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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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