk students to explain how they could use fraction strips to solve the problem.

Learning TaskDirect students’ attention to the stop sign and its number of equal parts.

• How many equal parts has the stop sign been divided into? (8)

• What unit fraction describes one part of the stop sign? ( 1 _ 8 )

• How many parts of the sign are shaded? (6)

• How many parts of the sign are not shaded? (2)

Literacy and MathematicsYou may choose one or both of the following activities.

• Have students write a story about going on a road trip and seeing a traffic sign. Have them describe one way the shape of the sign can be divided into equal parts.

• Have students draw a circle to represent a traffic sign. Have them divide the circle into four equal parts. Then ask them to write the unit fraction that each part represents.

How does a fraction name part of a whole?

Lesson 2.3 49A

Unlock the ProblemUnlock the Problem

16

16

16

16

16

16

16

16

16

16

16

16

16

16

16

16

16

16

16

16

16

Essential Question?

The numerator tells how many parts are being counted.

The denominator tells how many equal parts are in the

whole or in the group.

You can count equal parts, such as sixths, to make a whole.

1 __ 6 2 __

6 3 __

6 ___

6 ___

6 ___

6

2 parts not red → 3 equal parts in all →

Read: two thirds or two parts out of three equal parts

Write: 2 __ 3

So, _ of the flag is not red.

one 1 _ 6 part two 1 _ 6 parts three 1 _ 6 parts four 1 _ 6 parts five 1 _ 6 parts six 1 _ 6 parts

Name equal parts of a whole.

A fraction can name more than

1 equal part of a whole.

The flag is divided into 3 equal parts,

and 2 parts are not red.

The first pizzeria in America opened in New York

in 1905. The pizza recipe came from Italy. Look at

Italy’s flag. What fraction of the flag is not red?

▲ Italy’s flag has three equal parts.

2 __ 3

Number and Operations—3.3.A

MATHEMATICAL PROCESSES3.1.D, 3.1.F

2.3Name

Fractions of a Whole

How does a fraction name part of a whole?

Math IdeaWhen all the parts are shaded, one whole shape is equal to all of its parts. It represents the whole number 1.

3 __ 3 = 1

For example, 6 _ 6

= one whole, or 1.

2 _ 3

4 5 6

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Module 2 49

English Language Learners Language SupportELL

34

Leveled Activities ELPS

Beginning: Activity 19 1.A.1, 3.E, 4.F.7

Intermediate: Activity 22 1.A.1, 3.G.1, 4.C.1

Advanced: Activity 47 2.D.2, 2.I.5, 3.D.1

Advanced High: Activity 17 4.F.6, 4.F.10, 4.G.3

Go to thinkcentral.com for the ELL Activity Guide containing these leveled activities.

Strategy: Rephrase• Students demonstrate understanding of fractions by rephrasing the

definitions of numerator and denominator in their own words.• Write a fraction on the board. Have students read it aloud,

naming the numerator and denominator.• Write the definitions of numerator and denominator

on the board. Then have students rephrase the definitions in their own words and explain what each part of the fraction describes.

Verbal / LinguisticSmall Group

ELPS 2.C.4, 3.D.2, 4.G.2

Unlock the ProblemWhat are some different ways you can show a fraction?

What country’s flag is on this page? Read the problem to find out.

Check that students understand what information they need to solve the problem.

Guide students in finding what part of the flag is not red.

• Which part of the fraction tells the number of equal parts in the whole? the bottom number

• What does the top number tell you? the number of parts that are being counted

Direct students’ attention to the rectangles at the bottom of the page.

• What pattern do you see in the rectangles? Possible answer: each rectangle has 1 _ 6 more shaded than the rectangle before.

• What pattern do you see in the fractions? Possible answer: the numerators increase by 1. The denominators are all the same.

• Compare the numerator and denominator for 1 whole. They are equal; 6 = 6.

• What is another way to write 1 whole as a fraction? Possible answers: 3 _ 3 , 6 _ 6 , 8 _ 8 Why do each of these fractions represent 1 whole? When the numerator and denominator are the same it means all of the parts form one whole, and so each represent the whole number 1.

49 Module 2

Share and ShowShare and Show

Problem SolvingProblem Solving

Mathematical ProcessesMath Talk

1. Shade two parts out of eight equal parts.

Write a fraction in words and in numbers

to name the shaded part.

Think: Each part is 1 _ 8 .

Read: __ eighths Write: __

Write the fraction that names each part. Write a fraction in words and in numbers to name the shaded part.

2.

Each part is _.

__ fourths

3.

Each part is _.

__ sixths

4.

Each part is _.

__ fourths

Shade the fraction circle to model the fraction. Then write the fraction in numbers.

5. three fourths 6. three out of three 7. one out of two

Explain what the numerator and denominator of a

fraction tell you.

2 _ 4 3 _

6

1 _ 4 1 _

6 1 _

4

3 _ 4

two three three

two 2 _ 8

The numerator tells the number of parts being counted. The denominator tells the number of equal parts in the whole.

Possible shadings are shown.

1 _ 2 3 _

3 , or 1 3 _

4

50

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Go to Go to thinkcentral.com for additional enrichmentactivities in the Enrich Activity Guide.

Enrich

Materials: crayons

• Write the following descriptions of different flags on the board.

• Challenge students to draw each flag described. Check students’ drawings.

• Have students create their own flags and write a description for them using at least 2 fractions.

Verbal / KinestheticIndividual

1

2

3

a student misses the checked exercises

Quick Check

IF

THENDifferentiate Instruction withRtI Tier 1 Lesson 6

Math Talk Use Math Talk to focus on students’ understanding of a numerator and denominator.

Mathematical Processes

Share and ShowThe first problem connects to the learning model. Have students use the MathBoard to explain their thinking.

Use the checked exercises for Quick Check. Students should show their answers for the Quick Check on the MathBoard.

Problem SolvingAs students complete the exercises, ask the following questions.

• How do you know how many equal parts of the fraction circles to shade in Exercises 5–7? Possible answer: I read the number phrase and used the first number, which is the number of parts counted or shaded.

• For Exercise 6, what is another way to write the amount shaded? 1

• How is a numerator different from a denominator? The numerator tells the number of parts you are counting and the denominator tells the total number of equal parts in the whole.

A flag has 3 stripes. Of the stripes, 1 _ 3 are yellow, 1 _ 3 are blue, and 1 _ 3 are red.

Two sixths of a flag are red, three sixths are white, and one sixth is green.

Lesson 2.3 50

Problem SolvingProblem Solving

Pepperoni Cheese Veggie

Name

Mrs. Ormond ordered pizza. Each pizza had 8 equal slices. Use the pictures for 8–11.

8. What fraction of the pepperoni pizza

was eaten?

9. What fraction of the cheese pizza

is left?

10. Pose a Problem Use the picture of the veggie

pizza to write a problem that includes a fraction. Solve your

problem.

11. Multi-Step Marcos ate 1 _ 8 of the cheese pizza, 1 _

8 of the

pepperoni pizza, and 2 _ 8 of the veggie pizza. How many slices

of pizza did Marcos eat?

12. What’s the Error? Kate says that 2 _ 4 of the

rectangle is shaded. Describe her error. Write the correct

fraction for the shaded part.

2 _ 8

Possible answer: Kate used the number of unshaded parts as the

denominator. There are 6 equal parts and 2 are shaded, so 2 _ 6 is

the correct fraction.

4 slices

Problems will vary. Possible problem: Sadie ate 3 _ 8 of the veggie

pizza. How many slices of veggie pizza did Sadie eat? 3 slices

3 _ 8

Module 2 • Lesson 3 51

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Enrich© Houghton Mifflin Harcourt Publishing Company

Name

E8

Enrich 8

7. Draw your own flag. Divide it into equal parts. Shade some of the equal parts. Then write the fraction that names the shaded part of your flag.

Flag Fractions

Write a fraction to name the shaded part

of each fl ag.

1.

2.

3.

4.

5.

6.

1 _ 4

3 _ 6

, or 1 _ 2

3 _ 4

2 _ 3

4 _ 8 , or 2 _

4 , or 1 _

2 4 _

6 , or 2 _

3

Check students’ drawings. Possible

answer is given.

2 _ 6

, or 1 _ 3

1

© H

ou

gh

ton

Mif

flin

Har

cou

rt P

ub

lish

ing

Co

mp

any

Name

3.3.A

Some shapes can be cut into equal parts. A fraction can name more than 1 equal part of a whole.

Write a fraction in words and in numbers to name the shaded part.

How many equal parts make up the whole shape? 6 equal parts

How many parts are shaded? 3 parts

So, 3 parts out of 6 equal parts are shaded. Read: three sixths. Write: 3 _ 6

1. Shade three parts out of eight equal parts. Write a fraction in words and in numbers to name the shaded part.

Read: eighths

Write:

Fractions of a WholeOBJECTIVE Read, write, and model fractions that represent more than one part of a

whole that is divided into equal parts.

LESSON 6

Write the fraction that names each part. Write a fraction in words and in numbers to name the shaded part.

2.

Each part is .

sixths

3.

Each part is .

fourths

4.

Each part is .

eighths

three Possible shading is shown.

1 __ 6

4 __ 6

1 __ 4

2 __ 4

1 __ 8

5 __ 8

four two five

3 __ 8

Number and Operations 11

Enrich 8RtI Tier 1 Lesson 6

COMMON ERRORSError Students might confuse the numerator and the denominator.

Example Students might write the fraction in Problem 8 as 8 _ 2 .

Springboard to Learning Have students describe the fractional part using words, such as 2 out of 8 parts, and then write the numbers from top to bottom to form the fraction.

CE

Problem SolvingStudents use the pictures of the pizzas to solve Problems 8–11.

ProblemsFor Problem 10, students must use the picture to write and solve a problem that includes a fraction. Give students the opportunity to share their problems and solutions with the class.

Problem 12 requires students to find and describe an error, and then write the correct answer.

Math on the Spot Video Tutor

Through the Math on the Spot Video Tutor, students will be guided through an interactive solving of this type of H.O.T. problem. Use this video to also help students solve the H.O.T. problem in the Interactive Student Edition. With these videos and the H.O.T. problems, students will build skills needed in the TEXAS assessment.

MV

Math on the Spot videos are in theInteractive Student Edition and atthinkcentral.com.

1

2

3

51 Module 2

Daily Assessment TaskDaily Assessment Task

Mathematical Processes

TEXAS Test Prep

16. What fraction names the shaded part

of the shape?

A 2 _ 8

C 6 _ 8

B 8 _ 6

D 2 _ 6

Fill in the bubble for the correct answer choice.

13. Representations What fraction of this pizza garden

contains peppers?

A 3 _ 8

C 4 _ 8

B 2 _ 8

D 2 _ 6

14. Use Diagrams Jane is making a memory quilt from

some of her old favorite clothes that are too small. She

will use T-shirts for the shaded squares in the pattern.

Which names the part of the quilt that will be made of

T-shirts?

A three fourths C two eighths

B four sixths D four eighths

15. Multi-Step A pizza garden has six sections. Two

sections are planted with tomatoes. Which fraction

represents the part of the garden without tomatoes?

A 2 _ 6

C 4 _ 6

B 1 _ 6

D 3 _ 6

52

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Differentiated Centers Kit

ActivitiesFish for FractionsStudents complete orange Activity Card 11 by playing a Go Fish game in which they match fraction symbols, words, and pictures.

LiteraturePizza Parts!Students read about how to find equal parts to write fractions.

TEXAS Test Prep CoachTest Prep Coach helps teachers to identify common errors that students can make.

In the Test Prep exercise, if students selected:

A They named the unshaded part.

B They switched the numerator and denominator.

D They used the unshaded part as the numerator and the shaded part as the denominator.

Essential Question? WriteMathWriteMath

How does a fraction name part of a whole? Possible answer: the numerator tells how many equal parts are being counted and the denominator tells how many total parts there are.

THENIF

YES

NO

Daily Assessment Task 1

2

3

• Soar to Success MathWarm-Up 5.07, 5.09

• Enrich 8

• Homework and Practice Lesson 2.3

Can students write a fraction to name part of a whole?

Lesson 2.3 52

TEXAS Test PrepLesson CheckLesson Check

Fill in the bubble completely to show your answer.

6. What fraction of the pizza garden

contains onions?

A 2 __ 6

C 4 __ 8

B 2 __ 8

D 3 __ 8

7. What fraction names the shaded

part of the shape?

A 2 __ 6

C 1 __ 6

B 4 __ 4

D 4 __ 6

8. Cala plans to paint sections of a

piece of paper with different colors.

The diagram shows the colors she

will use. What fraction of the piece

of paper will be blue?

A 2 __ 8

C 1 __ 8

B 2 __ 4

D 4 __ 8

9. Multi-Step A flag is divided into

four equal sections. One section is

white. What fraction of the flag is

not white?

A 1 __ 4

B 2 __ 4

C 4 __ 4

D 3 __ 4

10. Multi-Step Two out of six equal

sections of a flower garden contain

daisies. The remaining sections

contain different kinds of lilies. What

fraction of the garden includes lilies?

A 2 __ 6

B 4 __ 6

C 3 __ 6

D 1 __ 6

red

red

blueyellow

yellow yellow

yellow

blue

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

54

Problem SolvingProblem Solving

Veggie

Homeworkand Practice

Name

Shade the fraction circle to model the fraction. Then write the fraction in numbers.

1. six out of eight

2. five sixths

3. one out of four 4. two thirds

5. Shayna ordered a veggie pizza. The

pizza had 8 slices. Shayna ate 3 slices.

What fraction of the pizza is left?

2.3 Fractions of a Whole

Number and Operations—3.3.A MATHEMATICAL PROCESSES 3.1.D, 3.1.F

1 _ 4

5 _ 8

2 _ 3

6 _ 8

5 _ 6

Possible shadings are shown.

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Module 2 • Lesson 3 53

555555555

Homework and PracticeUse the Homework and Practice pages to provide students with more practice on the concepts and skills of this lesson.

53-54 Module 2