equal shares and equal groups - everyday math - login€¦ · · 2011-07-15adjusting the activity...

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254 Unit 4 Multiplication and Division

Advance PreparationSee the Unit Organizer for literature links.

Prepare an area for an Arrays Exhibit. Write on the board:

pennies in all

children

pennies per child

pennies remaining

For the optional Readiness activity in Part 3, obtain a copy of The Doorbell Rang by Pat Hutchins

(HarperCollins Publishers, 1989).

Key Concepts and Skills• Use basic facts to solve division problems.

[Operations and Computation Goal 3]

• Use equal sharing and equal grouping to

model division.

[Operations and Computation Goal 6]

Key ActivitiesChildren practice division by solving equal-

sharing and equal-grouping number stories.

They form arrays with counters and draw

pictures of arrays.

Ongoing Assessment: Recognizing Student Achievement Use journal page 84. [Measurement and Reference Frames

Goal 4]

MaterialsMath Journal 1, p. 84

Home Link 4�2

per partnership: 30 pennies or counters

Playing Division ArraysStudent Reference Book, p. 282

Math Masters, p. 418 (optional)

per group: 1 each of number cards

6–18 (from the Everything Math Deck, if

available), 18 counters, 1 six-sided die

Children practice making arrays.

Math Boxes 4�3Math Journal 1, p. 85

Children practice and maintain skills

through Math Box problems.

Home Link 4�3Math Masters, p. 90

Children practice and maintain skills

through Home Link activities.

READINESS

Making Equal Groups of CookiesMath Masters, p. 91

The Doorbell Rang

Children explore solving equal-group

problems.

ENRICHMENTModeling Division with Base-10 Blocksper group: base-10 blocks, 4 pieces of paper,

half-sheet of paper

Children model equal sharing with large

numbers using base-10 blocks.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

Equal Shares andEqual Groups

Objective To review division as equal sharing and

equal grouping.e

��

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

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Lesson 4�3 255

NOTE The Math Message problem is an

example of an equal-sharing situation. The

number of groups and the total number of

objects are known. The number of objects in

each group is to be found.

Leah

Matthew

14 Î

14 pennies 2 children 7 pennies per child 0 pennies remaining

Leah and Matthew share 14 pennies equally.

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

Counters are a useful tool for solving equal-sharing and equal-grouping division problems. Have partners act out the Math Message problem with 14 pennies. Ask volunteers to share their solution strategies. Some examples are listed below.

Strategy 1

Count out the pennies, 1 or 2 at a time, until each child has the same number of pennies or 1 penny is left over. For example, “One for you, one for me. Two for you, two for me....”

Strategy 2

Think in terms of multiplication: 2 × ? = 14.

Strategy 3

Use the basic division fact 14 ÷ 2 = 7. If 2 children share 14 pennies, then each child will get 7 pennies.

Draw a picture on the board to illustrate the solution. Record the solution as shown in the margin.

If children begin to use the terms even and odd to describe the number of pennies, encourage them to do so.

Getting Started

Math Message Leah and Matthew share 14 pennies equally. How many pennies does each child get?

Home Link 4�2 Follow-Up Have children share array illustrations they have found. Begin an Arrays Exhibit. Encourage children to keep looking for pictures of arrays.

Mental Math and ReflexesChildren count from 1 to 30, clapping at the intervals indicated below.

Every 5th number 1, 2, 3, 4, 5 (clap); 6, 7, 8, 9, 10 (clap); 11, 12, 13, 14, 15 (clap); and so on to 30

Every 3rd number 1, 2, 3 (clap); 4, 5, 6 (clap); 7, 8, 9 (clap); and so on to 30

Every 4th number 1, 2, 3, 4 (clap); 5, 6, 7, 8 (clap); 9, 10, 11, 12 (clap); and so on to 30

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NOTE The problem below is an example of

an equal-grouping situation: The number of

objects per group and the total number of

objects are known. The number of equal

groups is to be found. It is not important for

children to be able to distinguish between

equal-sharing and equal-grouping number

stories; it is important, however, that they

have experience with both types.


30 pennies arranged in 6 equal groups

Leah

Matthew

15 Î

15 pennies 2 children 7 pennies per child 1 penny remaining

Leah and Matthew share 15 pennies equally.

� Solving Equal-Sharing WHOLE-CLASS ACTIVITY

Number Stories with CountersRepeat the Math Message activity with 15 pennies. Again, have children share strategies as you draw a picture and record the solution as shown in the margin. Discuss what happens: When pennies are shared equally, some pennies might be left over.

Pose other equal-sharing stories. Encourage children to use counters or draw pictures. Record the pictures and solutions on the board.

● 12 pennies, 3 children, 4 pennies per child, 0 remaining



● 18 band members are lined up in 3 equal rows. How many members are in each row? 6 members How many are left over? 0 members

Science Link Astronomers estimate that there are about 70 sextillion—7 with 22 zeros after it—stars in the

universe. To help children understand how big a number this is, explain that if all the people in the United States shared the stars equally, each person would have more than 230 trillion stars.

� Solving Equal-Grouping PARTNER ACTIVITY

Number StoriesPose the following problem to the class. Encourage children to use counters to solve it. Each child has 5 pennies. There are 30 pennies total. How many children have pennies? 6 children Have volunteers share their solution strategies. Some examples are listed below:

Strategy 1

Count out the pennies, 5 at a time to each child, until all of the pennies are distributed or it is not possible to make another group of 5. There are 6 groups of 5 pennies. There are no pennies left over.

Strategy 2

Think in terms of multiplication: 5 × ? = 30.

Strategy 3

Use the basic division fact 30 ÷ 5 = 6. If there are 30 pennies and each child has 5, then there must be 6 children.

Draw a picture on the board or use pennies on the overhead to illustrate the solution. Record the solution as shown in the margin.

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Adjusting the Activity

Division PracticeLESSON

4�3

Date Time

Use counters to find the answers. Fill in the blanks.

16¢ shared equally

1. by 2 people:

8 ¢ per person

0 ¢ remaining

25¢ shared equally

4. How many people

get 5¢?

5 people

0 ¢ remaining

30 stamps shared equally

7. by 10 people:

3 stamps per

person

0 stamps

remaining

2. by 3 people:

5 ¢ per person

1 ¢ remaining

5. How many people

get 3¢?

8 people

1 ¢ remaining

8. by 5 people:

6 stamps per

person

0 stamps

remaining

3. by 4 people:

4 ¢ per person

0 ¢ remaining

6. How many people

get 6¢?

4 people

1 ¢ remaining

9. 21 days

7 days per week

3 weeks

0 days remaining

Use may use the picture to help you solve.

10. Geri has 15 feet of ribbon. She needs 3 feet of ribbon for one bow.

How many bows can she make? 5 bows

15 feet

Try This

You may draw a picture or use counters to help you solve.

11. The animal hospital makes leashes for dogs. They can

make 3 leashes from 18 feet of rope. How many feet of

rope does it take to make 1 leash? 6 feet

84

�

79-101_EMCS_S_SMJ_G3_U04_576353.indd 84 1/26/11 9:11 AM

Math Journal 1, p. 84

Student Page

Lesson 4�3 257

20 legs, 4 legs per horse, 5 horses


20 pennies arranged into 6 equal

groups with 2 pennies remaining

Journal

Page 84 �

12 feet, 4 equal pieces, 3 feet each piece

As necessary, pose other equal-grouping stories. Encourage children to use counters or draw pictures. Record the pictures and solutions on the board.

● Each child must have 3 pennies. There are 20 pennies. How many children can have 3 pennies? 6 children with 2 pennies remaining

● 24 pennies, 8 pennies per child, 3 children, 0 pennies remaining




● Tyrone has 12 feet of rope, which he will cut into 4 equal pieces. How long will each piece of rope be? 3 feet long

● Anna was trying to determine how many horses were in a large stall. She could see only the horses’ legs. Anna counted 20 legs. How many horses were there? 5 horses

In solving the final two problems, children may find that drawing a

picture is more helpful than making an array with 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

� Solving Division Number PARTNER ACTIVITY

Stories(Math Journal 1, p. 84)

Children use counters or pictures, as necessary, to solve equal-sharing and equal-grouping division problems. (Problems 1–3, 7, 8, and 11 are equal-sharing situations. Problems 4–6, 9, and 10 are equal-grouping situations.)

Ongoing Assessment: Journal

Page 84 �Recognizing Student Achievement

Use the recorded time at the top of journal page 84 to assess children’s

progress toward telling time to the nearest minute and writing time in digital

notation. Children are making adequate progress if they are able to write the

time to the nearest 5 minutes. Some children may be able to write time to the

nearest minute; some may be able to record the seconds.

[Measurement and Reference Frames Goal 4]

ELL

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Adjusting the Activity

Links to the Future


5. Complete the number

model for the 4 by 4 array.

How many rows?

How many dots in each row?

� � 1644

4 dots

4 rows

3. Use �, �, or �.

9 � 9 13 � 5

13 � 4 11 � 5

11 � 4 13 � 8�

�

�

Date Time

2. Corinne wants new tires for her

bicycle. They cost $41.10 each,

with tax included. Estimate about

how much money she will need.

about $

Number model:

40 � 40 � 80

80.00

6. Write the number that is 100 more.

76

300

471

8,634

5,925 6,025

8,734

571

400

176

1. On the centimeter grid below,

draw a shape with an area of 10

square centimeters.

Math BoxesLESSON

4� 3

154–156

1350 51

191

64 65 18 19

Sample answer:

Unit

Sample answer:

150 151

4. Find the perimeter. Fill in the circle

for the best answer.

A 14 cm B 6 cm

C 7 cm D 12 cm

2 cm

2 cm

2 cm

2 cm

3 cm

3 cm

Math Journal 1, p. 85

Student Page

Games

Number card Die Array formed Leftovers? Score

10 2 no 10

9 2 yes 4

14 3 yes 4

Division ArraysMaterials � number cards 6–18 (1 of each)

� 1 six-sided die� 18 counters

Players 2 to 4Skill Division (with remainder) for equal groupingObject of the game To have the highest total score.Directions

1. Shuffle the cards. Place the deck number-side downon the table.

2. Players take turns. When it is your turn, draw a cardand take the number of counters shown on the card.You will use the counters to make an array.◆ Now roll the die. The number on the die is the

number of equal rows you must have in your array.◆ Make an array with the counters.◆ Your score is the number of counters in one row.

If there are no leftover counters, your score isdouble the number of counters in one row.

3. Players keep track of their scores. The player withthe highest total score at the end of 5 rounds wins.

Student Reference Book, p. 282

Student Page

The equal-sharing activities in this lesson are an early exposure to division

concepts. These concepts will be revisited throughout third grade. Using and

explaining strategies to divide a multidigit whole number by a 1-digit whole

number is a Grade 4 Goal.

2 Ongoing Learning & Practice

� Playing Division Arrays SMALL-GROUP ACTIVITY

(Student Reference Book, p. 282;

Math Masters, p. 418)

Children practice making arrays by playing Division Arrays. Have children read page 282 in the Student Reference Book for game directions.

Have children make arrays on square grid paper (Math Masters,

page 418).

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

� Math Boxes 4�3 INDEPENDENTACTIVITY

(Math Journal 1, p. 85)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 4-1. The skill in Problem 6 previews Unit 5 content.

� Home Link 4�3 INDEPENDENTACTIVITY

(Math Masters, p. 90)

Home Connection Children practice equal-sharing and equal-grouping division with number stories.

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Name Date Time

Division with CountersHOME LINK

4�3

Your child is beginning to use division to solve number stories. A first step is to use counters,such as uncooked macaroni or pennies, to represent each problem. This helps your child to understand the meaning of division.

Please return this Home Link to school tomorrow.

FamilyNote

73 74

Show someone at home how to do division using pennies, uncookedmacaroni, or other counters.

1. 25 counters are shared equally 2. 25 counters are shared equallyby 5 people. by 10 people.

counters per person counters per person

counters remaining counters remaining

3. 31 days in January 4. 22 children7 days per week 5 children per team

weeks in January teams

days remaining children remaining

5. Mrs. Blair has 34 pencils to give to her 15 students. How manypencils can she give each student?

pencils pencils left over

6. Caleb shared 22 jelly beans with his sister. How many jelly beansdid each child get?

jelly beans jelly beans left over011

42

2344

5025

UnitWrite these problems on the back of this page. Solve. Show your work.

7. � 614 � 37 8. 23 � 8 �

9. 123 � 678 � 80131577

Practice

Math Masters, p. 90

Home Link Master

LESSON

4�3

Name Date Time

Equal Groups of Cookies

1. Draw circles to show how many cookies are on each plate at the

beginning of the story.

2. How many cookies did Ma make altogether?

3. Tom and Hannah arrive. Now 4 children share the cookies. Draw a

picture to show how they share the cookies.

4. Draw a picture to show how 6 children share.

5. At the end, there are 12 children. If each child gets 3 cookies, how

many cookies do they have altogether? Draw a picture to show how

you found your answer.

There are 36 cookies in all.

12

EM3cuG3MM_U04_085-118.indd 91 2/25/10 2:51 PM

Math Masters, p. 91

Teaching Master

Lesson 4�3 259

3 Differentiation Options

READINESS INDEPENDENTACTIVITY

� Making Equal Groups 5–15 Min

of Cookies(Math Masters, p. 91)

To explore solving equal-group problems, have children read the book The Doorbell Rang. After they read the book together, have them complete Math Masters, page 91. Have children describe each new situation using words like share, split, divide, equal, same, and discuss what they have learned about making equal groups.

ENRICHMENT SMALL-GROUPACTIVITY

� Modeling Division with 15–30 Min

Base-10 BlocksTo further explore the concept of equal groups, have children model problems with base-10 blocks. Pose the following problem: You need to divide 653 paper clips into 4 boxes. How many paper clips will be in each box? Children use base-10 blocks to represent the paper clips. They use four pieces of paper to represent the boxes and distribute the blocks equally on the pieces of paper. Children will need to make trades: longs for flats and cubes for longs. They may use base-10 block shorthand to record solutions on a half-sheet of paper. There will be 163 paper clips in each box with 1 paper clip left over.

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equal shares and equal groups - everyday math - login€¦ · · 2011-07-15adjusting the activity...

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