equal parts of one

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eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

604 Unit 8 Fractions

Advance PreparationBefore beginning the Math Message, place the 8" by 8" squares of paper near the problem. Before

distributing Home Link 8�1 in Part 2, read about the Fractions Museum on page 603 of the Unit Organizer.

For the optional Extra Practice activity in Part 3, obtain the book Ed Emberley’s Picture Pie: A Cut and

Paste Drawing Book by Ed Emberley (Little, Brown, 2006). For an additional mathematics and literacy

connection, obtain a copy of Give Me Half! by Stuart Murphy (Steck-Vaughn, 1999).

Teacher’s Reference Manual, Grades 1–3 pp. 59, 60

Equal Parts of ONEObjective To review basic fraction concepts.

Key Concepts and Skills• Use manipulatives to model

1

_ 2 ,

1

_ 4 , and

1

_ 8 .

[Number and Numeration Goal 3]

• Divide shapes into equal parts.


• Write fractions to name equal parts.


Key ActivitiesChildren fold square pieces of paper into

two, four, and eight equal parts in various

ways; children color one or more parts of

the squares and name the fractions for

these parts.

Ongoing Assessment: Recognizing Student Achievement Use journal page 184. [Number and Numeration Goal 3]

Ongoing Assessment: Informing Instruction See page 607.

Key Vocabularycongruent � ONE (the whole) � fraction �

denominator � numerator

MaterialsMath Journal 2, p. 184

My Reference Book, pp. 14 and 15

slate � three 8" by 8" paper squares per

child � straightedge � crayons � scissors �

pattern blocks � Pattern-Block Template

(optional)

Bamboo Plant Number StoriesMath Journal 2, p. 185

meterstick (optional)

Children solve number stories about

the growth of a bamboo plant.

Math Boxes 8�1Math Journal 2, p. 186

Children practice and maintain skills

through Math Box problems.

Home Link 8�1Math Masters, p. 227

Children practice and maintain skills

through Home Link activities.

READINESS

Finding the Relationships among Patterns BlocksMath Masters, p. 228

pattern blocks � Pattern-Block Template

Children determine how many small

pattern blocks are needed to cover a

large pattern block.

ENRICHMENTDividing Shapes into Equal PartsMath Masters, p. 229

geoboard � rubber bands

Children divide geoboard shapes into

equal parts.

EXTRA PRACTICE

Naming Equal Parts Situations Found in LiteratureEd Emberley’s Picture Pie: A Cut and Paste

Drawing Book

Children name fractions shown by pictures in

literature and create their own circle designs.

ELL SUPPORT

Illustrating Numerator and Denominatorposterboard or chart paper

Children construct a poster to illustrate

the meaning of the terms numerator

and denominator.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

��

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Lesson 8�1 605

Mental Math and Reflexes

NOTE Point out that when the paper is

folded into equal parts, these equal parts are

congruent because they have the same size

and shape.

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-CLASS ACTIVITY

Check that each child has 12 squares about the same size.

� Folding Squares into Equal Parts PARTNER ACTIVITY

Ask each child to fold one of his or her squares into two equal parts (two halves). Ask: Is there more than one way to do this?

Have children work with a partner to fold other squares into four equal parts (four fourths) in as many different ways as possible.

Finally, ask children to fold some of the remaining squares into eight equal parts (eight eighths) in as many ways as possible.

Invite children to share their work with the rest of the class. If children do not suggest all the solutions shown above, ask them to look for other solutions or show the class the missing solutions.

To help children learn to associate objects, pictures, and concrete models with fractions, write all fractions on the board.

At the conclusion of the folding activity, have children sort their squares into piles according to the number of equal parts—squares showing two equal parts, four equal parts, and eight equal parts. If the squares are organized in this way, it will be easier for children to complete the following activity.

PROBLEMBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEMMMBLBLLEBLEBLELLLLBLEBLEBLEBLEBLEEBLEEEMMMMMMMMMMMMOOOOOOOOOOBBBBBBLBLBBLBLLBLLLLLPROPROPROPROPROPROPROPROPROPROPROPRPPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROOROROOROOPPPPPPP MMMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEEEEELELELEEEEEEEEELLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRRPROBLEMSOLVING

BBBBBBBBBBBBBBBBBBBBB EEELEMMMMMMMMOOOOOOOOOOBBBLBLBBLBLBLBBOOOROROROROROROROROROROO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGLLLLLLLLLLLLLVINVINVINVINVINVINNNVINVINVINNVINVINVINVINV GGGGGGGGGGGOOOLOOLOLOOLOO VINVINVVLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGGOLOOLOLOLOLOLOOOLO VVVVVVLLLLLLLLLLVVVVVVVVVOOSOSOSOSOSOSOSOSOSOOSOSOSOSOOOOSOOSOSOSOSOSOSOSOOOSOOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVLLLLVVVVVVVVLLLLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIISOLVING

Getting Started

Math MessageTake 3 sheets. Fold each one into fourths — 4 equal squares. Carefully cut the squares apart along the folds.

Have children record addition fact sums on their slates. For example:

Sum-equals-10 Doubles +1 and Doubles +2 Harder Facts

6 + 4 10 5 + 7 12 7 + 4 11

7 + 3 10 6 + 7 13 8 + 5 13

8 + 2 10 7 + 9 16 9 + 6 15

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Links to the FutureAt this time, it is not necessary for children to

use the words numerator and denominator.

They will learn them over time with repeated

exposure. Do, however, use these words, as

well as the informal “the number on the top”

and “the number on the bottom,” when you

discuss fractions.

�26� is equivalent to �

13�.

�26� � �

13�

12 12

3

4567

8

9

1011 12 1

2

3

4567

8

9

1011

Try It TogetherFind a whole object divided into equal parts. What fractionnames one part of the whole?

Numbers and Counting

Equivalent fractions name the same amount.

�12� is equivalent to �

24� because the same amount is shaded.

�12� � �

24�

12 12

3

4567

8

9

1011 12 1

2

3

4567

8

9

1011

�12� is shaded. �

24� is shaded.

My Reference Book, p. 15

Student Page

� Reviewing Basic Fraction WHOLE-CLASS ACTIVITY

Concepts(My Reference Book, pp. 14 and 15)

Ask children to take the square they folded into halves—two equal parts—and to color one of the parts. Review the following ideas:

� If you think of the square as representing ONE (the whole), then each part is half of ONE.

� The fraction 1 _ 2 names one of the parts. Have children count the parts. One half, two halves Tell them that two halves is the same as ONE (the whole).

Emphasize that the parts must be equal and that there is one shaded part out of two equal parts.

Continue with activities such as the following:

� Have children take one of the squares they folded into four equal parts—fourths. Have them color one part. Tell children that the fraction 1 _ 4 names one of the parts. Have them count the parts. One fourth, two fourths, three fourths, four fourths Tell children that four fourths is the same as ONE (the whole). Tell them what fraction names the part that is not colored. 3 _ 4

� Have children take another square they folded into four equal parts—fourths. Have them color two of the parts and tell what fraction names the colored part. 2 _ 4 or 1 _ 2

� Have children take another square they folded into four equal parts—fourths. Have them color four of the parts and tell what fraction names the colored part. 4 _ 4 Have them tell what fraction names the part that is not colored. 0 _ 4

� Have children take one of the squares they folded into eight equal parts—eighths. Have them color one part. Tell children that the fraction 1 _ 8 names one of the parts. Have them count the parts. One eighth, two eighths, and so on Tell children that eight eighths is the same as ONE (the whole). Tell them what fraction names the part that is not colored. 7 _ 8

� Repeat with other fractions, such as 3 _ 8 and 5 _ 8 , using squares folded into eight equal parts—eighths.

As you write fractions on the board, mention the following:

● The number under the fraction bar is called the denominator. What does the denominator of 3 _ 4 tell you? The whole is divided

into 4 equal parts. Emphasize again that the parts must be equal.

● The number above the fraction bar is called the numerator. What does the numerator of 3 _ 4 tell you? We are thinking about

3 equal parts of the whole.

Summary: The denominator of a fraction tells the total number of equal parts into which the whole is divided. The numerator of a fraction indicates the number of equal parts that you are thinking about.


Use a straightedge or Pattern-Block Template.

1. Divide the shape into 2 equal parts. Color 1 part.

Part colored = Part not colored =



3. Divide the shape into 3 equal parts. Color 2 parts.




Equal PartsLESSON

8 � 1

Date Time

1

2

8 � 2Sample answers:

1

51

2

2 2

1

2

66

3

4 4

3

�

184_208_EMCS_S_SMJ_G2_U08_57640X.indd 184 2/10/11 9:31 AM

Math Journal 2, p. 184

Student Page

Bamboo Plant Number StoriesLESSON

8 �1

Date Time

Bamboo is one of the world’s fastest-growing plants. Some types of bamboo grow more than 24 inches per day and reach heights close to 100 feet! For one week, a growing bamboo plant was measured. The chart below shows its height for each day.

Use the information above to solve the following number stories.

1. How many inches did the 2. How many inches did thebamboo plant grow from bamboo plant grow fromTuesday to Friday? Thursday to Friday?

Answer: 40 inches Answer: 17 inches Number model: Number model:

3. How many more inches tall 4. How many more inches tallwas the bamboo plant on was the bamboo plant on Saturday than on Tuesday? Saturday than Sunday?

Answer: 59 inches Answer: 87 inches Number model: Number model:

Bamboo Plant Growth for One Week

Sun. Mon. Tues. Wed. Thurs. Fri. Sat.

12 in. 26 in. 40 in. 57 in. 63 in. 80 in. 99 in.

Sample answer: 80 - 40 = 40

Sample answer: 99 - 40 = 59

Sample answer: 63 + 17 = 80

Sample answer: 12 + 87 = 99

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Student Page

Lesson 8�1 607

Adjusting the Activity

You may wish to read more about fractions as parts of a whole with your class in My Reference Book, pages 14 and 15.

� Writing Fractions for Parts INDEPENDENTACTIVITY

of Regions(Math Journal 2, p. 184)

Children divide shapes into equal parts and color one or two of the parts on each shape. Then children write fractions to name the colored and uncolored parts.

The shape in each of the first three problems is a pattern-block shape.

Children might find it helpful to use pattern blocks.

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

Ongoing Assessment: Journal

page 184

Problem 1 �Recognizing Student Achievement

Use journal page 184, Problem 1 to assess children’s ability to model fractions

as equal parts of a region and name the fraction. Children are making adequate

progress if they can successfully complete the problem. Some children may be

able to successfully complete the remaining problems.


Ongoing Assessment: Informing Instruction

Watch for children who have difficulty dividing the shapes into equal parts. Have

them use pattern blocks. For example, when finding 1

_ 2 of a hexagon, children

look for another pattern block that fits half of the hexagon (a trapezoid). They can

then trace the shape or use their Pattern-Block Template.

2 Ongoing Learning & Practice

� Bamboo Plant Number Stories INDEPENDENTACTIVITY

(Math Journal 2, p. 185)

Children solve number stories about the growth of a bamboo plant. Read the first paragraph on journal page 185 as a class and discuss the information given in the chart. To help children understand how quickly bamboo grows, you might use a meterstick to demonstrate the difference between Sunday’s and Monday’s heights. To support English language learners, show a picture of a bamboo plant and talk about its characteristics. Have children complete Problems 1–4 independently.

ELL

ELL



Math BoxesLESSON

8 � 1

Date Time

1. Write fractions.

The part shaded � .

The part not shaded � .

3. Complete the table.

6.

Which item is heavier?watermelon

watermelongrapes

4. Show 2 ways to make 50¢.Use ‰, Í, Â, and Î.

Sample answers:‰‰; ÍÍÍÍÍ

5. Circle the thing you are certainwill happen.

You will roll a 7 on a die.

The temperature will be exactly 20°F today.

An hour will pass.

2. Use a Pattern-Block Template.Draw a shape that has at leastone line of symmetry.Sample answer:

�26� or �

13�

�46� or �

23�

60

88 89100–102

Rule�12�

in out

2 1

4 28 4

10 5Answers vary.


Student Page

Name Date Time

HOME LINK

8�1 Equal Parts

Use a straightedge.


Part colored = 12

Part not colored = 12


Part colored = 34

Part not colored = 14

3. Fold some things into equal parts.

Examples: paper napkin, paper plate, magazine picture

Label each part with a fraction. Show your folded things to someone at home. Talk about what the fractions mean.

Bring the things you folded to school for the Fractions Museum.

I folded a into equal parts.

Each part shows .

Family Note

Help your child collect things that can be easily folded into equal parts. As your child works with fractions, remind him or her that the number under the fraction bar, the denominator, gives the total number of equal parts into which the whole is divided. The number over the fraction bar, the numerator, tells the number of equal parts that are being considered. Don’t expect your child to use these words. They will be learned over time with repeated exposure.

Please return this Home Link to school tomorrow.12

Math Master, p. 227

Student Page

� Math Boxes 8�1 INDEPENDENTACTIVITY

(Math Journal 2, p. 186)

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.

Writing/Reasoning Have children draw, write, or verbalize their answers to the following: How did you figure out the in number in Problem 3 when you only knew

the out number? Explain your strategy. Sample answer: The number that comes out is 1 _ 2 of the number that was put in. So 5 is

half of 10. So 10 goes in.

� Home Link 8�1 INDEPENDENTACTIVITY

(Math Masters, p. 227)

Home Connection Children practice writing fractions for parts of regions in Problems 1 and 2. In Problem 3, children show someone at home how they can fold things,

such as napkins, paper plates, or magazine pictures, into equal parts. Then children label each part of the whole with a fraction.Children will bring the folded objects to school to include them in a Fractions Museum.

3 Differentiation Options

READINESS INDEPENDENTACTIVITY

� Finding the Relationships 5–15 Min

among Pattern Blocks(Math Masters, p. 228)

To provide experience with finding fractional parts, have children determine how many of one kind of a smaller pattern block are needed to cover a larger pattern block. For example, ask: How many green (triangle) blocks are needed to cover a yellow (hexagon) block? 6 Children use the Pattern-Block Template to draw the arrangement of the smaller blocks on the larger block. This activity is designed to build readiness for work with fractions. You might want to ask questions such as: What fraction of a yellow(hexagon) block is a green (triangle) block? 1 _ 6

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Cover the larger block with smaller blocks. Use your template to show what you did.

1.

= 6

2.

= 3

3.

= 2

4. = 3

5.

= 2

Name Date Time

LESSON

8�1 Pattern-Block Equal Parts

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Math Masters, p. 228

Teaching Master

Do the following for each problem:

� Use 1 rubber band to make the shape on a geoboard.

� Use rubber bands to divide the shape into 6 equal parts.

� Record how you divided the shape.

� Repeat for the same shape. Divide it a different way into 6 equal parts.

� Record how you divided the shape the second way.

1.

2.

LESSON

8�1

Name Date Time

Equal Parts

227-251_EMCS_B_MM_G2_U08_576949.indd 229 2/9/11 12:34 PM

Math Masters, p. 229

Teaching Master

Lesson 8�1 609

ENRICHMENT INDEPENDENTACTIVITY

� Dividing Shapes into 5–15 Min

Equal Parts(Math Masters, p. 229)

To further explore fractions, have children divide shapes on a geoboard into equal parts. Allow time for children to share several solutions to each problem.

EXTRA PRACTICE SMALL-GROUP ACTIVITY

� Naming Equal Parts Situations 15–30 Min

Found in Literature

Literature Link Read the following book to groups of children, or have children read the book themselves.

Ed Emberley’s Picture Pie: A Cut and Paste Drawing Book by Ed Emberley (Little, Brown, 2006)

Summary: Circles cut into halves, fourths, or eighths are the basis for the artwork in the book. The circles are of various colors and form elaborate designs. Have children create their own circle designs and discuss the number of circles and fractional parts of circles used.

ELL SUPPORT INDEPENDENTACTIVITY

� Illustrating Numerator and DenominatorTo provide language support for understanding fractions, construct a poster like the one below illustrating the meaning of the terms numerator and denominator.

denominator The ∑bottom number tells what is being counted.

For example, eighths

are being counted.

38

Ò numerator The top number counts the parts or shares.

For example, there

are 3 eighths.

A fraction poster

PROBLEMBBBBBBBBBOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMBLBLBLBLBLEBLEBLELLLLBLEBLEBLEBLEBLEEEMMMMMMMMMMMMMMOOOOOOOOOOOBBBBLBLBBLBBLLLLLLPROPROPROPROPROPROPROPROPROPROPROPPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROOROROOROOPPPPPPP MMMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEELELEEELEEEEEEELLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRRPROBLEMSOLVING

BBBBBBBBBBBBBBBBBBBB EEELEMMMMMMMMOOOOOOOOOOBBBLBLBLBBLBBOOOROROROROROROROROROROO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGGLLLLLLLLLLLLLVINVINVINVINNNVINVINVINNVINVINVINVINVINVV GGGGGGGGGGGOOOLOOLOLOOLOO VINVINVVLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINV NGGGGGGGGGGOLOLOLOLOLOLOLOOOLO VVVVVLLLLLLLLLLVVVVVVVVOOSOSOSOSOSOSOSOSOSOOSOSOSOSOOOSOOSOSOSOSOSOSOSOOOSOOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVLLLLLVVVVVVVVVLLLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIIISOLVING

Planning AheadIf children have not already done so, have

them copy their Beat the Calculator data from

Math Journal 1, page 24 to Math Journal

2, page 311. See Planning Ahead on

Teacher’s Lesson Guide, page 417.


equal parts of one

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