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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�3 169

Additional InformationStudents take and score a practice 50-facts test. They will take a real test in Lesson 3�4. After that, the test

will be offered as an optional Part 3 Extra Practice activity about once per unit. Four versions of the test are

supplied on Math Masters, pages 410–413.

Teacher’s Reference Manual, Grades 4–6 pp. 269–271

Key Concepts and Skills• Rename a fraction as an equivalent

fraction and as a percent. 

[Number and Numeration Goal 5]

• 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 look for patterns in multiplication

facts. A 50-facts test for assessing students’

automaticity with multiplication facts is given.

Key Vocabularypercent

MaterialsMath Journal 1, p. 58 and inside front cover

Study Link 3�2 

Math Masters, p. 410

slate � pen or colored pencil � 

base-10 blocks (optional)

Playing Baseball MultiplicationStudent Reference Book, pp. 231

and 232

Math Masters, p. 460

per partnership: 4 pennies or other

markers, 2 six-sided dice, calculator,

counters (optional) � transparency

of Math Masters, p. 460 (optional)

Students practice multiplication facts.

Math Boxes 3�3Math Journal 1, p. 59

Students practice and maintain skills

through Math Box problems.

Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 3. [Operations and Computation Goal 6]

Study Link 3�3Math Masters, p. 78

Students practice and maintain skills

through Study Link activities.

READINESS

Exploring Skip-Count Patterns on the Hundreds GridMath Masters, p. 79

highlighter, colored pencil, or crayon

Students skip count on a hundreds grid

to identify patterns.

ENRICHMENTCalculating CombinationsMath Masters, p. 80

Students apply multiplication facts and

patterns to solve a combinations problem.

EXTRA PRACTICE

Exploring Prime and Composite NumbersMath Masters, pp. 77 and 403

Students use rectangular arrays to

investigate prime and composite numbers.

EXTRA PRACTICE

Playing Multiplication Top-ItStudent Reference Book, p. 264

Math Masters, p. 506

4 each of number cards 1–10 (from the

Everything Math Deck, if available)

Students practice multiplication facts.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

Multiplication Facts Practice

Objectives To introduce the 50-facts test; and to provide

practice with multiplication facts.

�������

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Getting Started

Math Message Find the 9s multiplication facts in the Multiplication/Division Facts Table on the inside front cover of your journal.

What patterns do you see? Write about them at the top of journal page 58.

Study Link 3�2 Follow-Up Have students determine which factors of 36 are prime.

Mental Math and Reflexes Pose multiplication facts and extended facts. Suggestions:

3 º 2 = 6 7 º 5 = 35 40 º 6 = 240

5 º 4 = 20 8 º 4 = 32 9 º 50 = 450

4 º 3 = 12 9 º 6 = 54 40 º 70 = 2,800

6 º 6 = 36 8 º 7 = 56 80 º 50 = 4,000

170 Unit 3 Multiplication and Division; Number Sentences and Algebra

Patterns in Multiplication FactsLESSON

3�3

Date Time

Math Message

Look at the Multiplication/Division Facts Table on the inside front cover of your journal.

1. Find a pattern in the 9s multiplication facts. Describe the pattern.

Sample answers: When you add the digits of the product

together, the sum is always 9. Halfway down the

column, the ones and tens digits switch places. The

ones digit decreases by one each time you move

down, and the tens digit increases by one.

2. Find a pattern in the 5s multiplication facts. Describe the pattern.

Sample answers: The last digit in the product is always

either 0 or 5. The tens digit is repeated twice as you

move down, then increases by one and repeats

twice again.

3. What other patterns can you find in the multiplication facts? Write about some of them.

Sample answers: The multiples of 3 always have digits

that add up to 3, 6, or 9. The chart is symmetrical on

either side of the square numbers. Multiples of 10 have

zero in the ones place. For the 2s facts, the digit in the

ones place of the product is an even number.

16

EM3MJ1_G4_U03_53-77.indd 58 11/10/10 3:15 PM

Math Journal 1, p. 58

Student Page

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

(Math Journal 1, p. 58; inside front cover)

Have students share their observations about the 9s multiplication facts. These might include the following:

� The sum of the two digits in a 9s product is 9. For example, 9 º 7 = 63 and 6 + 3 = 9.

� As you review the 9s facts in order, the 10s digit increases by 1, and the 1s digit decreases by 1.

� To find 9 times a number, find 10 times the number, and then subtract the original number from the result. For example, to find 9 º 8, think 10 º 8 = 80 and 80 - 8 = 72.

Have students complete journal page 58 and discuss their findings.

� Administering a Multiplication WHOLE-CLASS ACTIVITY

Facts Practice Test(Math Masters, p. 410)

Discuss with students the importance of memorizing multiplication facts:

� It allows you to solve problems you encounter in everyday life. For example, to determine how many cupcakes are in 6 packages with 6 cupcakes per package, you usemultiplication to solve the problem.

� It makes doing math much easier. If you have to stop and think what 7 ∗ 8 is when you are solving a problem, it slows you down. You are more likely to make a mistake or lose track of what you are doing.

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Getting Started

NOTE For Facts Practice Tests

with facts through 12 º 12, see

www.everydaymathonline.com.

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Tell students:

● Today you will practice taking a timed test on the multiplication facts.

● This test will help you measure your automaticity with the facts.

● In the next lesson, you will take a real test.

● Now take out a pencil and a pen or colored pencil.

● The tests will be passed out facedown.

● Do not turn the tests over until I give the signal to begin.

Next explain the procedure for the test.

One-Minute Start● On my signal, turn the tests over and work for one minute

in pencil, answering as many facts as possible. Do not skip any facts.

● Begin at the top of the first (left-most) column, work down that column, and continue at the top of the next column.

Two-Minute Finish● After one minute, I will give another signal. At this signal,

switch from pencil to pen or colored pencil. You will have two more minutes to complete as many facts as possible. Now you may skip facts.

Stop● At the end of three minutes, I will say “Stop.” You must

immediately put down your pen or colored pencil.

● Then you can use your pencil to fill in your name and the date.

Scoring● In the one-minute part of the test, correct answers will be

counted only up to the first fact missed. Answers that come after the first missed fact will not be counted. Therefore, do not skip any problems in this part of the test.

● The three-minute score will include all correct answers, which I will explain later.

Give each student a copy of 50-Facts Test 1 (Math Masters, page 410) facedown. Give the signal to begin, and follow the procedure described above.

Lesson 3�3 171

50-Facts Test 1

Name Date Time

7 º 7 �

5 º 6 �

3 º 8 �

7 º 9 �

0 º 4 �

6 º 6 �

4 º 5 �

3 º 5 �

9 º 5 �

4 º 1 �

2 º 4 �

5 º 9 �

4 º 3 �

9 º 8 �

4 º 7 �

2 º 0 �

4 º 9 �

1 º 0 �

2 º 7 �

8 º 4 �

8 º 2 �

2 º 6 �

4 º 8 �

8 º 6 �

6 º 5 �

6 º 3 �

5 º 8 �

5 º 3 �

7 º 8 �

6 º 4 �

3 º 9 �

7 º 6 �

5 º 5 �

9 º 9 �

7 º 2 �

2 º 9 �

4 º 4 �

8 º 8 �

5 º 7 �

5 º 2 �

9 º 4 �

6 º 9 �

8 º 9 �

7 º 3 �

5 º 4 �

9 º 7 �

9 º 6 �

8 º 7 �

7 º 5 �

3 º 3 � 9

35

56

54

63

20

21

72

54

36

10

35

64

16

18

14

81

25

42

27

24

56

15

40

18

30

48

32

12

16

32

14

0

36

0

28

72

12

45

8

4

45

15

20

36

0

63

24

30

49

1-Minute Score: � � %

3-Minute Score: � � %

10050

10050

Math Masters, p. 410

Teaching Aid Master

NOTE This test will be administered as

a whole-class activity in this lesson and in

Lesson 3-4. It should be used as a screening

tool to help identify any students who have

not yet memorized the multiplication facts.

This test then becomes an optional Part 3

Extra Practice activity that can be used with

students who have been identified in the initial

screening. The 50-Facts Test routine can be

used to show students’ progress over time.

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172 Unit 3 Multiplication and Division; Number Sentences and Algebra

Adjusting the Activity

� Scoring the Practice Test WHOLE-CLASS ACTIVITY

(Math Masters, p. 410)

Students will calculate two scores for the test: a one-minute score and a three-minute score. The one-minute score includes only correct answers in pencil up to the first fact answered incorrectly or skipped. The three-minute score includes all correct answers.

Read the facts and answers so that students can correct their work. In the pencil part of the test, they should draw a line above the first fact they answered incorrectly or skipped. In this first part, a skipped fact counts as incorrect.

Have students record the number of correct answers in one minute (the number of problems above the line drawn), and the total number of correct answers in three minutes, at the bottom of the test. Scores are first recorded as a fraction of the 50 facts—for example, 40 correct would be 40 _ 50 .

Next show students how to rename each score as a percent. Remind them that percent means “per hundred,” so they must rename the first fraction as a fraction whose denominator is 100.For example, the fraction 40 _ 50 can be renamed as 80 _ 100 which meansthat getting 40 correct answers out of 50 is equivalent to getting 80 correct answers out of 100—which is 80 percent (80%).

40 _ 50 = 80 _ 100 = 80%

Do a few sample conversions with the class. Then have students convert their own scores, writing the score as a fraction with a denominator of 100 and then as a percent.

Have students use base-10 blocks to illustrate 80 out of 100, or 80%.

Students cover a flat with 8 longs or 80 cubes.

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

ELL

NOTE The one-minute scoring criterion is

tough, but recall should be fast and error free.

If students are allowed to skip around, then

they can avoid harder facts, thus appearing to

know the facts better than they really do.

Date Time

Math Boxes LESSON

3�3

4. Complete.

a. 3 yd � ft

b. 4 ft � in.

c. 54 in. � ft in.

d. �12� yd � ft in.

e. 17�12� yd � in.630

6164

489

6. Solve mentally or with a paper-and-pencilalgorithm.

a. $10.97 b. $4.56� $15.60 � $2.07

1. Write �, �, or � to make each numbersentence true.

a. 45,699 45,609

b. 67,749 66,749

c. 208,775 200 million

d. 1,000,000 858,192

e. 2 million 20,000,000�

�

�

�

�

2. Number of days it took 10 students to complete their science projects:

6, 4, 10, 11, 8, 6, 14, 9, 3, 12

a. What is the range for this set ofnumbers?

b. What is the median?

8.5

11

3. Make a ballpark estimate. Write a numbermodel to show your strategy.

a. 1,459 � 291

� �

b. 1,381 � 646

� � 7506501,400

1,8003001,500

6 149

181

160 161 34–37

129

73

$26.57 $2.49

�Sample answers:

5. Complete.

a. 20, 35, 50, , ,

Rule:

b. , 68, , 94, , 120

Rule:

c. 58, , , , , �2

Rule: �1210223446

�138155

�15958065

107

Math Journal 1, p. 59

Student Page

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Adjusting the Activity

2 Ongoing Learning & Practice

� Playing Baseball Multiplication PARTNER ACTIVITY

(Student Reference Book, pp. 231 and 232;

Math Masters, p. 460)

Students play Baseball Multiplication to maintain automaticity with multiplication facts.

Have Multiplication/Division Facts Tables, counters to make arrays, and

calculators for skip counting readily available. Refer students to game variations

in the Student Reference Book, page 232.

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 3�3 INDEPENDENTACTIVITY

(Math Journal 1, p. 59)

Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 3-1 and 3-5. The skill in Problem 6 previews Unit 4 content.

Writing/Reasoning Have students write a response to the following: Suppose the measurements given in Problems 4a–4d represent the lengths of four pieces of fabric Suma purchased at a craft store. What is the total number of feet of fabric she purchased? 19 feet What is the total number of inches? 228 inches

Ongoing Assessment: Math Boxes

Problem 3 �Recognizing Student Achievement

Use Math Boxes, Problem 3 to assess students’ ability to estimate reasonable

solutions for whole-number addition and subtraction problems. Students are

making adequate progress if the number models for their ballpark estimates

include “close-but-easier” numbers. Some students may be able to show more

than one possible solution.

[Operations and Computation Goal 6]

� Study Link 3�3 INDEPENDENTACTIVITY

(Math Masters, p. 78)

Home Connection Students complete Multiplication/Division Fact Triangles. Each Fact Triangle gives the factors; students find each product. Students will also solve multiplicative comparison problems.

STUDY LINK

3�3 Fact Triangles

Name Date Time

Complete these Multiplication/Division Fact Triangles.

•

3 8

24

º, /

•

9 6

54•

4 7

28

•

8 2

16•

5 9

45•

6 3

18

Practice

13. Name 4 multiples of 7. 14,

21,

28,

35

14. List all the factors of 18. 1, 2, 3, 6, 9, 18

15. List the factors of 18 that are prime. 2, 3

16. List all the factor pairs of 20.

1 and 20,

2 and 10,

4 and 5

4. 5. 6.

1. 2. 3.

16

Sample answers:

º, / º, /

º, / º, / º, /

Complete the statements.

7. 40 is 4 times as many as 10. 8. 25 is 5 times as many as 5.

9. 48 is 6 times as many as 8. 10. 63 is 9 times as many as 7.

11. 64 is 8 times as many as 8. 12. 42 is 7 times as many as 6 .

EM3MM_G4_U03_072-105.indd 78 11/10/10 1:57 PM

Math Masters, p. 78

Study Link Master

Lesson 3�3 173

LESSON

3�3

Name Date Time

Skip-Count Patterns

1. Start at 0. Skip count by 2s. 2. Start at 0. Skip count by 3s.

Record the pattern. Record the pattern.

3. Start at 0. Skip count by 4s. 4. Start at 0. Skip count by 6s.

Record the pattern. Record the pattern.

5. On the back of this page, write about the skip-count patterns you see in each grid.

03

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03

100999897969594939291

90898887868584838281807978777675747372717069686766656463626160595857565554535251504948474645444342414039383736353433323130292827262524232221201918171615141312111098765421

03

10099989796959493929190898887868584838281807978777675747372717069686766656463626160595857565554535251504948474645444342414039383736353433323130292827262524232221201918171615141312111098765421

03

100999897969594939291

90898887868584838281807978777675747372717069686766656463626160595857565554535251504948474645444342414039383736353433323130292827262524232221201918171615141312111098765421

16

Math Masters, p. 79

Teaching Master

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174 Unit 3 Multiplication and Division; Number Sentences and Algebra

LESSON

3�3

Name Date Time

Calculating Combinations

Super Sweet sells ice-cream sundaes.

Each sundae comes with one scoop

of ice cream and one topping.

1. How many different sundaes that have one scoop of

ice cream and one topping can Super Sweet sell? sundaes

Use an organized list, table, or picture to solve the problem. Show your work.

Sample answer:

20

Ice-Cream Flavors Toppings

chocolate hot fudge

vanilla whipped cream

strawberry sprinkles

cookie dough nuts

fudge swirl

hot fudge whipped sprinkles nutscreamchocolate ✓ ✓ ✓ ✓

vanilla ✓ ✓ ✓ ✓

strawberry ✓ ✓ ✓ ✓

cookie dough ✓ ✓ ✓ ✓

fudge swirl ✓ ✓ ✓ ✓

2. Super Sweet has decided to add butterscotch to the list of available

toppings. How many different sundaes can Super Sweet sell now? sundaes

Explain how you found your answer.

3. Explain how you might use multiplication to solve a problem like this.

ice-cream flavors by the number of toppings.

Sample answer: Multiply the number of

to my table.

Sample answer: I added another column

25

Math Masters, p. 80

Teaching Master

3 Differentiation Options

READINESS INDEPENDENTACTIVITY

� Exploring Skip-Count Patterns 5–15 Min

on the Hundreds Grid(Math Masters, p. 79)

To provide a visual model for understanding multiplication facts, have students color skip-count patterns on the number grid. They then write about the patterns they see in the rows and columns.

Encourage students to think about how they might use skip-count patterns to solve multiplication facts.

ENRICHMENT INDEPENDENTACTIVITY

� Calculating Combinations 5–15 Min

(Math Masters, p. 80)

To apply students’ understanding of multiplication, have them find all possible sundaes that can be made by combining one scoop of ice cream and one topping from a variety of choices.

When solving a combination problem such as this, students count the number of pairs that can be made from two or more groups of objects. Multiplication can be used to solve such problems. The factors are the number of objects in each group; the product is the number of combinations that is possible.

EXTRA PRACTICE PARTNER ACTIVITY

� Exploring Prime and 5–15 Min

Composite Numbers(Math Masters, pp. 77 and 403)

To extend students’ work with factors, have them construct arrays for various numbers to determine if they are prime or composite.

EXTRA PRACTICE PARTNER ACTIVITY

� Playing Multiplication Top-It 5–15 Min

(Student Reference Book, p. 264; Math Masters, p. 506)

To maintain automaticity with multiplication facts, have students play Multiplication Top-It. See Lesson 3-6 for additional information.

NOTE For facts practice through 12 º 12, have students include number cards

11 and 12 when playing Multiplication Top-It.

NOTE For additional

information about solving

combination problems, see

www.everydaymathonline.com.

LESSON

3�3

Name Date Time

Prime and Composite Numbers

7 8

You can use arrays to help you determine whether a counting number is prime

or composite. If there is only one array for a number, the number has only two

factors, so it is a prime number. If two or more arrays can be made for a

number, then it is a composite number.

Example: Two different arrays can be

made for 8.

1, 2, 4, and 8 are factors of 8.

8 is a composite number.

1. On centimeter grid paper, draw as many arrays as you can for each of the following

numbers: 2, 3, 4, 6, 7, 11, 12, 15, 16.

Label each array with a number model and its turn-around fact, as shown in the

examples above.

2. Use the arrays to decide if each number is prime or composite. Write the numbers

on the appropriate line below.

Prime numbers: 2, 3, 7, 11 Composite numbers: 4, 6, 12, 15, 16

3. There are 20 prime numbers that are greater than 11, but less than 100. List

them below.

13, 17, 19, 23, 29, 31, 37, 41, 43, 47,

53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Example: Only one array can be made

for 5.

1 and 5 are factors of 5.

5 is a prime number.

1 º 8 = 8 1 º 5 = 5 5 º 1 = 58 º 1 = 8

4 º 2 = 8

2 º 4 = 8

EM3MM_G4_U03_072-105.indd 77 11/10/10 1:57 PM

Math Masters, p. 77

Teaching Master

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LESSON

3�3

Name Date Time

Prime and Composite Numbers

77

Copyright

© W

right

Gro

up/M

cG

raw

-Hill

7 8

You can use arrays to help you determine whether a counting number is prime

or composite. If there is only one array for a number, the number has only two

factors, so it is a prime number. If two or more arrays can be made for a

number, then it is a composite number.

Example: Two different arrays can be

made for 8.

1, 2, 4, and 8 are factors of 8.

8 is a composite number.

1. On centimeter grid paper, draw as many arrays as you can for each of the following

numbers: 2, 3, 4, 6, 7, 11, 12, 15, 16.

Label each array with a number model and its turn-around fact, as shown in the

examples above.

2. Use the arrays to decide if each number is prime or composite. Write the numbers

on the appropriate line below.

Prime numbers:

Composite numbers:

3. There are 20 prime numbers that are greater than 11, but less than 100. List

them below.

Example: Only one array can be made

for 5.

1 and 5 are factors of 5.

5 is a prime number.

1 º 8 = 8 1 º 5 = 5 5 º 1 = 58 º 1 = 8

4 º 2 = 8

2 º 4 = 8

EM3MM_G4_U03_072-105.indd 77EM3MM_G4_U03_072-105.indd 77 11/10/10 1:57 PM11/10/10 1:57 PM

STUDY LINK

3�3 Fact TrianglesC

opyrig

ht ©

Wrig

ht G

roup/M

cG

raw

-Hill

78

Name Date Time

Complete these Multiplication/Division Fact Triangles.

•

3 8º, /

•

9 6

•

4 7

•

8 2

•

5 9

•

6 3

Practice

13. Name 4 multiples of 7. , , ,

14. List all the factors of 18.

15. List the factors of 18 that are prime.

16. List all the factor pairs of 20.

and , and , and

4. 5. 6.

1. 2. 3.

16

º, / º, /

º, / º, / º, /

Complete the statements.

7. is 4 times as many as 10. 8. is 5 times as many as 5.

9. is 6 times as many as 8. 10. 63 is times as many as 7.

11. is 8 times as many as 8. 12. 42 is 7 times as many as .

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