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LESSON
66
HOMEWORK
PART 1
Review: Estimate the answers to the following problems.
Then solve by hand or use a calculator to find the exact answers.
1.
398
⫹ 447
ᎏᎏ
Estimate: ____
Exact Answer: ____
4. 212
⫻7
ᎏ
Estimate: ____
Exact Answer: ____
2.
12,037
⫺ 9,122
ᎏᎏᎏ
Estimate: ____
Exact Answer: ____
5.
Estimate: ____
Exact Answer: ____
Estimate: ____
Exact Answer: ____
6. 27冄苶2苶,8
苶0苶2苶
3. 52冄苶2苶,4
苶9苶6苶
89
⫻6
ᎏ
Estimate: ____
Exact Answer: ____
PART 2
Tell how many units are in each array. Then, for each problem, draw another array on
your paper with the same number of units but with a different number of rows.
Answer: The array has 12 units.
EXAMPLE
You could draw another
array with 12 units like this:
1.
2.
3.
4.
5.
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Unit 5 Factors, Patterns, and Multiples
263
LESSON
67
HOMEWORK
PART 1
Review: Estimate the answers to the following problems.
Then solve by hand or use a calculator to find the exact answers.
1.
33,201
- 29,976
ᎏᎏᎏ
Estimate: ____
Exact Answer: ____
4. 1,020
⫻9
ᎏᎏ
Estimate: ____
Exact Answer: ____
2.
476
⫹ 329
ᎏᎏ
Estimate: ____
Exact Answer: ____
5. 9冄苶1苶0苶3苶
Estimate: ____
Exact Answer: ____
Estimate: ____
Exact Answer: ____
6. 989
⫻6
ᎏ
Estimate: ____
Exact Answer: ____
3. 29冄苶6苶0苶9苶
PART 2
Tell how many units are in the array. Then draw another array on your paper with the
same number of units but with a different number of rows.
EXAMPLE
Answer: The array has 8 units.
You could draw another array with 8 units like this:
1.
2.
3.
4.
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Unit 5 Factors, Patterns, and Multiples
265
LESSON
68
HOMEWORK
PART 1
Write multiplication problems for the following arrays.
Then tell what numbers are the factors in each problem.
EXAMPLE
Answer: 3 ⴛ 4 ⴝ 12
V
1.
3.
2.
4.
3 and 4 are the factors.
PART 2
Make a table on your paper like the one shown here. For each number in the table, first
write all the multiplication problems. Remember, write facts or multiplication problems
just once. Don’t turn them around. Then write all the factors. Remember, when we write
factors, we don’t write the same number twice. (That means no duplicates.)
EXAMPLE
12
The multiplication problems for 12 are 1 ⴛ 12, 2 ⴛ 6, 3 ⴛ 4.
The factors are 1, 2, 3, 4, 6, and 12.
Number
Multiplication Problems
Factors
8
15
7
25
268
Unit 5 Factors, Patterns, and Multiples
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LESSON
69
HOMEWORK
PART 1
Review: Solve the following basic and extended facts.
Write what X, Y, or Z equals.
4ⴙ6ⴝY
V
You would write: Y ⴝ 10.
4. 8 ⫻ 4 ⫽ Y
5. Z ⫻ 9 ⫽ 18
6. X ⫼ 7 ⫽ 6
1. 9 ⫹ 9 ⫽ X
2. X ⫺ 7 ⫽ 8
3. Z ⫺ 4 ⫽ 7
EXAMPLE
7. 36 ⫼ 9 ⫽ Z
8. 7 ⫹ Y ⫽ 12
9. Y * 8 ⫽ 16
PART 2
List the factors for the following numbers. Draw a factor rainbow to help you find all
the factors in order. Remember: No repeats!
EXAMPLE
List all the factors of 18.
1
2
3
6
9 18
The factors of 18 are 1, 2, 3, 6, 9, and 18.
1.
2.
3.
4.
List all the factors of 3.
List all the factors of 6.
List all the factors of 9.
List all the factors of 24.
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Unit 5 Factors, Patterns, and Multiples
271
PART 3
What is the area of each figure?
1.
2.
3.
4.
272
Unit 5 Factors, Patterns, and Multiples
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Lesson 69 Homework
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LESSON
70
HOMEWORK
PART 1
Review: Solve the following basic and extended facts.
Write your answer in the form X ⫽ ____.
4ⴙ6ⴝX
V
You would write: X ⴝ 10.
4. X ⫺ 40 ⫽ 70
5. X * 9 ⫽ 18
6. X * 90 ⫽ 180
1. 9 ⫹ 9 ⫽ X
2. 90 ⫹ 90 ⫽ X
3. X ⫺ 4 ⫽ 7
EXAMPLE
7. 36 ⫼ 9 ⫽ X
8. 360 ⫼ 90 ⫽ X
9. 360 ⫼ 9 ⫽ X
PART 2
List the factors for the following numbers. Draw a factor rainbow to help you find all
the factors in order. Remember: No repeats!
1. 7
2. 12
3. 14
4. 24
PART 3
Write the list of factors for each of the following numbers. The multiplication problems
for the numbers have been provided for you.
1. 21
2. 27
3. 36
V
V
V
Student Textbook
1 ⫻ 21 ⫽ 21
3 ⫻ 7 ⫽ 21
1 ⫻ 27 ⫽ 27
3 ⫻ 9 ⫽ 27
1 ⫻ 36 ⫽ 36
2 ⫻ 18 ⫽ 36
3 ⫻ 12 ⫽ 36
4 ⫻ 9 ⫽ 36
6 ⫻ 6 ⫽ 36
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Unit 5 Factors, Patterns, and Multiples
275
LESSON
71
HOMEWORK
PART 1
List the factors for the following numbers.
1.
2.
3.
4.
5
14
17
25
PART 2
In each of these lists of numbers, one number is prime. Tell which number is prime.
1.
2.
3.
4.
5.
6.
7.
2, 4, 6, 8
1, 3, 21, 25
4, 8, 16, 31
9, 10, 11, 12
21, 23, 25, 27
33, 35, 37, 39
42, 44, 47, 49
PART 3
In each of these lists of numbers, one number is composite. Tell which number is
composite.
1.
2.
3.
4.
5.
6.
7.
2, 3, 4, 5
19, 20, 23, 29
23, 33, 43, 53
17, 27, 37, 47
49, 59, 19, 29
47, 67, 87, 107
37, 39, 41, 43
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Unit 5 Factors, Patterns, and Multiples
279
LESSON
72
HOMEWORK
PART 1
List the factors for the following numbers.
1.
2.
3.
4.
7
16
21
32
PART 2
In each of these lists of numbers, one number is not prime. It is composite. Tell which
number is composite.
1.
2.
3.
4.
282
3, 4, 5, 7
7, 9, 11, 13
13, 15, 17, 19
19, 23, 25, 29
Unit 5 Factors, Patterns, and Multiples
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PART 3
Area of Rectangles
1. Which of the following rectangles has the biggest area?
2. How much bigger is its area than the area of the smallest rectangle?
A
B
C
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Lesson 72 Homework
283
LESSON
73
HOMEWORK
PART 1
Review: Estimate the answers to the following problems. Then
solve the problems by hand or use a calculator to find the exact
answers.
1.
12,398
⫹ 1,447
ᎏᎏᎏ
Estimate: ____
Exact Answer: ____
4.
16,988
⫺ 9,997
ᎏᎏᎏ
Estimate: ____
Exact Answer: ____
2. 701
⫻3
ᎏ
Estimate: ____
Exact Answer: ____
5.
99
⫻8
ᎏ
Estimate: ____
Exact Answer: ____
3. 6冄苶3苶0苶2苶
Estimate: ____
Exact Answer: ____
6. 5冄苶4苶9苶9苶
Estimate: ____
Exact Answer: ____
PART 2
List all of the factors for the following numbers. The factors for the first numbers have
been filled in for you.
Number
Factors
18
1, 2, 3, 6, 9, 18
22
6
30
13
4
286
Unit 5 Factors, Patterns, and Multiples
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PART 3
Perimeter of Rectangles. You looked at these rectangles in the last lesson. This time,
instead of finding the area, find the perimeter of each rectangle. Then answer the
questions. The squares on the grid have an approximate height of 1 cm and a base of 1 cm.
1. Which of the rectangles has the biggest perimeter?
2. How much bigger is the largest perimeter than the smallest perimeter for these
rectangles?
A
B
C
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Lesson 73 Homework
287
LESSON
74
HOMEWORK
PART 1
Which of the following numbers are not prime?
1
4
7
23
30
100
1,000
PART 2
List all of the factors for the following numbers. The factors for the first number have
been filled in for you.
Number
Factors
10
1, 2, 5, 10
14
16
17
24
28
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Unit 5 Factors, Patterns, and Multiples
291
PART 3
Fill in the missing numbers in these factor trees.
EXAMPLE
32
4
a
8
2
b
4
c
d
The missing numbers are (a) 2, (b) 2, (c) 2, and (d) 2.
24
1.
3
8
a
4
b
27
2.
9
a
3
b
36
3.
4
a
9
b
c
d
42
4.
6
a
c
b
49
5.
a
292
c
Unit 5 Factors, Patterns, and Multiples
b
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Lesson 74 Homework
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LESSON
75
HOMEWORK
PART 1
List all of the factors for the following numbers.
Number
Factors
10
20
30
40
50
PART 2
Fill in the missing numbers in these factor trees.
36
1.
4
a
9
b
c
20
2.
2
10
a
294
d
Unit 5 Factors, Patterns, and Multiples
b
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30
3.
10
a
3
b
60
4.
10
a
6
b
c
d
45
5.
9
a
c
b
25
6.
a
b
PART 3
What is the perimeter of this object? Assume the squares on the grid have a height of 1
cm and a base of 1 cm.
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Lesson 75 Homework
295
LESSON
76
HOMEWORK
PART 1
Review: Pulling out the 10s. Complete the following table.
The first row has been filled in for you.
Number
10s
100s
1,000s
7,000
700 ⫻ 10
70 ⫻ 100
7 ⫻ 1,000
80
90
700
500
6,000
9,000
5,000
8,000
PART 2
Draw prime factor trees for the following numbers. Look back to Lesson 74 if you need help.
1.
2.
3.
4.
Draw the prime factor tree for 15.
Draw the prime factor tree for 27.
Draw the prime factor tree for 22.
Draw the prime factor tree for 12.
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Unit 5 Factors, Patterns, and Multiples
297
PART 3
Read the bar graph. Then answer the questions that follow it.
Sarah Evans is an outstanding player for the Williamsburg Hornets basketball team. The bar
graph shows the points she scored in the last six games.
Points by Evans in 6 Games
60
Number of Points
50
40
30
20
10
0
Game Game Game Game Game Game
1
2
3
4
5
6
Games
QUESTIONS:
1. About how many more points did Sarah score in her highest-point game than in her
lowest-point game?
2. Did Sarah have more total points in her first three games or in her last three games?
3. Let’s say that Sarah’s teammates scored 3 times as many points in Game 5 than Sarah
did. How many points did the teammates score? What was the Hornets’ total score in
that game?
298
Unit 5 Factors, Patterns, and Multiples
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Lesson 76 Homework
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LESSON
77
HOMEWORK
PART 1
Estimate the answers to the following problems. Then solve the
problems by hand or use a calculator to find the exact answers.
1.
1,698
⫹ 2,442
ᎏᎏᎏ
Estimate: ____
Exact Answer: ____
4. 999
⫻5
ᎏ
Estimate: ____
Exact Answer: ____
2.
506
403
⫹ 988
ᎏᎏ
Estimate: ____
Exact Answer: ____
5. 602
⫻6
ᎏ
Estimate: ____
Exact Answer: ____
3. 4冄苶4苶1苶0苶
Estimate: ____
Exact Answer: ____
6. 5冄苶4苶9苶7苶
Estimate: ____
Exact Answer: ____
PART 2
List all of the factors for the following numbers.
Factors
Number
10
12
14
16
18
PART 3
Draw prime factor trees for the following numbers. Look back to Lesson 74 if you need help.
1. Draw the prime factor tree for 18.
2. Draw the prime factor tree for 21.
3. Draw the prime factor tree for 24.
300
Unit 5 Factors, Patterns, and Multiples
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LESSON
78
HOMEWORK
PART 1
Draw all of the arrays for each of the following numbers.
Be sure to label them (number of rows ⫻ number of columns).
1. 12
2. 7
3. 16
4. 21
PART 2
List the factors for the following numbers.
1. 12
2. 7
3. 16
4. 21
PART 3
Draw factor rainbows for the following numbers. Then list the factors for each of the
numbers.
1. 12
2. 7
3. 16
4. 21
PART 4
Tell whether the following numbers are (a) prime or (b) composite. Write (a) or (b) for
your answer.
1. 12
2. 7
3. 16
4. 23
PART 5
Draw prime factor trees for the following numbers.
1. 12
2. 27
304
Unit 5 Factors, Patterns, and Multiples
3. 15
4. 28
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PART 6
Each square in this grid has an approximate base of 1 cm and a height of 1 cm. Find
the area for each of the following objects. Write your answer using square units. Then
find the perimeter for Objects 1 and 2.
1
2
3
4
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Lesson 78 Homework
305
LESSON
79
HOMEWORK
PART 1
Review: Solve the following basic multiplication facts.
1.
2.
3.
4.
5.
6.
7.
8.
5 * 5 ⫽ ____
8 * 7 ⫽ ____
4 * 8 ⫽ ____
3 * 9 ⫽ ____
6 * 9 ⫽ ____
9 * 7 ⫽ ____
5 * 6 ⫽ ____
8 * 3 ⫽ ____
PART 2
Tell which division rule or rules can be used to divide these numbers. Use your calculator
to check your answers.
EXAMPLE
1.
2.
3.
4.
5.
6.
984
Answer: The 2, 3, and 6 rules.
14
93
75
150
366
5,420
PART 3
Think of the dividing rules. Then answer each of the following questions.
1.
2.
3.
4.
5.
310
What is a number that can be divided evenly by 2?
What is a number that can be divided evenly by 3?
What is a number that can be divided evenly by 5?
What is a number that can be divided evenly by 6?
What is a number that can be divided evenly by 10?
Unit 5 Factors, Patterns, and Multiples
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LESSON
80
HOMEWORK
PART 1
List the factors for the following numbers.
1.
2.
3.
4.
36
27
20
45
PART 2
Tell which division rule or rules can be used to divide these numbers.
EXAMPLE
1.
2.
3.
4.
5.
6.
84
Answer: The 2, 3, and 6 rules.
88
222
156
90
105
360
PART 3
Fill in the missing numbers in these prime factor trees.
16
1.
4
a
4
b
c
36
2.
6
a
312
d
6
b
Unit 5 Factors, Patterns, and Multiples
c
d
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49
3.
a
b
27
4.
a
3
b
3
15
5.
a
b
PART 4
Look at the following pairs of shapes. Write at least one way that the shapes in each
pair are alike.
EXAMPLE
Answer: Both shapes have four corners.
1.
2.
3.
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Unit 5 Factors, Patterns, and Multiples
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Lesson 80 Homework
313
LESSON
81
HOMEWORK
PART 1
List the factors for the following numbers.
1.
2.
3.
4.
22
13
28
33
PART 2
Tell which division rule or rules can be used to divide these numbers.
EXAMPLE
1.
2.
3.
4.
5.
6.
80,105
Answer: The 5 rule.
633
12,406
12,408
190
33,875
600
PART 3
Draw a prime factor tree for each of the following numbers.
EXAMPLE
16
Answer:
16
4
2
1.
2.
3.
4.
5.
316
4
2
2
2
20
18
25
12
9
Unit 5 Factors, Patterns, and Multiples
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PART 4
Copy this table onto a sheet of lined paper.
Shapes With
Straight Sides
Shapes With
at Least Four
Corners
Shapes With
Curved Sides
Shapes That
Are Closed
Put the letter of each of the following shapes below in the correct place in the table.
Some of the shapes will be listed in more than one category.
A
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Number Sense
C
D
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E
䊉
Lesson 81 Homework
317
LESSON
82
HOMEWORK
PART 1
List the factors for the following numbers.
1.
2.
3.
4.
45
27
40
60
PART 2
Tell which division rule or rules can be used to divide these numbers.
EXAMPLE
3,672
Answer: The 2, 3, and 6 rules.
1.
2.
3.
4.
5.
6.
750
1,416
955
652
75,000
843
PART 3
Draw a prime factor tree for each of the following big numbers.
200
EXAMPLE
200
10
5
20
2
2
10
2
5
1. 112
2. 210
3. 140
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Unit 5 Factors, Patterns, and Multiples
319
LESSON
83
HOMEWORK
PART 1
List the common factors for the following pairs of numbers.
1. 8 and 10
8
1
2
3
4
5
10
1
2
3
4
5
The common factors are: ____
2. 12 and 14
12
1
2
3
4
5
14
1
2
3
4
5
The common factors are: ____
3. 12 and 15
12
1
2
3
4
5
15
1
2
3
4
5
The common factors are: ____
6
6
7
7
8
8
9
9
10
10
6
6
7
7
8
8
9
9
10
10
11
11
12
12
13
14
6
6
7
7
8
8
9
9
10
10
11
11
12
12
13
14
15
PART 2
Tell which division rule or rules can be used to divide these numbers.
EXAMPLE
663
Answer: The 3 rule.
1. 1,042
2. 963
3. 141
4. 180,000
5. 366
6. 755
PART 3
Draw a prime factor tree for each of the following big numbers.
110
110
10
2
1. 125
2. 130
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11
5
3. 140
4. 145
䊉
EXAMPLE
Number Sense
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5. 150
Unit 5 Factors, Patterns, and Multiples
321
LESSON
84
HOMEWORK
PART 1
List the common factors for the following numbers.
1. 7 and 9
2. 18 and 21
3. 25 and 30
4. 32 and 37
PART 2
Tell which division rule or rules can be used to divide these numbers.
EXAMPLE
984
Answer: The 3 rule.
3. 850
4. 15
1. 10,984
2. 665
5. 36
6. 54
PART 3
Look at the lists of factors for each problem. Tell the greatest common factor (GCF).
EXAMPLE
The factors of 9 are 1, 3, and 9.
The factors of 6 are 1, 2, 3, and 6.
Answer: The GCF of 9 and 6 is 3.
1. The factors of 18 are 1, 2, 3, 6, 9, and 18.
The factors of 21 are 1, 3, 7, and 21.
What is the GCF of 18 and 21?
2. The factors of 25 are 1, 5, and 25.
The factors of 35 are 1, 5, 7, and 35.
What is the GCF of 25 and 35?
3. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
What is the GCF of 24 and 36?
4. The factors of 19 are 1, and 19.
The factors of 23 are 1, and 23.
What is the GCF of 19 and 23?
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Unit 5 Factors, Patterns, and Multiples
325
LESSON
85
HOMEWORK
PART 1
List the common factors for the following numbers.
1. 20 and 25
2. 9 and 13
3. 40 and 50
4. 21 and 22
PART 2
Look at the lists of factors for each problem. Tell the greatest common factor (GCF).
EXAMPLE
The factors of 12 are 1, 2, 3, 4, 6, and 12.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
Answer: The GCF of 12 and 18 is 6.
4.
1. The factors of 9 are 1, 2, 3, and 9.
The factors of 27 are 1, 3, 9, and 27.
What is the GCF of 9 and 27?
2. The factors of 16 are 1, 2, 4, 8, and 16.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 5.
and 24.
What is the GCF of 16 and 24?
3. The factors of 30 are 1, 2, 3, 5, 6, 10, 15,
and 30.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20,
and 40.
What is the GCF of 30 and 40?
The factors of 49 are 1, 7, and 49.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21,
and 42.
What is the GCF of 49 and 42?
The factors of 60 are 1, 2, 3, 4, 5, 6, 10,
12, 15, 20, 30, and 60.
The factors of 70 are 1, 2, 5, 7, 10, 14,
35, and 70.
What is the GCF of 60 and 70?
PART 3
Draw a prime factor tree for each of the following big numbers.
EXAMPLE
95
95
5
1. 99
2. 102
3. 105
328
Unit 5 Factors, Patterns, and Multiples
19
4. 108
5. 200
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LESSON
86
HOMEWORK
PART 1
Draw a prime factor tree for each of the following numbers.
84
EXAMPLE
84
2
42
6
2
1.
2.
3.
4.
5.
7
3
4
16
32
25
125
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Unit 5 Factors, Patterns, and Multiples
331
LESSON
87
HOMEWORK
PART 1
List the common factors for the following numbers.
1. 18 and 20
2. 20 and 22
3. 20 and 25
4. 25 and 30
PART 2
Draw a prime factor tree for each of the following large numbers.
EXAMPLE
63
63
7
9
3
3
4. 190
5. 210
1. 44
2. 108
3. 150
PART 3
Look at the lists of factors for each problem. Tell the greatest common factor (GCF).
EXAMPLE
The factors of 25 are 1, 5, and 25.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
Answer: The GCF of 25 and 30 is 5.
1. The factors of 34 are 1, 2, 17, and 34.
The factors of 36 are 1, 2, 3, 4, 6, 9,
12, 18, and 36.
What is the GCF of 34 and 36?
2. The factors of 50 are 1, 2, 5, 10, 25,
and 50.
The factors of 60 are 1, 2, 3, 4, 5, 6,
10, 12, 15, 20, 30, and 60.
What is the GCF of 50 and 60?
334
Unit 5 Factors, Patterns, and Multiples
3. The factors of 87 are 1 and 87.
The factors of 93 are 1, 3, 31, and 93.
What is the GCF of 87 and 93?
4. The factors of 55 are 1, 5, 11, and 55.
The factors of 65 are 1, 5, 13, and 65.
What is the GCF of 55 and 65?
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LESSON
88
HOMEWORK
PART 1
Tell what division rule or rules can be used to divide the
following numbers. Remember, the division rules are (a) divide by 2,
(b) divide by 3, (c) divide by 5, (d) divide by 6, and (e) divide by 10.
1. 117
2. 324
3. 2,020
4. 4,113
PART 2
Find the area of the following squares, rectangles, and triangles. Remember, the formulas are:
Area of a square ⫽ base ⫻ height
Area of a rectangle ⫽ base ⫻ height
Area of a triangle ⫽ half of the base ⫻ height
1.
2.
2 units
W 8 units V
X
5 units
W 6 units V
3.
Y
X
6 units
W 6 units V
338
Y
Unit 5 Factors, Patterns, and Multiples
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PART 3
Draw prime factor trees for the following large numbers.
1. 125
2. 200
3. 750
PART 4
Find the common factors for the following numbers.
1. 6 and 8
2. 3 and 4
3. 6, 9, and 12
PART 5
Find the greatest common factor for the following numbers.
1. 6 and 8
2. 3 and 4
3. 6, 9, and 12
PART 6
Tell which of the following shapes are congruent.
A
B
F
C
G
D
H
E
I
PART 7
Find the greatest common factor for the following numbers using the prime
factorization method.
1. 125 and 150
2. 200 and 400
3. 750 and 900
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䊉
Lesson 88 Homework
339
LESSON
89
HOMEWORK
PART 1
List the common factors for the following numbers.
1.
2.
3.
4.
12 and 15
20 and 24
32 and 36
42 and 49
PART 2
Which numbers in this list are odd?
13
15
26
103
158
279
388
411
527
1,987
525
694
4,289,002
PART 3
Which numbers in this list are even?
28
42
69
116
327
448
PART 4
Without solving these addition problems, tell whether the answers are going to be odd
or even. Check with a calculator.
39 ⴙ 42 ⴝ ?
EXAMPLE
Answer: The answer will be odd. An odd plus an even is an odd.
Check on calculator: 39 ⴙ 42 ⴝ 81. Yes, it’s odd.
1.
2.
3.
4.
64 ⫹ 82 ⫽ ____
129 ⫹ 377 ⫽ ____
468 ⫹ 599 ⫽ ____
1,987 ⫹ 9,888 ⫽ ____
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Unit 5 Factors, Patterns, and Multiples
343
PART 5
Without solving these multiplication problems, tell whether the answers are going to be
odd or even. Check with a calculator.
EXAMPLE
39 * 42 ⴝ ?
Answer: The answer will be even. An odd times an even is always
even.
Check on calculator: 39 * 42 ⴝ 1,638. Yes, it’s even.
1.
2.
3.
4.
344
78 * 44 ⫽ ____
137 * 141 ⫽ ____
528 * 603 ⫽ ____
5,111 * 8,222 ⫽ ____
Unit 5 Factors, Patterns, and Multiples
䊉
Lesson 89 Homework
Student Textbook
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Number Sense
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LESSON
90
HOMEWORK
PART 1
Solve the following basic multiplication facts.
1.
2.
3.
4.
5.
6.
4 ⫻ 4 ⫽ ____
8 ⫻ 8 ⫽ ____
5 ⫻ 5 ⫽ ____
6 ⫻ 6 ⫽ ____
9 ⫻ 9 ⫽ ____
2 ⫻ 2 ⫽ ____
PART 2
Which of the following numbers are square numbers?
3
4
7
9
12
16
25
32
36
49
56
81
PART 3
Draw the following arrays using rectangles.
1.
2.
3.
4.
3 ⫻ 3 array
4 ⫻ 4 array
5 ⫻ 5 array
2 ⫻ 2 array
PART 4
There is one square number in each of the following groups of numbers. Which number is it?
1.
2.
3.
4.
29, 39, 49, 59
61, 62, 63, 64
12, 14, 16, 18
25, 26, 27, 28
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Unit 5 Factors, Patterns, and Multiples
347
LESSON
91
HOMEWORK
PART 1
Review: Solve the following basic multiplication facts.
1.
2.
3.
4.
5.
6.
3 ⫻ 3 ⫽ ____
7 ⫻ 7 ⫽ ____
1 ⫻ 1 ⫽ ____
4 ⫻ 4 ⫽ ____
6 ⫻ 6 ⫽ ____
10 ⫻ 10 ⫽ ____
PART 2
Which of the following numbers are square numbers?
11
12
16
24
25
37
48
64
81
111
121
144
PART 3
Fill in the missing numbers in the following number sentences. Label your answers with
the letters provided.
a ⫹ 3 ⫽ ____
b
1 ⫻ 1 ⫽ ____
c ⫹ 5 ⫽ ____
d
2 ⫻ 2 ⫽ ____
e ⫹ 7 ⫽ ____
f
3 ⫻ 3 ⫽ ____
g ⫹ 9 ⫽ ____
h
4 ⫻ 4 ⫽ ____
i ⫹ 11 ⫽ ____
j
5 ⫻ 5 ⫽ ____
k ⫹ 13 ⫽ ____
l
6 ⫻ 6 ⫽ ____
350
Unit 5 Factors, Patterns, and Multiples
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Number Sense
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LESSON
92
HOMEWORK
PART 1
Which of the following numbers are square numbers?
15
25
35
49
64
81
100
112
121
134
144
PART 2
Use boxes to draw each of these triangular numbers.
EXAMPLE
3
Answer:
1. 6
2. 10
3. 15
PART 3
Fill in the missing numbers in the following number sentences. Label your answers with
the letters provided.
a ⫹ 1 ⫽ ____
b
3 ⫻ 8 ⫽ ____
c ⫹ 1 ⫽ ____
d
6 ⫻ 8 ⫽ ____
e ⫹ 1 ⫽ ____
f
10 ⫻ 8 ⫽ ____
354
Unit 5 Factors, Patterns, and Multiples
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Number Sense
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LESSON
93
HOMEWORK
PART 1
Review: Fill in the missing numbers in the following number
sentences. Notice that we are pulling out the 10s.
1. 50 ⫽ ____ ⫻ 10
2. 400 ⫽ ____ ⫻ 10 ⫻ 10
3. ____ ⫻ 10 ⫽ 70
4. 10 ⫻ 10 ⫻ 10 ⫻ ____ ⫽ 8,000
PART 2
Rewrite each of the following using exponents.
10 ⴛ 10 ⴛ 10 ⴝ ____
EXAMPLE
1. 10 ⫻ 10 ⫽ ____
2. 5 ⫻ 5 ⫻ 5 ⫽ ____
Answer: 103
3. 7 ⫻ 7 ⫽ ____
4. 10 ⫻ 10 ⫻ 10 ⫻ 10 ⫻ 10 ⫽ ____
PART 3
Rewrite each of the following as a multiplication string.
103 ⴝ ____
EXAMPLE
1. 102 ⫽ ____
2. 23 ⫽ ____
Answer: 103 ⴝ 10 ⴛ 10 ⴛ 10
3. 33 ⫽ ____
4. 106 ⫽ ____
PART 4
Draw prime factor trees for the following numbers. Then rewrite the numbers using exponents.
100 ⴝ 2 ⴛ 2 ⴛ 5 ⴛ 5, or 22 ⴛ 52
100
2
EXAMPLE
1.
2.
3.
4.
358
49
50
63
81
Unit 5 Factors, Patterns, and Multiples
50
2
25
5
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䊉
Number Sense
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LESSON
94
HOMEWORK
PART 1
Review: Fill in the missing numbers in the following number
sentences. Notice that we are pulling out the 10s.
1.
2.
3.
4.
90 ____ 10
500 ____ 10
____ 10 700
10 10 10 ____ 9,000
PART 2
Rewrite each of the following using exponents.
10 10 10 ____
Answer: 103
EXAMPLE
1.
2.
3.
4.
2 2 2 2 ____
3 3 3 3 3 3 ____
5 5 5 ____
10 10 10 10 10 10 10 10 10 10 10 ____
PART 3
Use the lists of multiples in each problem to identify common multiples for the numbers
given.
EXAMPLE
What are some common multiples of 6 and 3?
6
12
18
24
Multiples of 6
3 6 9 12 15 18 21 24 27
Multiples of 3
Answer: 6, 12, 18, and 24
1. What are some common multiples of 5 and 10?
Multiples of 5
5 10 15 20 25 30
Multiples of 10
10
20
30
362
Unit 5 Factors, Patterns, and Multiples
35
40
40
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Number Sense
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2. What are some common multiples of 4 and 8?
Multiples of 4
4
8 12 16 20 24
Multiples of 8
8
16
24
28
3. What are some common multiples of 6 and 10?
Multiples of 6
6
12
24 30
Multiples of 10
10
20
30
36
4. What are some common multiples of 2, 4, and 8?
Multiples of 2
2
4
6
8 10 12 14
Multiples of 4
4
8
12
Multiples of 8
8
32
32
42
48
40
16
16
16
54
50
60
60
18
PART 4
For each problem, tell whether the drawing shows a slide, a flip, or a turn.
EXAMPLE
V
Answer: a slide
1.
2.
3.
V
V
V
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Lesson 94 Homework
363
LESSON
95
HOMEWORK
PART 1
Practice counting by different numbers. Fill in the missing numbers in
the lists for each problem. Use the letters provided to label your answers.
1.
2.
3.
4.
Counting by 6s
Counting by 8s
Counting by 9s
Counting by 10s
V
V
V
V
a , 30, ____
b , 42, 48, ____
c
6, 12, 18, ____
a , 40, ____
b , 56, 64, ____
c
8, 16, 24, ____
a , 27, ____
b , 45, 54, ____
c , 72, 81
9, ____
a , 50, ____
b , 70, 80, ____
c
10, 20, 30, ____
PART 2
Find the least common multiple (LCM) for the pairs of numbers in each problem.
1. What is the least common multiple of 4 and 8?
4
4
8 12 16 20 24 28 32
8
8 16 24 32 40 48 56 64
36
72
40
80
2. What is the least common multiple of 7 and 9?
7
7 14 21 28 35 42 49 56
9
9 18 27 36 45 54 63 72
63
81
70
90
3. What is the least common multiple of 5, 6, and 10?
5
5 10 15 20 25 30 35 40 45 50
6
6 12 18 24 30 36 42 48 54 60
10 10 20 30 40 50 60 70 80 90 100
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Unit 5 Factors, Patterns, and Multiples
367
PART 3
Tell which of these objects are drawn with a line of symmetry. Then redraw the other
objects in a way that shows symmetry.
EXAMPLE
The following object is an example of a drawing that does not
show symmetry.
Here’s how I would draw it showing symmetry.
368
A.
C.
B.
D.
Unit 5 Factors, Patterns, and Multiples
䊉
Lesson 95 Homework
Student Textbook
䊉
Number Sense
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LESSON
96
HOMEWORK
PART 1
Review: Practice counting by different numbers. Fill in the missing
numbers in the lists for each problem. Use the letters provided to
label your answers.
1.
2.
3.
4.
Counting by 5s
Counting by 6s
Counting by 7s
Counting by 11s
V
V
V
V
a , 25, ____
b , 35, 40, ____
c
5, 10, 15, ____
a , 30, ____
b , 42, 48, ____
c
6, 12, 18, ____
a , 21, ____
b , 35, 42, ____
c , 56, 63
7, ____
a , 55, ____
b , 77, 88, ____
c
11, 22, 33, ____
PART 2
Find the least common multiple (LCM) for the pairs of numbers in each problem.
372
1. What is the least common multiple of 4 and 2?
4
4
8 12 16 20 24 28 32
2
2
4
6
8 10 12 14 16
36
18
40
20
2. What is the least common multiple of 6 and 7?
7
7 14 21 28 35 42 49 56
6
6 12 18 24 30 36 42 48
63
54
70
60
3. What is the least common multiple of 6 and 9?
6
6 12 18 24 30 36 42 48
9
9 18 27 36 45 54 63 72
54
81
60
90
Unit 5 Factors, Patterns, and Multiples
Student Textbook
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Number Sense
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LESSON
97
HOMEWORK
PART 1
Find the least common multiple (LCM) for the pairs of numbers
in each problem.
1. What is the least common multiple of 3 and 8?
3
3
6
9 12 15 18 21 24
8
8 16 24 32 40 48 56 64
27
72
30
80
2. What is the least common multiple of 6 and 8?
6
6 12 18 24 30 36 42 48
8
8 16 24 32 40 48 56 64
54
72
60
80
PART 2
For each problem, tell whether the drawing shows a slide, a flip, or a turn.
V
EXAMPLE
Answer: a slide
1.
V
2.
V
3.
V
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Unit 5 Factors, Patterns, and Multiples
375
LESSON
98
HOMEWORK
PART 1
Find the least common multiple (LCM) for the numbers
in each problem.
1. What is the least common multiple of 10 and 12?
10 10 20 30 40 50 60 70 80 90 100
12 12 24 36 48 60 72 84 96 108 120
2. What is the least common multiple of 7 and 11?
7
7 14 21 28 35 42 49 56
11 11 22 33 44 55 66 77 88
63 70 77
99 110
84
91
98
3. What is the least common multiple of 6, 9, and 12?
6
6 12 18 24 30 36 42 48 54 60 66 72 78 84
9
9 18 27 36 45 54 63 72 81 90 99 108 117
12 12 24 36 48 60 72 84 96 108 120
PART 2
For each problem, tell whether the object is symmetrical around a line of symmetry or a
point of rotation.
378
1.
3.
2.
4.
Unit 5 Factors, Patterns, and Multiples
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PART 3
Look at the pairs of pictures in each problem. Tell which picture in each pair shows a
line of symmetry.
(a)
EXAMPLE
(b)
Answer: (a) shows symmetry.
1. (a)
(b)
2. (a)
(b)
3. (a)
(b)
4. (a)
(b)
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䊉
Lesson 98 Homework
379
LESSON
99
HOMEWORK
PART 1
Find the least common multiple (LCM) for the pairs of numbers
in each problem.
1. What is the least common multiple of 20 and 40?
20 20 40 60 80 100 120 140 160 180 200
40 40 80 120 160 200
2. What is the least common multiple of 8 and 12?
8
8 16 24 32 40 48 56 64 80 88 96 104 112
12 12 24 36 48 60 72 84 96 108 120 132
PART 2
Using what you have learned in this unit, describe the number in each problem in at
least four different ways.
EXAMPLE
1.
2.
3.
4.
382
16
Answer: 16 can be divided by 2.
16 is even.
16 is composite.
16 is a square number.
42 ⴝ 16.
25
100
237
558
Unit 5 Factors, Patterns, and Multiples
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Number Sense
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LESSON
100
HOMEWORK
PART 1
Without solving these addition problems, tell whether the
answers are going to be odd or even. Check with a calculator.
1. 14 32 ____
2. 429 577 ____
3. 868 399 ____
4. 6,987 2,888 ____
PART 2
Without solving these multiplication problems, tell whether the answers are going to be
odd or even. Check with a calculator.
1. 34 * 52 ____
2. 429 * 177 ____
3. 368 * 299 ____
4. 3,987 * 4,888 ____
PART 3
There is one square number in each of the following groups of numbers. Which number is it?
1. 24, 25, 26, 27
2. 16, 17, 18, 19
3. 47, 48, 49, 50
4. 78, 79, 80, 81
PART 4
Fill in the missing numbers in the following number sentences. Use the letters provided
to label your answers.
a 13 ____
b
6 6 ____
c 15 ____
d
7 7 ____
386
Unit 5 Factors, Patterns, and Multiples
e 17 ____
f
8 8 ____
g 19 ____
h
9 9 ____
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Number Sense
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PART 5
Use squares to draw the following triangular numbers.
EXAMPLE
3
Answer:
1. 6
2. 10
3. 15
PART 6
Rewrite each of the following using exponents.
10 10 10 ____
Answer: 103
1.
2.
3.
4.
5.
EXAMPLE
7 7 ____
3 3 3 ____
5 5 ____
10 10 10 10 10 ____
2 2 2 2 2 2 2 2 ____
PART 7
Use the lists of multiples in each problem to identify common multiples for the numbers
given.
1. What are some common multiples of 5 and 10?
Multiples of 5
5 10 15 20 25 30
Multiples of 10
10
20
30
35
40
40
2. What are some common multiples of 4 and 8?
Multiples of 4
4
8 12 16 20 24
Multiples of 8
8
16
24
28
32
32
Student Textbook
Number Sense
Unit 5 Factors, Patterns, and Multiples
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Lesson 100 Homework
387