EM3cuG4TLG1 163 U03L02 - Everyday Math · • Find factors and multiples of numbers. [Number and...

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eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

Lesson 3�2 163

Advance PreparationFor Part 1, have plastic bags or envelopes available for storing the Fact Triangles. Think about how to pair

students for this activity so they will be at similar skill levels.

Teacher’s Reference Manual, Grades 4–6 pp. 16, 79, 80, 267–269

Key Concepts and Skills• Find factors and multiples of numbers.

[Number and Numeration Goal 3]

• Identify prime and composite numbers.


• Identify square numbers.


• Solve multiplication facts.

[Operations and Computation Goal 3]

• Identify and use patterns in the

Multiplication/Division Facts Table.

[Patterns, Functions, and Algebra Goal 1]

Key ActivitiesStudents cut out Multiplication/Division Fact

Triangles. They discuss the Multiplication/

Division Facts Table, symbols, and

vocabulary for multiplication. Students

identify prime and composite numbers. They

use Fact Triangles to maintain automaticity

with multiplication facts.

Key Vocabularymultiplication facts � factors � products �

factor pair � multiples � square numbers �

turn-around facts � prime number �

composite number

MaterialsMath Journal 1, inside front cover; p. 56;

Activity Sheets 1–4 � Student Reference

Book, pp. 8, 178A, and 178B � Study Link 3�1

transparencies of Math Masters, pp. 408

and 409 (optional) � paper clips � envelopes

or resealable plastic bags � scissors �

calculator � counters (optional)

Playing Name That NumberStudent Reference Book, p. 254

Math Masters, p. 489

deck of number cards (the Everything

Math Deck, if available)

Students practice representing

numbers in different ways.

Ongoing Assessment: Recognizing Student Achievement Use Math Masters, page 489. [Number and Numeration Goal 4]

Math Boxes 3�2Math Journal 1, p. 57

Students practice and maintain skills

through Math Box problems.

Study Link 3�2Math Masters, p. 75

Students practice and maintain skills

through Study Link activities.

READINESS

Making Rectangular ArraysMath Masters, p. 76

centimeter cubes � 4 each of number cards

1–10 (from the Everything Math Deck, if

available)

Students practice multiplication facts using

a concrete model.

EXTRA PRACTICE

Playing Buzz and Bizz-BuzzStudent Reference Book, p. 234

Students practice naming multiples.

ELL SUPPORTBuilding a Math Word BankDifferentiation Handbook, p. 140

Students add the term square numbers

to their Math Word Banks.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

Multiplication FactsObjectives To review strategies for solving multiplication facts;

to help students maintain automaticity with multiplication facts;

and to introduce prime and composite numbers.

t

��

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164 Unit 3 Multiplication and Division; Number Sentences and Algebra

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

Tell the class they will use Fact Triangles to practice multiplication facts and another tool, the Multiplication/Division Facts Table, to discuss the terms factor, product, and multiple.

� Reviewing the Multiplication/ WHOLE-CLASSDISCUSSION

Division Facts Table(Math Journal 1, inside front cover; Math Masters, p. 408)

Introducing the Symbols º and /Ask students to look at the inside front cover of Math Journal 1. Display an overhead transparency of Math Masters, page 408. Remind students of the following:

� The table shows the multiplication facts.

� The 0s facts have been omitted to avoid confusion about division by 0 (which is not possible).

� The 10s facts are included.

Point out the ∗ and / symbols in the upper left-hand corner of the table. Explain that in Grades 4, 5, and 6 of Everyday Mathematics, an asterisk (∗) is usually used to indicate multiplication. A slash (/) is often used to indicate division, but the ÷ and the �

_ RR symbols are also used.

NOTE The symbols ∗ and / are used for multiplication and division on computer

keyboards. The asterisk helps avoid confusion between the × symbol and the

variable x in algebra. Using the slash for division clearly relates division to

fractions. 1 / 2, 1

_ 2 , 1 ÷ 2, and 2 �

_ 12 all represent the same number.

ELL

Getting Started

Math Message Cut apart the Multiplication/Division Fact Triangles on Activity Sheets 1–4 at the back of your journal. Write your initials on the back of each one.

Put the Fact Triangles and two paper clips into a plastic bag or envelope.

Study Link 3�1 Follow-Up Have partners discuss the pattern in Problem 1 and explain why the numbers will always change from odd to even or even to odd when moving from the in column to the out column.

Mental Math and Reflexes In preparation for discussing multiples, pose calculator skip-counting problems, starting with 0. Suggestions:

20s 0, 20, 40, 60, 80, 100, ...

50s 0, 50, 100, 150, 200, 250, ...

6s 0, 6, 12, 18, 24, 30, ...

8s 0, 8, 16, 24, 32, 40, ...

Back by 4s 0, -4, -8, -12, -16, -20, ...

Back by 7s 0, -7, -14, -21, -28, -35, ...

1

1 2 3 4 5 6 7 8 9 10

1 10

2 4

7

8

9

10

3 9

4 16

5 25

6 36

49

64

81

908070605040302010

20

30

24 40

50

60

70

80

90

100

squarenumbers

factor

factor product

multiplesof 10

multiples

of 10

∗,/

Multiplication/Division Facts Table from the inside front

cover of Math Journal 1 and Math Masters, page 408

NOTE For Multiplication/

Division Fact Triangles and

a Facts Table with facts

through 12 º 12, see

www.everydaymathonline.com.

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Reviewing the Meaning of Factors, Products, and MultiplesRemind students that the numbers in the shaded row and shaded column in the table are called factors, and the rest of the numbers are called products. For example, in 4 ∗ 6 = 24, 4 and 6 are factors of 24, and 24 is the product of 4 and 6. 4 and 6 are a factor pair of 24. A number may have more than one factor pair. For example, the factor pairs for 24 are 1 and 24, 2 and 12, 3 and 8, and 4 and 6. To support English language learners, label and identify the factors and products on the transparency of Math Masters, page 408 as students do so on the inside front cover of Math Journal 1.

Direct students to look across a row or down a column to find the multiples of a number. The multiples of 10, for example, are 10, 20, 30, 40, and so on. Point out that a whole number is a multiple of each of its factors.

Reviewing Square NumbersNext point out the shaded products on the diagonal. Remind students that these products are called square numbers. Each square number is the product of a counting number multiplied by itself. For example, 9 is a square number, because 3 ∗ 3 = 9.

Reviewing Turn-Around FactsPoint out that the products above the diagonal of square numbers are “mirror images” of the products below the diagonal. For example, 6 ∗ 3 and 3 ∗ 6 both equal 18. These are called turn-around facts. If you know a fact, you also know its turn-around fact. To support English language learners, ask: Why do you think these facts are called turn-around facts?

Reviewing Other Multiplication ShortcutsAsk students if they know any other multiplication shortcuts. For example:

� 0 times any number equals 0.

� 1 times any number equals the number.

� To find 2 times a number, double the number.

� To find 10 times a number, write 0 after the number.

� Factors Pairs of Prime WHOLE-CLASS ACTIVITY

Numbers(Student Reference Book, p. 8; Math Journal 1, p. 56;

Math Masters, p. 409)

On the board, draw the Fact Triangle in the margin, or fill in the numbers on a transparency of Math Masters, page 409.

Have students identify the product and the factors. Product: 2. Factors: 1, 2. Point out that every Fact Triangle illustrates a factor pair of the product. For example, the Fact Triangle in the margin shows that 1 and 2 make up a factor pair of the product, 2.

Lesson 3�2 165

Adjusting the Activity

Have students find common multiples of 2

and 3 or common multiples of 2, 3, and 5 and

organize them in Venn diagrams. For example:

ELL

Multiplesof 5

Multiplesof 3

Multiplesof 2

2

22

26

10 6 12

30

15

935

14

4 8

16

28

20 18 24

272125

Multiplesof 2

Multiplesof 3

2 4

8 10

14 16

6 3 9

1512

18

AUDITORY � KINESTHETIC � TACTILE � VISUAL

•

1 2

2

∗, /



Then have students complete Problem 1 on journal page 56. They may use their Fact Triangles or a Multiplication/Division Facts Table. Ask students to name the numbers in the table that have only one factor pair. 2, 3, 5, 7, and 11 Explain that there is a name for numbers that have only one factor pair. Ask: Does anyone know what these numbers are called? Prime numbers List the prime numbers on the board along with their factor pairs:

Prime Number Factor Pair

2 1 and 2

3 1 and 3

5 1 and 5

7 1 and 7

11 1 and 11

Ask students if they notice anything about the factor pairs of the prime numbers. If no one suggests it, point out that each factor pair consists of 1 and the original number. Explain that a counting number is a prime number if it has exactly two factors: 1 and itself.

Next, ask students to name the numbers that are not prime. 4, 6, 8, 9, 10, and 12 Tell students that these are called composite numbers. A composite number is a counting number with more than two factors. Composite numbers have at least two factor pairs.

For more information about prime and composite numbers, students can refer to Student Reference Book, page 8. Ask students to complete journal page 56.

� Reviewing the Models WHOLE-CLASS ACTIVITY

of Multiplication(Student Reference Book, pp. 178A and 178B)

Tell students that thinking about what a multiplication fact means can help them figure out facts they can’t remember. For example, a student who could not remember the answer to 7 ∗ 6 could think about this fact in several ways:

� Equal groups: How many objects are in 7 groups of 6?

� Arrays or area: How many objects are in an array with 7 rows and 6 objects in each row?

� Multiplicative comparison: What number is 7 times as many as 6?

These interpretations are described on Student Reference Book, pages 178A and 178B.

Suggest additional facts and have students record the corresponding questions on their slates. For example:

● 8 ∗ 7 ● 9 ∗ 4 ● 6 ∗ 9

Date Time

Factor Pairs of Prime NumbersLESSON

3�2 8

1. In the table below, list all the factor pairs of each number.

Number Factor Pairs

2 1 and 2

3

4

5

6 1 and 6 2 and 3

7

8

9

10

11

12

2. Name a number in the table above that is not a prime number. Explain how you

know it is not prime.

3. Name at least three prime numbers that are not in the table above.

4. Choose one of your answers from Problem 3. Explain how you know it is a

prime number.

1 and 3

1 and 5

1 and 7

1 and 11

1 and 4; 2 and 2

1 and 8; 2 and 4

1 and 9; 3 and 3

1 and 10; 2 and 5

1 and 12; 2 and 6; 3 and 4

Sample answer: 12; it has three factor pairs: 1 and

12, 2 and 6, and 3 and 4. A prime number has only one factor pair.

Sample answers: 13, 17, 19

Sample answer: 13 is a prime number because its

only factor pair is 1 and 13.

EM3MJ1_G4_U03_53-77.indd 56 1/6/11 10:43 AM

Math Journal 1, p. 56

Student Page


2 Ongoing Learning & Practice

� Playing Name That Number PARTNER ACTIVITY

(Student Reference Book, p. 254; Math Masters, p. 489)

Students play Name That Number to practice representing numbers in different ways. See Lesson 2-2 for additional information.

Ongoing Assessment: Math Masters

Page 489

� Recognizing Student Achievement

Use Math Masters, page 489 to assess students’ ability to use

numerical expressions involving one or more of the basic four arithmetic

operations to give equivalent names for whole numbers. Students are making

adequate progress if they are able to create numerical expressions to name the

target number for two rounds of play. Some students may write numerical

expressions that include parentheses or exponents.


Date Time

Math Boxes LESSON

3 �2

3. Earth is covered by a rocky outer layer called the

crust, which is made up of many elements.

a. Is there more aluminum or silicon in Earth’s crust?

b. What percentage of Earth’s crust is aluminum?

c. Which element makes up most of Earth’s crust?

oxygen

8%

silicon

Oxygen

47%Silicon

28%

Iron, Calcium,

Sodium,

Potassium,

Others

17%

Aluminum

8%

Elements Found in Earth’s Crust(percent by weight)

1. The numbers 28, 35, and 42 are all

multiples of __. Circle the best answer.

A 7

B 4

C 6

D 2

2. Complete the “What’s My Rule?” table

and state the rule.

Rule: �95

9 162–166

in out

236 331

682 777

391 486

938

647 742

A B C D

5. Put these numbers in order from smallest

to largest.

0.6 0.06 0.43 0.9

0.9

0.6

0.43

0.06

32 3390

4. Name as many line segments as you can

in the figure below.

AB��, AC��, AD��, BC��, BD��, CD��

1,033

Math Journal 1, p. 57

Student Page

Lesson 3�2 167

��

�, �

“6 times 7 equals what number?” or

“What number is 6 times as many as 7?”

� Sorting Fact Triangles PARTNER ACTIVITY

(Math Journal 1, inside front cover; Math Masters, p. 409)

Ask students to count the Fact Triangles they stored—there should be 36.

Draw a large Multiplication/Division Fact Triangle on the board, or display a transparency of Math Masters, page 409, with numbers inserted. Remind students that the numbers in the bottom corners of the triangle are factors and that the number under the dot is the product of the two factors. Demonstrate how to use the Fact Triangle by covering the product.

Divide the class into partnerships. As students practice their facts, remind them to sort the Fact Triangles into two piles —“OK” and “Try Again”—as they did with the +, - Fact Triangles in Unit 1.

Use this Fact Triangle session to screen the class to determine which students are proficient with the basic multiplication facts. Students with triangles in the “Try Again” pile will need additional support. Games and Fact Triangles are available to provide opportunities for students to practice these facts. See the Teacher’s Reference Manual for ideas on establishing a game routine in your classroom. Students identified in this initial screening as needing additional support should participate in the 50-Facts Test routine throughout the year. See Lesson 3-3 for more information.

Adjusting the Activity

Encourage the use of tools and strategies,

such as:

� counters or pictures to illustrate facts,

� calculators for skip counting to find

products, and

� the Multiplication/Division Facts Table to

find products.

ELL

AUDITORY � KINESTHETIC � TACTILE � VISUAL



3 Differentiation Options

READINESS PARTNER ACTIVITY

� Making Rectangular Arrays 5–15 Min

(Math Masters, p. 76)

To provide experience with multiplication facts using a concrete model, have students make rectangular arrays with centimeter cubes and record a number model for each array.

EXTRA PRACTICE SMALL-GROUP ACTIVITY

� Playing Buzz and Bizz-Buzz 5–15 Min

(Student Reference Book, p. 234)

To practice naming multiples, have students play Buzz and Bizz-Buzz. Before playing the game, remind students that a whole number is a multiple of each of its factors.

ELL SUPPORT SMALL-GROUP ACTIVITY

� Building a Math Word Bank 5–15 Min

(Differentiation Handbook, p. 140)

To provide language support for multiplication, have students use the Word Bank Template found on Differentiation Handbook, page 140. Ask students to write the term square numbers, draw pictures relating to the term, and write other related words. See the Differentiation Handbook for more information.

LESSON

3�2

Name Date Time

Rectangular Arrays

7

Rectangular arrays can be used to model multiplication facts.

Follow these steps to build arrays with centimeter cubes.

1. Place a deck of number cards (1�10) facedown on the table.

Turn over 2 cards.

◆ Use one card for the number of rows in the array.

◆ Use the other card for the number of cubes in each row.

2. Use centimeter cubes to build the array.

Example:

If and are turned

over, you can make either array:

3. Record some of the arrays you made in the table below.

2

2

4

4

2 rows,

4 cubes per row

4 rows,

2 cubes per row

How many How many cubes How many Number rows? in each row? cubes in all? model

4 2 8 4 º 2 � 8

Math Masters, p. 76

Teaching Master

STUDY LINK

3�2 Multiplication Facts 16 20

Name Date Time

1 6

2

7

8

9

3 3 9

4 8

5

6

14

1 2 3 4 5 7 8 9 10

10 10 40 50 60 70 80 9020 30 100

2 4 6 8 10 12 14 16 18 20

6 12 15 18 21 24 27 30

4 12 16 20 24 28 32 36 40

5 10 15 20 25 30 35 40 45 50

6 12 18 24 30 36 42 48 54 60

7 21 28 35 42 49 56 63 70

8 32 40 48 5616 24 64 72 80

9 36 45 54 63 7218 27 81 90

1 2 3 4 5 6 7 8 9 10º, /

1. Complete the Multiplication/Division Facts Table below.

2. List all the factors of 36.

3. List the factor pairs of 16. and , and , and

4. Name the product of 8 and 7.

5. Name four multiples of 4. , , , 2420168

56

4482161

1, 2, 3, 4, 6, 9, 12, 18, 36

Practice

Sample answers:

6. � 91 � 38 7. � 630 � 242 8. 1,462 � 697 � 76538853

Math Masters, p. 75

Study Link Master

NOTE For practice with

facts through 12 º 12, have

students use the Online Master at

www.everydaymathonline.com

in place of Study Link 3�2.

� Math Boxes 3�2 INDEPENDENTACTIVITY

(Math Journal 1, p. 57)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 3-4. The skill in Problem 5 previews Unit 4 content.

� Study Link 3�2 INDEPENDENTACTIVITY

(Math Masters, p. 75)

Home Connection Students complete a Multiplication/Division Facts Table and name factors, products, and multiples of numbers.


EM3cuG4TLG1 163 U03L02 - Everyday Math · • Find factors and multiples of numbers. [Number and...

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