Multiples of Equal Groups - Everyday Math Unit 6 Whole-Number Operations and Number Stories ... Multiples of Equal Groups ... Have children share strategies for solving comparison

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Interactive Teacher’s

Lesson Guide

CurriculumFocal Points

Family Letters

EM Facts Workshop Game™

Algorithms Practice

eToolkitePresentations AssessmentManagement

Common Core State Standards

412 Unit 6 Whole-Number Operations and Number Stories

Advance PreparationFor the optional Extra Practice activity in Part 3, obtain the book Each Orange Had 8 Slices:

A Counting Book by Paul Giganti, Jr. (Greenwillow Books, 1992).

Teacher’s Reference Manual, Grades 1–3 pp. 90, 91

Key Concepts and Skills• Count the total number of objects in

several groups.

[Number and Numeration Goal 1]

• Make arrays to represent equal groups.

[Operations and Computation Goal 4]

• Use various strategies to solve

equal-groups number stories.


Key ActivitiesChildren are introduced to diagrams to

identify the known and unknown quantities

in multi plication problems and to complete

number models to summarize the solutions.

Children also solve number stories about

equal groups of things.

Ongoing Assessment: Recognizing Student Achievement Use the Math Message. [Operations and Computation Goal 4]

Key Vocabularyequal groups � multiplication � times �

multiplied by

MaterialsMath Journal 1, p. 148

My Reference Book, pp. 112 and 113

Home Link 6�6

Math Masters, p. 415

per group: 40 pennies or other counters �

6 boxes or bags to hold pennies or other

counters (for demonstration) � pennies or

other counters (for demonstration)

Practicing with +/- Fact Triangles+/- Fact Triangles in an envelope

Children use Fact Triangles to practice

addition and subtraction facts.

Math Boxes 6�7Math Journal 1, p. 149

Children practice and maintain skills

through Math Box problems.

Home Link 6�7Math Masters, p. 179

Children practice and maintain skills

through Home Link activities.

READINESS

Finding Totals for Equal GroupsMath Masters, p. 180

calculator

Children use their calculators and repeated

addition to solve equal-groups problems.

ENRICHMENTSolving Equal-Groups RiddlesMath Masters, p. 181

Children create and solve equal-groups

number riddles.

EXTRA PRACTICE

Equal Groups in LiteratureEach Orange Had 8 Slices: A Counting Book

Children identify and solve multiplication

problems found in literature.

ELL SUPPORT

Building a Math Word BankDifferentiation Handbook, p. 142

Children add the term multiplication to their

Math Word Banks.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

Multiplesof Equal Groups

Objective To introduce multiplication as a way to find the total

number of things in several equal groups.

��

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Lesson 6�7 413

�

5 + 5 + 5 = 15

105 15

1 pack

1 pack 15 sticks

1 pack}

////\

////\

////\

////\

////\ ////\

Some solution strategies for the Math Message

problem

Getting Started

Home Link 6�6 Follow-Up Children draw the different arrays they made with 24 Xs. Be sure to include the following arrays: 1 row of 24 Xs and 24 rows of 1 X each. Show children any other possible arrays that they do not suggest.

Mental Math and ReflexesHave children share strategies for solving comparison number stories like the following:

Vivianna is 40 inches tall. Jennifer is 30 inches tall. How much taller is Vivianna than Jennifer? 10 inches taller

Cecilia’s pencil was 19 centimeters when it was new. Now it is 9 centimeters shorter. How long is Cecilia’s pencil now? 10 centimeters long

Josh caught a fish that was 15 inches long. Jackie caught a fish that was 7 inches longer. How long was Jackie’s fish? 22 inches

Math MessageJane bought 3 packs of gum. There are 5 sticks of gum per pack. How many sticks of gum did she buy? Show how you found your answer on an Exit Slip ( Math Masters, page 415).

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

Ongoing Assessment: Math Message �

Recognizing Student Achievement

Use the Math Message to assess children’s understanding of combining equal

groups to find the total. Children are making adequate progress if they can find

the answer by counting by 1s, 5s, drawing a picture, creating tally marks, or

adding the equal groups. Some children may be able to write a multiplication

number model for the problem.


Ask children to share their solution strategies. Expect a variety of strategies: count by 1s; count by 5s; add 5s; double 5, and then add 5. Some children might draw pictures or use tallies. (See margin.)

Use the Math Message problem to lead into a discussion about equal groups. Write equal groups on the board. Ask children to name things that come in equal groups and write their responses on the board. To support English language learners, draw pictures of any unfamiliar contexts. In the Math Message problem, the packs of gum are equal groups, because each pack has five sticks of gum in it. Six-packs of soft drinks are another familiar example of equal groups, because each six-pack has six cans or bottles in it. Ask children to name things that do not come in equal groups. Sample answers: Families, classroom sizes

ELL

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Tell children that they can find the total number of things in several equal groups by multiplication. Emphasize that in a multiplication situation, each group must have the same number of things.

Show children some possible number models for the number story: 5 + 5 + 5 = 15 or 3 × 5 = 15. Mention that 3 × 5 is read “3 times 5” or “3 multiplied by 5.” To support English language learners, review the meaning of times in this context.

� Solving Number Stories WHOLE-CLASS ACTIVITY

about Equal Groups

Algebraic Thinking Divide the class into groups of 4 or 5. Display several boxes of an item, such as pennies, paper clips, dominoes, or crayons. Each box should contain the same number of the item selected.

Example: Display five boxes and put four pennies in each one. Tell the class that there are four pennies per box. Ask children to find the total number of pennies in all the boxes by using counters to act out a solution.

Suggested questions:

● How many groups of pennies are there? 5, because there are 5 boxes

● How many pennies are in each group? 4 Are they equal groups? Yes, because there is an equal number of pennies in each box.

● How many pennies are there in all? 20

● What number model can we write for this problem?5 × 4 = 20 or 4 + 4 + 4 + 4 + 4 = 20

Draw a diagram on the board that identifies the known and unknown quantities. Point out that the numbers in the diagram tell the quantities we know and that the question mark indicates the quantity we are trying to find. Once children have found the answer, erase the question mark, write in the answer 20, and circle it. (See below.)

boxes pennies per box pennies in all

5 4 20

5 × 4 = 20

4 + 4 + 4 + 4 + 4 = 20

Make up other stories by changing the number of boxes and the number of items per box. Emphasize the language of equal groups: for example, three boxes with seven marbles per box and three boxes with seven crayons in each box.

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ELL

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Adjusting the Activity

Lesson 6�7 415

Multiplication StoriesLESSON

6 �7

Date Time

Solve each problem. Draw pictures or use counters to help.

Example: How many cans are in three 6-packs of juice?

/// /// /// /// /// /// 6 12 18

Answer: 18 cans

1. Mr. Yung has 4 boxes of 2. Sandi has 3 bags of marbles.markers. There are 6 markers Each bag has 7 marbles in it.in each box. How many How many marbles does shemarkers does he have in all? have in all?

Answer: markers Answer: marbles

3. Mrs. Jayne brought 4. After the picnic, 5 boys each5 packages of buns to picked up 4 soft-drink cans tothe picnic. Each package recycle. How many cans did had 6 buns in it. How many the boys pick up all together? buns did she bring in all?

Answer: buns Answer: cans

24

30

21

20

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Math Journal 1, p. 148

Student Page

Mia has 4 packs of gum.There are 5 sticks of gum in each pack.How many sticks of gum are there in all?

packs sticks per pack sticks in all

4 5 ?

Number of groups

You know thenumber of groups.

You know thenumber of objects

in each group.

You don’t knowthe total number

of objects.

Total number of objects

Number of objects in each group

Number model: 4 5 ?

You can use a diagram to help you solve a number story about groups with equalnumbers of objects.

Number Stories

My Reference Book, p. 112

Student PageChildren should continue using counters, pictures, doodles, or anything else that might help them find the total number of items. As they share solution strategies, write number models on the board and read the models aloud. For example:

� 5 + 5 + 5 = 15 5 plus 5 plus 5 equals 15.

� 3 × 7 = 21 3 times 7 is 21.

� 4 × 6 = 24 6 multiplied by 4 equals 24.

Continue to fill in a diagram for each of the problems on the board. Write in the known quantities, and write a question mark for the unknown quantity. Ask children to help you complete the diagrams as you discuss problems, but do not expect children to come up with diagrams on their own. Repeated exposure to such diagrams will help children understand the meanings of multiplication and division.

Next, make up several number stories that do not require boxes of items as props. Fill in diagrams as before. As children share solutions, write number models on the board. Suggestions:

6 children have wet shoes, 2 shoes per child. How many wet shoes? 12

3 children took 4 crackers each. How many crackers? 12

4 packs of juice, 6 cans per pack. How many cans? 24

2 weeks, 7 days per week. How many days? 14

Pose problems using larger numbers. For example:

• 3 hours, 50 miles per hour. How many miles? 150

• 5 toys, 99 cents per toy. Total cost? $4.95

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 Number Stories PARTNER ACTIVITY

about Equal Groups(Math Journal 1, p. 148; My Reference Book,

pp. 112 and 113)

Algebraic Thinking You may wish to read about number stories with equal groups in My Reference Book, pages 112 and 113 with your class. Partners act out and solve the multiplication stories on the journal page. Ask them to show how they solved the problems. Children might draw pictures or use counters.

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Name Date Time

In today’s lesson, your child learned that multiplication is an operation used to find the total number of things in several equal groups. As you help your child solve the following problems, emphasize that each group has the same number of things. Your child can use objects, draw pictures, count, or use any other helpful devices to find the answers.

Please return this Home Link to school tomorrow.

1 pica to top rule1 pica to left rule

style sheet: No Style

char style: G1_MM Prob Num bol

HOME LINK

6�7 How Many?

Example: How many apples in 4 packages?

There are 20 apples in 4 packages.

1.

How many sides on each triangle? sides

How many sides in all? sides

2.

How many wheels on each bike? wheels

How many wheels in all? wheels

3. How many fingers for each person?

fingers

How many fingers in all?

fingers

82

183

80

10

5 � 5 � 5 � 5 � 20

////\ ////\ ////\\\ ////\\\

Family Note

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Home Link Master

Math BoxesLESSON

6 �7

Date Time

1. Write the number.

2. Make ballpark estimates. Write a number model foreach estimate.

32 + 59

+ = 51 + 27

+ =

Unit

cm

4.

How many? Cross out 23 cubes.

How many are left? Write a number model.

- =

5. Lauren’s birthday is on the tenth day in the shortest month of the year. In what month is her birthday?

6. Double.

2 4 10 50

3. Measure the line segment.

Draw a line segment 3 cm shorter.

Unit

10 11

31

85

92–94

32530

50

60

30

90

80

51

28

282351

4820100

9

Sample estimates.

February

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Math Journal 1, p. 149

Student Page

2 Ongoing Learning & Practice

� Practicing with PARTNER ACTIVITY

+/- Fact TrianglesHave children work with a partner using the Fact Triangles as flash cards. Remind children that when their partner misses a fact, they should flash the other fact problems on the triangle and then return to the fact that was missed.

� Math Boxes 6�7 INDEPENDENTACTIVITY

(Math Journal 1, p. 149)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 6-9. The skill in Problem 6 previews Unit 7 content.

Writing/Reasoning Have children draw, write, or verbalize their answers to the following: In Problem 5, if Lauren was born the same year as you, is she older or younger? What strategy did you use to solve the problem?

Sample answer: She is older than me; I was born in June, so she would turn 8 years old first. She is younger than me, I was born in January, so I would turn 8 years old first.

� Home Link 6�7 INDEPENDENTACTIVITY

(Math Masters, p. 179)

Home Connection Children can use objects, draw pictures, count, or use any other helpful device to solve problems about equal groups.

3 Differentiation Options

READINESS

INDEPENDENTACTIVITY

� Finding Totals for Equal Groups 5–15 Min


To provide experience with solving equal-groups problems, have children use their calculators and repeated addition. Some children may want to program the calculator to skip count, while others may want to enter + repeatedly. When they have finished solving the problems, have them compare their answers. They should rework problems on which they don’t agree. Have volunteers share their strategies for solving the problems. Consider having children record addition number sentences to show how they solved problems.


You may use your calculator to help you solve the problems.

1. How many people are in my group?

How many hands do the people in my group have all together?

How many fingers do the people in my group have all together?

2. How many tables are in the classroom?

How many legs do the tables have?

3. One flower has 5 petals.

How many petals do 6 flowers have?

4. Make up your own problem like the ones above. Draw a picture to help someone solve your problem.

LESSON

6�7

Name Date Time

Finding Totals for Equal Groups

Answers vary.



Teaching Master

What Number Am I?

1. If you put me into 7 equal groups with 3 in each group and 5 are left over, what number am I?

Draw a picture of what you did. Sample answer:

2. I am a number between 20 and 30. When you put me into 6 equal groups, there is an even number in each group and 1 is left over.

What number am I?

Draw a picture of what you did. Sample answer:

3. Try writing your own equal-groups riddle.

25

26

Name Date Time

LESSON

6�7 Equal-Groups Riddles

Answers vary.



Teaching Master

Lesson 6�7 417

ENRICHMENT SMALL-GROUP ACTIVITY

▶ Solving Equal-Groups Riddles 15–30 Min


To further explore the concept of equal groups, have children use Math Masters, page 181 to create and solve equal-groups riddles.

EXTRA PRACTICE SMALL-GROUP ACTIVITY

▶ Equal Groups in Literature 15–30 Min

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

Each Orange Had 8 Slices: A Counting Book by Paul Giganti, Jr. (Greenwillow Books, 1992) Summary: Multiplication concepts are explored in the full-color book. In the first presentation, 3 red flowers are seen; each flower has 6 petals, and each petal has 2 black bugs. Questions are posed about the number of flowers, the number of petals, and the number of bugs. Have children answer the questions posed in the book.

ELL SUPPORT SMALL-GROUP ACTIVITY

▶ Building a Math Word Bank 5–15 Min

(Differentiation Handbook, p. 142)

To provide language support for multiplication, have children use the Word Bank template found on Differentiation Handbook, page 142. Ask children to write the term multiplication, draw a picture representing the term, and write other related words. See the Differentiation Handbook for more information.

Planning Ahead

Have children copy their Beat the Calculator results from Math Journal 1, page 24 to Math Journal 2, page 311. Children will continue to record the facts for which they can beat the calculator. The Fact Power Table on journal page 311 will become a cumulative record of children’s progress toward addition fact power during Beat the Calculator game situations.

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Documents

Multiples of Equal Groups - Everyday Math Unit 6 Whole-Number Operations and Number Stories ... Multiples of Equal Groups ... Have children share strategies for solving comparison