naming parts with fractions - everyday math - login 648 unit 8 fractions naming parts with fractions...

$: Naming Parts with Fractions - Everyday Math - Login 648 Unit 8 Fractions Naming Parts with Fractions Objective To guide children as they use fractions to name a of b equal parts.e$
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648 Unit 8 Fractions

Naming Partswith Fractions

Objective To guide children as they use fractions to name a of b

equal parts.e

Advance Preparation

Teacher’s Reference Manual, Grades 1–3 pp. 59–62

Key Concepts and Skills• Use manipulatives to solve problems

involving fractional parts of collections.

[Number and Numeration Goal 2]

• Identify equivalent halves and fourths

of a shaded region.


• Use shaded regions to compare fractions.


• Use equal sharing to solve fractional

part-of-a-collection problems.

[Operations and Computation Goal 6]

Key ActivitiesChildren review basic fraction concepts

and notation. They name fractional parts

of regions and sets of objects.

Ongoing Assessment: Informing Instruction See pages 650

and 651.

Ongoing Assessment: Recognizing Student Achievement Use journal page 180. [Number and Numeration Goal 2]

Key Vocabularyequal � whole (the ONE) � denominator �

numerator � unit fraction

MaterialsMath Journal 2, pp. 180 and 181

slate � 25 pennies or counters

Practicing with Fact Triangles×, ÷ Fact Triangles

Children practice multiplication and

division facts with Fact Triangles.

Math Boxes 8�1Math Journal 2, p. 182

Children practice and maintain skills

through Math Box problems.

Home Link 8�1Math Masters, p. 237

Children practice and maintain skills

through Home Link activities.

READINESS

Exploring FractionsMath Masters, p. 238

counters � ruler or straightedge

Children explore the concept of a fraction

of a set.

ENRICHMENTSolving Fraction PuzzlesMath Masters, p. 239

centimeter cubes

Children solve Fraction Puzzles to create

the whole when a part is given.

ELL SUPPORT

Building a Math Word BankDifferentiation Handbook, p. 132

Children add the terms numerator and

denominator to their Math Word Banks.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

��

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

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180

Date Time

Fraction ReviewLESSON

8�1

Math Message1. Draw an X through 2

_ 3 of the circles.

Label each picture with one of the following numbers: 0, 0–4,

1–4,

1–2,

2–4, or

3–4.

2. 3. 4. 5.

4–4 or 1

0 or 0—4

1

_ 4

3

_ 4

1 _ 2 or

2

_ 4

Each whole figure represents ONE.

Write a fraction that names each region inside the figure.

6. 7. 8.

9. 10. 11.

1212

14

14

14

14

13

13

13

12

12

14 1

4

12

12 1

414

34

14

14

1414

18

18

� � �

�

Each whole figure represents ONE. Write a fraction that names each

region inside the figure.

12. 13.

Try This

EM3MJ2_G3_U08_180-203.indd 180 1/19/11 5:04 PM

Math Journal 2, p. 180

Student Page

Lesson 8�1 649

NOTE To extend fraction review, have

children compare the fractions in

Problems 2– 5, Math Journal 2, page 180.

Interactive whiteboard-ready

ePresentations are available at

www.everydaymathonline.com to

help you teach the lesson.

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

(Math Journal 2, p. 180)

Go over the answers to the Math Message problems while reviewing the use of fractions to express parts of wholes. Be sure to include the following points in the discussion:

� Fraction notation is one way to express equal parts of any whole. (Decimal notation is another way.)

� Fractions are not meaningful unless they refer to a part of a particular whole (the ONE). Throughout this unit, consistently ask children to identify the ONE in problem situations. For example, 1 __ 4 of a large pizza is not the same as 1 __ 4 of a small pizza.

� A fraction has two parts. The denominator names the number of equal parts into which the whole (the ONE) has been divided. The numerator names the number of those equal parts being used or considered.

3 numerator

7 denominator

� A fraction with the same numerator and denominator names all the parts of the whole (the ONE). For example, 3 __ 3 , 4 __ 4 , and 5 __ 5 are all equivalent names for 1.

� A fraction with 1 in the numerator is called a unit fraction. 1 __ 4 , 1 __ 8 , and 1 __ 25 are examples of unit fractions.

Mental Math and ReflexesPose problems like the following. Children write their answers on slates and share their strategies. Encourage children to write number models to show their strategies.

A fin whale weighs about 50 tons. About how much do 6 fin whales weigh? 6 × 50 T = 300 T

1 ton = 2,000 pounds. About how much does 1 fin whale weigh in pounds? 50 × 2,000 lb = 100,000 lb

A 9-year-old’s heart beats about 90 times per minute. About how many times does it beat per hour? 60 × 90 beats = 5,400 beats About how many times does it beat in 10 hours? 54,000 beats

Getting Started

Math MessageTurn to page 180 in your journal. Do Problems 1–5 only.

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NOTE The numerator of a fraction can be 0;

for example, 0

_ 1 ,

0

_ 2 , and

0

_ 3 are names for no

parts of the whole, or 0. The denominator of a

fraction cannot be 0. Because the reason for

this is beyond the grasp of most third graders,

do not mention this unless someone makes

up a fraction with 0 in the denominator. You

might also enter a fraction such as 3

_ 0 into a

calculator to see what the display shows.

Some calculators will display an error

message when the = key is pressed. Others

will not allow 0 to be entered.

Adjusting the Activity

Have one child divide a slate in half and shade one half, and another child divide

another slate into 4 equal parts and shade 2 fourths. Then compare the shaded parts.

Explain that 1

_ 2 and

2

_ 4 are equivalent fractions.

AUDITORY � KINESTHETIC � TACTILE � VISUAL

ELL

� Any whole number can be named as a fraction with 1 in the denominator. For example, a fraction name for 6 is 6 _ 1 . The numerator 6 tells how many copies you have of the unit fraction with the denominator 1:

6 _ 1 = 6 × 1 _

1

= 1 _ 1 + 1 _

1 + 1 _

1 + 1 _

1 + 1 _

1 + 1 _

1

= 1 + 1 + 1 + 1 + 1 + 1

= 6

Ongoing Assessment: Informing Instruction

Watch for children who have difficulty remembering which part of a fraction is the

numerator and which part is the denominator. Explain that they might remember

the numerator by thinking that the word has a u for up and denominator has a d

for down.

As you continue to discuss fractions with children, emphasize the importance of equal parts and consistently ask them to identify the ONE in problem situations.

� Reviewing Fractions as Names WHOLE-CLASS ACTIVITY

for Parts of RegionsWhen a slate is divided into equal parts, each part can be expressed as a fraction. The slate’s drawing surface is the ONE. Lead the class in activities such as the following:

● Divide the slate into 2 equal parts. First shade one part, and then the other. What is equal to the two halves? The whole slate, or the ONE How would you write this as a fraction? 2 _ 2

● Divide the slate into 3 equal parts. What fraction of the slate is each part? 1 _ 3 of the slate Divide it into 6 equal parts. What is each part called? 1 _ 6 of the slate Share your strategies for shading 1 _ 6 of the slate. Use one line to divide the thirds in half. Or add three more parts by dividing each third with a line.

● Divide the slate into 4 equal parts. Shade 3 of the 4 parts. What fractional part of the slate have you shaded? 3 _ 4 of the slate What fractional part is not shaded? 1 _ 4 of the slate

● Which is larger, 1 _ 2 or 1 _ 4 of the slate? 1 _ 2 Why? With the fraction 1 _ 2 , the slate is divided into fewer equal parts so each of those parts is larger. Which is smaller, 1 _ 2 or 2 _ 4 ? Neither; they’re equal. Why? The same amount is shaded.

● Divide the slate into 6 equal parts. Shade 0 sixths. How much of the slate is shaded? Nothing is shaded. How would you write that as a fraction? 0 _ 6

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Adjusting the Activity

Date Time

Fraction Review continuedLESSON

8�1

14. a. Show 1–4 of a set of8 counters. Howmany counters is that?

15. a. Show 1–3 of a set of12 counters. Howmany counters is that?

16. a. Show 1–5 of a set of 15 counters. Howmany counters is that?

18. Show 2–3 of a set of 18 counters. Howmany counters?

b. Show 2–4 of the set. Howmany counters?



19. Five counters is 1–5 of a set. How manycounters are in thewhole set?

c. Show 3–4 of the set. Howmany counters?

c. Show 3–3 of the set. Howmany counters?

17. Show 3–4 of a set of 20 counters. Howmany counters?

20. Six counters is 1–3 of a set. How manycounters are in thewhole set? 18

15

12

6

25

12

8

4

12

3

4

2

21. Twelve counters is 3–4 of a set. How many counters are in the complete set?

22. Pretend that you have a set of 15 cheese cubes. What is �

12� of that set? Use a fraction

or decimal in your answer.

16 counters

71—2 or 7.5 cheese cubes

You need at least 25 pennies or other counters to help you solve these problems. Share solution strategies with others in your group. Unit

counters

Try This


Student Page

Lesson 8�1 651

Ongoing Assessment: Informing Instruction

Watch for children who are having difficulty

solving the fractional part-of-a-set number

stories. Have them divide their slates and act

out the problems. For example, to show 3

_ 4 of

a set of 20 counters, have children divide

their slates into 4 sections. They distribute

the 20 counters equally among the sections

and then count to find the total in 3 of the

4 sections.

� Reviewing Fractions as Names WHOLE-CLASS ACTIVITY

for Parts of SetsAsk 5 children to lend their journals to make a set of books. Show the pile of 5 books. The 5 books are the whole set, or the ONE. To support English language learners, discuss the meaning of the word set in this context. Hold up several books, and ask children to name the fractional part of the set.

Ask: What fractional part of the set is 1 book? 1 _ 5 3 books? 3 _ 5 No books? 0 _ 5 5 books? 5 _ 5 , the whole set, or the ONE

Name a fractional part, and ask children to tell you how many books to hold up.

Ask: How many books are 2 _ 5 of the set? 2 books 4 _ 5 of the set? 4 books

Repeat with a set of 9 books.

Ask: How many books are in 8 _ 9 of the set? 8 books How many books are 1 _ 3 of the books? 3 books What fractional part are 6 of the books? 6 _ 9 or 2 _ 3

Continue with similar questions.

Ask children how many books each child would get if 3 children were to

share the 9 books equally. 3 books Each share is 1

_ 3 of the set. Ask: How many

total books would 2 of the children get? 6 books What fraction of books do the

2 children get? 2

_ 3 of the set Have children model this and other situations using

counters.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

Say that you have a case of juice boxes. Five juice boxes are 1 _ 2 of the case. Ask: How many juice boxes are in the whole case? 10 juice boxes

Say that 4 apples are 1 _ 4 of a bag. How many apples are in the whole bag? 16 apples

Say that 8 girls are 2 __ 3 of a group. How many children are in the group? 12 children

Continue with similar questions.

� Using Fractions to Name Parts INDEPENDENTACTIVITY

of Regions and Sets(Math Journal 2, pp. 180 and 181)

Children work alone or with a partner to complete the journal pages. They can use counters to help solve problems involving fractional parts of sets. Bring the class together to discuss children’s solutions.

ELL

ELL

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EM3cuG3TLG2_649-653_U08L01.indd 651EM3cuG3TLG2_649-653_U08L01.indd 651 1/14/11 9:22 AM1/14/11 9:22 AM


Name Date Time

Fractions All AroundHOME LINK

8�1

Help your child understand the idea of the ONE as well as fractions of objects and sets. Help your child look for objects and pictures that have fractions or decimals printed on them.

Please return this Home Link to school tomorrow.

FamilyNote

22–24

Each square flag below represents the ONE. Write the fractions that nameeach region inside each flag.

1. 2. 3.

Write the fractions.

4. of the buttons have 4 holes.

5. of the buttons have 2 holes.

Look for items around your home that have fractions or decimals on them, suchas recipes, measuring cups, wrenches, package labels, or pictures in newspapers.Ask permission to bring them to school to display in our Fractions Museum.

Solve. Show your work.

6. 275 7. 684 8. 429� 88 � 97 � 237

192587187

�27�

�57�

12

12 1

4

14 1

414

14

34

PracticeUnit

Math Masters, p. 237

Home Link Master

Date Time

5. Shade of the circle.

What fraction is unshaded? 58

38

3. This drawing shows a rectangular prism.

It has faces.

It has edges.

It has vertices.8126

2. Fill in the missing numbers.

4. Complete the number models.

(4 + 3) � 2 �

10 � 6 + (2 + )

� 3 � (9 � 0)

(5 � 5) � 4 � 2127

25

6. 9 cups. 9 ice cubes per cup. Howmany ice cubes in all? Fill in thecircle for the best answer.

A 18 ice cubes

B 81 ice cubes

C 90 ice cubes

D 99 ice cubes

1. Double each amount.

$0.25

$0.50

$0.75

$1.25

$5.00 $10.00$2.50$1.50$1.00$0.50

Math BoxesLESSON

8�1

115 16

22 23 66 67

�, � 700 60

8 5,600 4807 4,900 420


Student Page

Journal

Page 180�Problems 6–9

Ongoing Assessment:Recognizing Student Achievement

Use journal page 180, Problems 6–9 to assess children’s ability to identify and

write fractions that name regions. Children are making adequate progress if they

are able to successfully complete Problems 6–9. Some children may be able to

complete problems 10 and 11.


2 Ongoing Learning & Practice

� Practicing with Fact Triangles PARTNER ACTIVITY

Partners practice basic facts by flashing ×, ÷ Fact Triangles. Children can keep track of the facts they miss so they can focus on those facts during a second round.

� Math Boxes 8�1 INDEPENDENTACTIVITY

(Math Journal 2, p. 182)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 8-3. The skill in Problem 6 previews Unit 9 content.

� Home Link 8�1 INDEPENDENTACTIVITY

(Math Masters, p. 237)

Home Connection Children use fractions to name parts of objects and sets. They are asked to bring in items with fractions or decimals printed on them for the Fractions Museum.

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LESSON

8�1

Name Date Time

Exploring Fractions

1. Explain how you can tell whether something shows �14�.

For Problems 2 and 3—� Take the number of counters.� Figure out how to show �

14� of

the counters.� Use the rectangles to the right to

make four equal piles of counters.� Draw a picture to record your answer.

2. Take 8 counters. Show �14� of 3. Take 20 counters. Show �

14�

the counters. of 20 counters.

one part is represented, then that shows �14�.

Sample answer: If something has four equal parts and

4. Divide the figure below into four 5. Divide the figure below into fourequal parts. equal parts another way.

Sample answer: Sample

answer:

Is �14� in Problem 4 larger or �

14� in Problem 5 larger? Explain your answer on the

back of your paper.

These show �14�. These do NOT show �

14�.


Teaching Master

LESSON

8�1

Name Date Time

Fraction Puzzles

Use centimeter cubes to help you solve the puzzles.

1. The 1st graders are building a little house with centimeter cubes. The drawing shows �

23� of

the floor of their house. Use centimeter cubes to build the whole floor of the house. Then finish the picture.

2. This drawing shows �170� of a line segment. Use centimeter cubes to

figure out how long the line segment is. Figure out how much longerthe line segment should be to make it whole. Use a ruler to draw therest of the whole line segment.

3. Make up a puzzle. Ask a partner to solve it. Answers vary.This drawing shows — of a .

Draw the whole .

Sampleanswer:


Teaching Master

Lesson 8�1 653

NOTE Remind children to continue to record

the sunrise, sunset, and length of day in their

journals on pages 279–281. They will also

continue to record the national high and low

temperatures on journal page 175 and then

graph the temperature ranges on journal

pages 176 and 177.

3 Differentiation Options

READINESS PARTNER ACTIVITY

� Exploring Fractions 5–15 Min


To explore the concept of a fraction of a collection, have children solve the fraction problems on Math Masters, page 238. When children have finished the page, have them discuss how they can find 1 _ 4 of any number. Sample answer: I can divide the number into four equal piles or the area into 4 equal parts. Each pile or part is 1 _ 4 .

ENRICHMENT PARTNER ACTIVITY

� Solving Fraction Puzzles 5–15 Min


To apply children’s understanding of fractions as parts of wholes, have them solve Fraction Puzzles on Math Masters, page 239.

ELL SUPPORT PARTNER ACTIVITY

� Building a Math Word Bank 5–15 Min

(Differentiation Handbook, p. 132)

To provide language support for fractions, have children use the Word Bank template found on Differentiation Handbook, page 132. Ask children to write the terms numerator and denominator, draw a picture representing each term, and write other related words. See the Differentiation Handbook for more information.


naming parts with fractions - everyday math - login 648 unit 8 fractions naming parts with fractions...

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