Table of Contents
Number and Operation
Lesson 1
IIII Minutes to IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Prime and Composite Numbers
Lesson 2
Gateway to America . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Exponents
Lesson 3
Looking at Lepidoptera . . . . . . . . . . . . . . . . . . . . . . . 17
Order of Operations
Lesson 4
A Perfect 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
LCM and GCF
Lesson 5
A Sticky Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Division with Fractions
Lesson 6A Tale of No Tails . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Multiply with Decimals
Lesson 7Happy Centennial! . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Fractions, Decimals, and Percents
Geometry
Lesson 8M.C. Escher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Angle Sums
Lesson 9
Sue’s Discovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Translations
Lesson 10Flag Mail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Central Angles
Measurement
Lesson 11
La Alhambra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Area of a Parallelogram
Ancient Wonder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Area of a Triangle
Lesson 13
Big Ben . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Circumference
Lesson 14Leaning Tower of Pisa . . . . . . . . . . . . . . . . . . . . . . . 83
Area of a Circle
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Lesson 12
Algebra
Lesson 15
Football Frenzy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Add Integers
Lesson 16Underwater World . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Subtract Integers
Lesson 17
The United Nations . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Translate Verbal Expressions
Lesson 18
Aesop’s Fables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Solve 1-Step Equations
Lesson 19
Read All About It! . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Ratio and Proportion
Data Analysis and Probability
Lesson 20
The 8th Wonder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Circle Graphs
Lesson 21The Stanley Cup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Measures of Central Tendency
Lesson 22Lewis, Clark, and Company . . . . . . . . . . . . . . . . . . 131
Probability of Independent Events
Math Tools
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Sieve of Eratosthenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1
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Perimeter and Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Geometric Figures and Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Fractions, Decimals, and Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Prime and
Composite Numbers
1
IIII Minutes to IV
In ancient Rome, capital letters were used to represent numbers.
These letters—I, V, X, L, C, D, and M—are known today as
Roman numerals. In Roman numerals, the number 4 is written
IV. But on many clock faces, the number 4 is represented by
IIII. Why?
There are many theories. Some people believe that IIII is used
on many clock faces because IV is not wide enough—it would
make the clock face look unbalanced. Others say that the use
of IIII came before the use of IV, and it was never changed on
clocks. Whatever the reason, on many clock faces today, you
will still see IIII instead of IV.
Get Started
One way to express a number is as a product of factors.
Express the numbers below as different products of factors.
Then list all the factors.
6
11
6  1  6
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6  2  3
Factors: 1, 2, 3, 6
Factors:
Factors:
12
15
Factors:
Lesson 1: Prime and Composite Numbers
5
Working with Prime and Composite Numbers
You can use what you know about factors to learn
about prime numbers and composite numbers.
•If a number has only two different factors, one and itself,
it is a prime number. For example, 5 is a prime number
because its only factors are 1 and 5:
515
•If a number has more than two different factors, it is a
composite number. For example, 8 is a composite number
because its factors are 1, 2, 4, and 8:
818
824
•The number 1 is neither prime nor composite. It has only
one factor:
111
Complete the table below. Decide whether each number is prime or composite.
Number
1.
2.
9
1  9, 3  3
Factors
Prime or Composite
1, 3, 9
Composite
13
15
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3.
Products
6
Level F
Practice
Write prime or composite to describe each number below.
Show your work.
Number
4.
5.
6.
7.
8.
9.
Products
Factors
Prime or Composite
21
40
18
19
29
33
It’s a Fact!
Solve a Problem
10. How many prime numbers are there
between 1 and 25? List them and
explain how you found your answer.
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A horizontal line over a Roman numeral meant to multiply that number by 1,000. So the Roman numeral above represents the number 5,000.
Lesson 1: Prime and Composite Numbers
7
Finding Prime and Composite Numbers
A method called the Sieve of Eratosthenes can be used to find
prime numbers less than a given number.
Use the steps below to find the prime numbers less than 36.
STEP 2 Start with 2, which is the
first prime number. Circle 2.
Cross out every second
number after 2, because
these are multiples of 2.
STEP 3 Find the next number that
is not crossed out. This
number, 3, is the next
prime number. Circle 3.
Cross out all the other
multiples of 3. Some numbers
may already be crossed out.
STEP 4 Find the next number
that is not crossed out.
This number, 5, is the
next prime number.
Circle 5. Cross out all the
other multiples of 5.
2
3
4
5
Level F
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
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
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
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
Continue this pattern until all the prime numbers are circled.
8
6
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STEP 1 List whole numbers
between 1 and 36 in
order. Use a chart
like the one at the right.
Show What You Know
Use the number chart below and the steps you learned to
find all the prime numbers less than 50.
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
1.List the prime numbers less than 50:
2.How would you describe the numbers that are crossed
out in the chart? Explain your answer.
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3.Is 57 a prime number? Use the number chart
above and the steps you learned to find out.
On Your Own
On Your Own
Continue the activity above to
find the prime numbers less
than 100. List all the prime
­numbers less than 100.
Lesson 1: Prime and Composite Numbers
9
1
Test Yourself
1. Which shows all the factors of 8?
 1, 2, 4
 1, 8
 1, 8, 16
 1, 2, 4, 8
5. How many prime numbers are
there between 20 and 30?
Explain your answer.
2. What do we call a number that has
only two different factors?
 composite number
 odd number
6. A. List all the factors of 55.
 prime number
B. How many factors does 55 have?
 even number
3. Which of the numbers below is a
prime number?
C. Is 55 prime or composite?
 15
 37
 51
 91
7. Think Back Explain in your own
words what a factor is. Explain what
a multiple is.
 19
 29
 47
 51
10
Level F
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4. Which of the numbers below is a
composite number?