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Grade 8 SAMPLER
MCAS Mathematics
Student Set
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MCAS Finish Line
MCAS Performance Indicator
Contents
Introduction to MCAS Finish Line Mathematics 8. . . . . . . . . . . . . . . . . . . . . . 5
Understanding Mathematical Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Unit 1: Number Sense
Lesson 1 Integers and Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Lesson 2 Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Lesson 3 Percents and Equivalent Forms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Lesson 4 Comparing Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Lesson 5 Ratios and Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Lesson 6 Factors, Multiples, and Primes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Number Sense Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Unit 2: Operations, Part 1
Lesson 1 Operations with Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Lesson 2 Operations with Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Lesson 3 Operations with Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Lesson 4 Operations with Percents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Operations, Part 1 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Unit 3: Operations, Part 2
Lesson 1 Exponents and Square Roots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Lesson 2 Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Lesson 3 Operation Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Lesson 4 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Operations, Part 2 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Unit 4: Geometry
Lesson 1 Pythagorean Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Lesson 2 Intersecting Lines and Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Lesson 3 Angles of Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Lesson 4 Constructing Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Lesson 5 Solid Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Lesson 6 Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Lesson 7 Congruence and Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Geometry Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Unit 5: Patterns, Relations, and Algebra
Lesson 1 Algebraic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Lesson 2 Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Lesson 3 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Lesson 4 Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Lesson 5 Graphing Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
133
Lesson 7 Relationships Between Two Variables . . . . . . . . . . . . . . . . . . . . . . . 137
Patterns, Relations, and Algebra Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Lesson 6 Slope and Intercepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Unit 6: Measurement
Lesson 1 Units of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Lesson 2 Converting Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Lesson 3 Perimeter and Circumference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Lesson 4 Area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Lesson 5 Surface Area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Lesson 6 Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Measurement Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Unit 7: Data Analysis, Statistics, and Probability
Lesson 1 Data and Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Lesson 2 Box-and-Whisker and Stem-and-Leaf Plots . . . . . . . . . . . . . . . . . . . 177
Lesson 3 Histograms and Circle Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Lesson 4 Scatterplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Lesson 5 Venn Diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Lesson 6 Probability of Compound Events . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Data Analysis, Statistics, and Probability Review. . . . . . . . . . . . . . . . . . . . . . 197
LESSON
Factors, Multiples,
and Primes
6
Indicator
,
8.N.5
The greatest common factor (GCF) of two or more numbers
is the greatest number that is a factor of all the numbers.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 16: 1, 2, 4, 8, 16
The GCF of 12 and 16 is 4.
,
The least common multiple (LCM) of two or more numbers is
the least number that is a multiple of all the numbers.
Multiples of 2: 2, 4, 6, 8, 10, 12, …
Multiples of 3: 3, 6, 9, 12, …
The first 6 prime numbers:
2
Two numbers are relatively prime if their GCF is 1.
Every composite number may be expressed as a product of its
prime factors, factors that are prime numbers.
You can use a factor tree to find the prime factors.
Write the number:
6
Continue until all the factors are prime:
2
2
The prime factorization of 60 is 2 2 3 5.
Using exponents, you can write 60 22 3 5.
Unit 1
7
11
13
The numbers 0 and 1 are
special cases. They do
not have two or more
factors, so they are
neither prime nor
composite.
60 6 10
2 3 2 5 22 3 5
10
3
5
Every factor tree of a
number results in the
same prime factorization.
60
Write any two factors whose
product equals the number:
3
The only even prime
number is 2. All other
even numbers are
composite.
15 and 16 are relatively prime because there is no number
greater than 1 that is a factor of both 15 and 16.
,
To find the multiples of a
number n, multiply n by
1, then by 2, then by 3,
and so on.
24 is divisible by 6.
A number is prime if it has only two factors, itself and 1. A
number that is not prime is composite.
13 is prime because its only factors are 1 and 13.
15 is composite; it has other factors besides 1 and 15.
,
To find the factors of a
number n, find all pairs of
numbers that multiply to
equal n. Then list the
numbers in order.
If a number x is a
multiple of a certain
number n, we say x is
divisible by n.
The LCM of 2 and 3 is 6.
,
Remember—
5
or
60 2 30 2 2 15
2 2 3 5 22 3 5
33
Number Sense
© The Continental Press, Inc. Do not duplicate.
Read each problem. Circle the letter of the best answer.
1 Which of these numbers can be written as
the product of two prime numbers?
A
12
C
14
B
13
D
18
6 Lewis wants to cut this rectangular paper
into the largest possible congruent (equalsized) squares.
16 cm
The correct answer is C. 14 is the product
of 2 7, and both 2 and 7 are prime
numbers. Choices A and D can each be
written as a product in many different ways,
but not as the product of two primes. In
choice B, 13 can only be written as 1 13,
and 1 is not prime.
2 What is the greatest common factor (GCF)
of 15, 20, and 30?
A
1
C
10
B
5
D
15
of 3, 5, and 6?
15
C
30
B
18
D
60
The side length in centimeters of each
square will be the greatest common factor
(GCF) of 16 and 20. What will be the side
length of each square?
A
2 cm
C
8 cm
B
4 cm
D
10 cm
7 A cable television station broadcasts a
3 What is the least common multiple (LCM)
A
20 cm
4 What is the prime factorization of 36?
A
23
C
2 2 32
B
49
D
4 2 92
5 Which set contains only prime numbers?
cooking show once every 4 days and a
home repair show once every 6 days. How
often does the station broadcast the
cooking show and the home repair show
on the same day?
A
once every 12 days
B
once every 18 days
C
once every 24 days
D
once every 48 days
8 Which pair of numbers is relatively prime?
A
3 and 6
A
{2, 3, 4}
B
4 and 10
B
{3, 5, 6}
C
5 and 15
C
{4, 6, 8}
D
8 and 15
D
{5, 7, 11}
34
Unit 1
© The Continental Press, Inc. Do not duplicate.
Number Sense
Read each problem. Write your answers.
9 Ms. Harvey buys flowerpots in stacks of 12. She buys tulip bulbs in
bags of 10. If Ms. Harvey wants to buy the same number of
flowerpots and tulip bulbs, what is the least number of flowerpots
she can buy?
60
Answer: ____________
The number of flowerpots Ms. Harvey buys has to be a multiple of 12. The number of tulip
bulbs she buys has to be a multiple of 10. The least common multiple of 12 and 10 is 60.
10 What is the prime factorization of 120?
Answer: ________________________
11 Explain why the numbers 10 and 21 are relatively prime.
__________________________________________________________________________
__________________________________________________________________________
12 There are between 25 and 30 students in Terence’s math class. It is
not possible to divide the students into 2 or more equal groups. How
many students are there in the math class?
Answer: ____________
13 What is the least common multiple (LCM) of 4, 5, and 8?
Answer: ____________
Unit 1
35
Number Sense
© The Continental Press, Inc. Do not duplicate.
Read the problem. Write your answer for each part.
14 The sieve of Eratosthenes is a method for finding prime numbers
less than 100. It uses a chart like this:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
a. On the chart above, cross out 1. Then find the first prime
number, circle it, and cross out all of its multiples. Repeat
with the next prime number and the next, until only primes
(circled numbers) are left.
Ask Yourself
What is the first prime
number? What are its
multiples?
List all the primes less than 100.
________________________________________________________________________
________________________________________________________________________
b. What was the last number whose multiples you actually needed
to cross out? Explain why.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
36
Unit 1
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Number Sense
5
The Venn diagram shows the number of students at a middle
school who went to the first school dance and/or the second
school dance.
148
185
204
123
1st Dance
2nd Dance
How many students went to the second dance?
A 123
B 204
C 327
D 352
6
The table shows the distances 4 snowboarders jumped in
a contest.
SNOWBOARD JUMP CONTEST
Contestant
Distance Jumped
(in meters)
Adam
6.3
Sean
6
Kate
6.26
Jamal
6
2
7
1
3
Which list shows the distances in order from greatest to least?
1
2
A 6 3 , 6 7 , 6.26, 6.3
1
2
B 6 3 , 6.3, 6 7 , 6.26
2
1
2
1
C 6 7 , 6 3 , 6.26, 6.3
D 6 7 , 6 3 , 6.3, 6.26
Session One
5
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Go On
➧
14 The diagram shows the result of a
13 Look at this photograph.
transformation of 䉭ABC.
y
8
7
6
5
4
3
2
1
–8 –7 –6 –5 –4 –3 –2 –1 0
–1
B –2
–3
–4
–5
–6
–7
A
C –
8
9 in.
12 in.
According to the measurements
marked, which of these is similar in
shape to the photograph above?
A
6 in.
8 in.
B
A
C
1 2 3 4 5 6 7 8 x
Which best describes this
transformation?
B
A reflection across the x-axis
5 in.
B rotation 180° clockwise around the
origin
8 in.
C
C translation 4 units left and 4 units
down
4 in.
D translation 8 units left and 9 units
down
6 in.
D
15 A cat bowl holds 400 milliliters of water.
3 in.
What is the equivalent amount in liters?
A 0.04 L
6 in.
B 0.4 L
C 40,000 L
D 400,000 L
Session One
9
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Go On
➧