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272 Unit 4 Multiplication and Division

Advance PreparationWhen you send Home Link 4�6 home, copy and attach Math Masters, pages 101 and 102.

Teacher’s Reference Manual, Grades 1–3 pp. 16, 17

Key Concepts and Skills• Use Fact Triangles and the Facts Table

to generate multiplication and division

fact families.

[Operations and Computation Goal 3]

• Look for patterns on the Facts Table.

[Patterns, Functions, and Algebra Goal 1]

• Explore the inverse relationship between

multiplication and division fact families.


• Apply the turn-around rule

(Commutative Property of Multiplication).


Key ActivitiesChildren use the Multiplication/Division

Facts Table and Fact Triangles to find fact

families and to practice multiplication and

division facts.

Ongoing Assessment: Recognizing Student Achievement Use the Math Message. [Patterns, Functions, and Algebra Goal 2]

Key VocabularyMultiplication/Division Facts Table

MaterialsMath Journal 1, inside front cover

Math Journal 1, Activity Sheets 1 and 2;

Activity Sheets 3 and 4 (optional)

Student Reference Book, pp. 52 and 53

Home Link 4�5

Math Masters, p. 98 (optional); p. 421

transparencies of Math Masters, pp. 98 and

421 (optional) � scissors � slate � paper �

envelope � half-sheet of paper

Practicing with ×, ÷ Fact Triangles×, ÷ Fact Triangles

Children practice multiplication and

division with Fact Triangles.

Math Boxes 4�6Math Journal 1, p. 90

Children practice and maintain skills

through Math Box problems.

Home Link 4�6Math Masters, pp. 99–102

Children practice and maintain skills

through Home Link activities.

READINESS

Practicing Multiplication Facts with a CalculatorMath Masters, p. 103

calculator

Children skip count with calculators.

ENRICHMENTExamining a PatternMath Masters, p. 98 or Math Journal 1,

inside front cover

per partnership: half-sheet of paper,

highlighters (optional)

Children examine a pattern in the

Multiplication/Division Facts Table.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

Multiplication and Division Fact Families

Objectives To review fact families and the Multiplication/Division

Facts Table; and to guide children as they practice multiplication

and division facts.

��

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

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Name Date TimeName Date Time

�,�

Multiplication/Division Fact Triangle

Math Masters, p. 421

Teaching Aid Master

Lesson 4�6 273

�

•

4 3

12

×,÷

3 × 4 = 12 12 ÷ 4 = 3

4 × 3 = 12 12 ÷ 3 = 4

Fact family for the numbers 4, 3, and 12

Math

Message �

1 Teaching the Lesson

� Math Message WHOLE-CLASS ACTIVITY

Follow-UpAsk a volunteer to share the fact family for 2, 2, and 4. 2 + 2 = 4, and 4 - 2 = 2. The fact family 2, 2, and 4 is a doubles fact family. Mention that just like addition and subtraction fact families, there are also multiplication and division fact families.

Ongoing Assessment: Recognizing Student Achievement

Use the Math Message to assess children’s progress toward using the +, -,

and = symbols. Children are making adequate progress if they are able to write

the fact family. Some children may notice that the same numbers (2, 2, and 4)

can be used to write a multiplication fact and a division fact using the ×, ÷, and

= symbols.


� Introducing Multiplication/ WHOLE-CLASS ACTIVITY

Division Fact Families(Math Masters, p. 421)

Use a transparency of a blank Fact Triangle (Math Masters, page 421) or draw one on the board.

Write the three numbers from a multiplication fact—for example, 3, 4, and 12—in the corners of the triangle. Be sure the product is at the top under the large dot.

Ask volunteers to name the fact family (the two multiplication facts and two division facts) for those numbers. 3 × 4 = 12, 4 × 3 = 12, 12 ÷ 3 = 4, and 12 ÷ 4 = 3

Getting Started

Math MessageWrite the +,- fact family for the numbers 2, 2, and 4 on a half-sheet of paper.

Home Link 4�5 Follow-Up Have partners discuss the multiplication-fact shortcuts they like the best.

Mental Math and Reflexes Have children count chorally. They may use number grids, number lines, or calculators as needed.

Skip count forward and backward by 2s, 5s, and 10s.

Skip count forward and backward by 3s and 6s.

Skip count forward and backward by 4s and 8s.

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LESSON

0�0

Name Date Time

Page Title

Name Date Time

Page Title

Name Date Time

Page TitleLESSON

4�6

Name Date Time

Multiplication/Division Facts Table


�,� 1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

8 8 16 24 32 40 48 56 64 72 80

9 9 18 27 36 45 54 63 72 81 90

10 10 20 30 40 50 60 70 80 90 100

Math Masters, p. 98

Teaching Master

Write a few more triplets of numbers in the triangle. Children write the fact families on their slates. A volunteer reads the results as the others check their slates.

In the previous lesson, children used arrays to demonstrate a turn-around rule for multiplication. Ask: Is there a turn-around rule for the division facts in each fact family? No Have children give examples to show that there is no turn-around rule for division; for example, 6 divided by 3 gives a different answer than 3 divided by 6. Some children may recognize that division problems, such as 3 ÷ 6, can be thought of as fractions: 3 ÷ 6 is equivalent to 3 _ 6 or 1 _ 2 .

� Finding Patterns in the WHOLE-CLASSDISCUSSION

Facts Table(Math Journal 1, inside front cover; Math Masters, p. 98)

Algebraic Thinking Ask children to study the Multiplication/Division Facts Table on the inside front cover of the journal. You may also display a transparency of the table (Math Masters, page 98). Give children a few minutes to examine the table. Have them describe patterns they find. Examples:

� Going across the second row and down the second column, the numbers increase by 1. In the third row and third column, the numbers increase by 2, and so on.

� In the 10-column and the 10-row, all of the numbers end in 0.

� In the 5-column and the 5-row, all of the numbers end in 0 or 5.

� In the 2-column and the 2-row, all of the numbers end in an even number.

� In the diagonal, moving from upper left to lower right, the numbers increase by 3, 5, 7, 9, and so on.

� Using the Facts Table and WHOLE-CLASS ACTIVITY

Fact Families(Student Reference Book, pp. 52 and 53)

Model how to use the table to find products.

Example: 5 × 7 = ? and 7 × 5 = ?

● Find the 5-row. Go across the 5-row to the 7-column. That number is 35. This shows that 5 × 7 = 35.

● Find the 7-row. Go across the 7-row to the 5-column. That number is 35. This shows that 7 × 5 = 35.

Have children practice other multiplication examples, including 8 × 1 = ? and 1 × 4 = ?. Use the Multiplication/Division Facts Table to highlight the special property of 1 in multiplication. If a number is multiplied by 1, the number is not changed. 8 × 1 = 8; 1 × 4 = 4.

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Links to the Future

Adjusting the Activity

Activity Sheet 1

Multiplication/Division Fact Triangles 1LESSON

4 �6

Date Time

2

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2

4

2

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3

6

3

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3

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EM3MJ1_G3_U04_79-101.indd 169 12/20/10 7:31 AM

Math Journal 1, Activity Sheet 1

Student Page

Lesson 4�6 275


3 ,4 1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

8 8 16 24 32 40 48 56 64 72 80

9 9 18 27 36 45 54 63 72 81 90

10 10 20 30 40 50 60 70 80 90 100


3 ,4 1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

8 8 16 24 32 40 48 56 64 72 80

9 9 18 27 36 45 54 63 72 81 90

10 10 20 30 40 50 60 70 80 90 100

The guide may be positioned either way to show

4 × 7 = 28, 7 × 4 = 28; or 28 ÷ 4 = 7 and

28 ÷ 7 = 4.

Next, demonstrate how to use the Multiplication/Division Facts Table to find quotients.

Example: 28 ÷ 4 = ?

� Find the 4-row. Go across the 4-row until you find 28. Go up that column to the heading, which is 7. This also shows that 28 ÷ 4 = 7.

� Find the 4-column. Go down the column until you find 28. Go across the row to the heading, which is 7. This also shows that 28 ÷ 4 = 7.

Have children practice other division examples including 6 ÷ 1 = ? and 7 ÷ 7 = ?. Use the Multiplication/Division Facts Table to highlight the special property of 1 in division. If a number is divided by 1, the number is not changed. If a number is divided by itself, the result is 1. For example, 6 ÷ 1 = 6 and 7 ÷ 7 = 1.

Call out multiplication facts. Ask children to highlight the facts with a sheet of paper as shown in the margin. Then children state the corresponding division facts. Alternately, children highlight division facts on the table as you call them out. They then state the corresponding multiplication facts.

� Practicing with Fact Triangles PARTNER ACTIVITY

(Math Journal 1, Activity Sheets 1 and 2)

Have children cut out the Multiplication/Division Fact Triangles from Activity Sheets 1 and 2 at the back of their journals.

Review the procedure for practicing the facts with Fact Triangles. While one child covers a number on a Fact Triangle, the partner tells the multiplication or division fact for the exposed numbers.

NOTE Have children store their Fact Triangles in their tool kits in envelopes.

Some teachers have children write the fact families on the backs of the Fact

Triangles. This should be an ongoing project, done a few at a time.

These Fact Triangles present the “easier” facts. In Unit 7, children will use the

harder Fact Triangles (Activity Sheets 3 and 4). Do not expect all children to

master all of the easier facts at this time. Children will have more opportunities to

practice the facts in later units.

Have children practice with the Fact Triangles on Activity Sheets 3 and 4

as appropriate.

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



Name Date Time

Page TitleHOME LINK

0�0 Page Title�, � Fact Triangles continuedHOME LINK

4�6

4.

16 � 8 � 2

16 � 2 � 8

8 � 2 � 16

2 � 8 � 16

5.

20 � 4 � 5

20 � 5 � 4

4 � 5 � 20

5 � 4 � 20

6.

60 � 6 � 10

60 � 10 � 6

6 � 10 � 60

10 � 6 � 60

10 6�,�

Tell someone at home about multiplication/division fact families.

1. The numbers 2, 5, and 10 form the following facts:

2 � 5 � � 2 � 5

5 � 2 � � 5 � 2

2. Knowing 6 � 2 � and 2 � 6 �

helps me know � 2 � 6 and � 6 � 2.

3. The numbers 2, 7, and 14 form this multiplication/division fact family:

Write the fact family for each �, � Fact Triangle.

14 � 7 � 27 � 2 � 14

14 � 2 � 72 � 7 � 14

1212

1212

1010

1010

2 8

16

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5 4

20

�,�

60


Home Link Master

5. Lengths (in.) of 13 cats, includingthe tails:

30, 29, 28, 24, 29, 35, 16, 27, 29,36, 28, 31, 32

What is the maximum length? Fillin the oval for the best answer.

36 inches 16 inches

29 inches 30 inches

3. Complete.

Date Time

90

2. Write the fact family.

45 � 9 � 545 � 5 � 99 � 5 � 455 � 9 � 45

4. Use the dots to show a 7-by-6 array.

What is the number model?

� � 4267

6. Fill in the emptyframes.

1. Write �, �, or �.

3 � 2 2 � 3

4 � 1 8 � 0

5 � 3 5 � 4

9 � 0 0 � 7�

�

�

�

Math BoxesLESSON

4� 6

13 56 55

64 65

79 200 201

5 9

45�,�

Rule

t

�3

yd ft

2 65 153 9

10 30Answers vary.

52203 204

Rule

�1,000

3,107

4,1075,1076,107

7,107

2,1071,107

yd

ft

Math Journal 1, p. 90

Student Page

2 Ongoing Learning & Practice

� Practicing with ×, ÷ Fact PARTNER ACTIVITY

TrianglesHave partners use their Fact Triangles to practice basic multiplication and division facts. At first, children should limit themselves to finding products. That is, one partner covers the number below the large dot, and the other gives the product of the uncovered factors. When children are well on their way to learning products, they can cover one of the other two numbers to practice finding missing factors.

� Math Boxes 4�6 INDEPENDENTACTIVITY

(Math Journal 1, p. 90)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 4-9. The skill in Problem 6 previews Unit 5 content.

Writing/Reasoning Have children answer the following question: When a number is multiplied by 1, the number does not change. What can you say about dividing a

number by 1? Sample answer: When a number is divided by 1, the number does not change.

� Home Link 4�6 INDEPENDENTACTIVITY

(Math Masters, pp. 99–102)

Home Connection Children review multiplication and division fact families. Send home copies of Math Masters, pages 101 and 102, which contain Fact Triangles.

3 Differentiation Options

READINESS INDEPENDENTACTIVITY

� Practicing Multiplication Facts 15–30 Min

with a Calculator(Math Masters, p. 103)

To provide experience skip counting on a calculator, have children use their calculators to complete the tables on Math Masters, page 103. Review the steps for counting by 1s on the calculator. Children can program the calculator using the following steps:

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Lesson 4�6 277

2

2

63

6

31

4

9

Name Date Time

Multiplication Facts & Calculator Counts

1. Use your calculator to count by 3s. Complete the table below.



4. How can counting on your calculator help you learn your

multiplication facts?

Sample answer: If I can count by 3s, I know

the products to the �3 facts. If I can count by

any number, then I know which numbers are

the products to that number’s multiplication

facts.

One 3 Two 3s Three 3s Four 3s Five 3s Six 3s Seven 3s Eight 3s Nine 3s Ten 3s

3 6 9 12 15 18 21 24 27 30


4 8 12 16 20 24 28 32 36 40


6 12 18 24 30 36 42 48 54 60

LESSON

4�6


Teaching Master

Starting Sum ofNumber 5 Numbers

4 4 + 2 + 6 + 6 +2 = 20

Sample recording sheet

TI

1. Press ON/C . This clears your calculator.

2. Press 0. This is the starting number.

3. Press + . This tells the calculator to count up.

4. Press 1. This tells the calculator to count by 1s.

Casio

1. Press . This clears your calculator.

2. Press 1. This tells the calculator to count by 1.

3. Press . This tells the calculator to count up.

4. Press 0. This is the starting number.

Now the calculator is ready to count by 1s. Without clearing their

calculators, have children press the

=

key. Press the

=

key repeatedly as the class counts together by 1s. Once they recall this routine, have them work on Math Masters, page 103. When children have completed the page, discuss how calculator counting might help them learn their facts. Have children read aloud the counts they have recorded on the master.

ENRICHMENT PARTNER ACTIVITY

� Examining a Pattern 15–30 Min

(Math Masters, p. 98; or Math Journal 1, inside front cover)

To further explore the Multiplication/Division Facts Table, have children examine a pattern in the table. Together, they circle a number on the table. Then, they

circle the number in the square above, to the right, below, and to the left of the chosen number. Next, they add the starting number plus the four circled numbers.

Children record their starting number and the sum of the five circled numbers on a half-sheet of paper as shown. They repeat this several times and look for a pattern in the recorded numbers. The product of the starting number and 5 is always equal to the sum of the five numbers. Ask: How does this pattern work? Sample answer for the example: “I made the 6s into 4s and added the leftovers to the 2s to make them into 4s. So I had five 4s.”


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