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Master Arizona’s 15 most challenging mathematics skills with
SkillBridge. With lesson topics chosen based on actual state test
data, SkillBridge offers help in the skills that truly are the most
troublesome. As students move through each lesson, they are
equipped with guidance and connections that allow them to show
independent skill mastery by the end of the lesson. Arizona
references in each lesson offer a unique and familiar
point of entry into difficult skills.
Mathema
tics
Arizona’s 15 most challenging skills
in mathematics, grade 7
• Scientific Notation
• Sequences
• Fractions
• Translations and Reflections
• Adding and Subtracting
Integers
• Rotations
• Multiplying and Dividing
Integers
• Three-Dimensional Figures
• Percents
• Solving Problems
• Evaluating Expressions
• Proportions
• Data Analysis
• Circle Graphs
• Vertex-Edge Graphs
London Bridge over Lake Havasu, Arizona
Catalog Number AZB2066W1
ISBN 0-7836-6520-2
P.O. Box 2180
Iowa City, Iowa 52244-2180
50599
STUDENT NAME
PHONE: 800-776-3454
FAX: 877-365-0111
www.BuckleDown.com
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Table of Contents
Scientific Notation (S1.C2.PO11).................................................. 4
Fractions (S1.C2.PO3, S1.C2.PO4).................................................... 8
Adding and Subtracting Integers (S1.C2.PO1, S1.C2.PO2)........... 12
Multiplying and Dividing Integers (S1.C2.PO5, S1.C2.PO6).......... 16
Percents (S1.C2.PO10)................................................................ 20
Solving Problems (S1.C2.PO3).................................................. 24
Evaluating Expressions (S3.C3.PO1, S3.C3.PO2).......................... 28
Sequences (S3.C1.PO1–S3.C1.PO3, S3.C2.PO1).................................. 32
Translations and Reflections (S4.C2.PO2)............................... 36
Rotations (S4.C2.PO1, S4.C2.PO2).................................................. 40
Proportions (S4.C4.PO8)............................................................ 44
AZ7 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW.
Three-Dimensional Figures (S4.C1.PO2).................................. 48
Data Analysis (S2.C1.PO6). ....................................................... 52
Circle Graphs (S2.C1.PO4, S2.C1.PO5)........................................... 56
Vertex-Edge Graphs (S2.C4.PO1).............................................. 60
Acknowledgments................................................................ 64
S1.C2.PO11
AZ
At the beginning of each lesson, you will see a box with the shape of
Arizona and a performance objective code in it. This code tells you
what is being covered in the lesson.
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S1.C2.PO11
AZ
Scientific Notation
When numbers are very large, they can be hard to
read and use in math problems. Such numbers are
easier to manage when they are written in scientific
notation.
For example, 3,800 is written as 3.8 3 103 in
scientific notation.
Example 1
Write 1.287 3 1010 in standard form.
The exponent tells you how many places to move
the decimal point to the right. Add zeros to the
end of the number until you get to the decimal
point.
1.2870000000
Add commas in the correct places to write the
number in standard form.
1.287 3 1010 5 12,870,000,000
The Dorrance Planetarium is
part of the Arizona Science
Center in Phoenix. When
scientists study the large
distances between objects
in space, they often express
numbers in scientific notation.
Build A Bridge 1
Write each number in
standard form.
A: 8.4 3 106
B: 3.01 3 105
AZ7 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW.
Scientific notation is a way to write large numbers
using exponents and powers of 10. In scientific
notation, a number is expressed as the product of a
factor and a power of 10. The factor must be greater
than or equal to 1 and less than 10.
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Example 2
What is 295,000,000 written in scientific notation?
Build A Bridge 2
A 2.95 3 107
B 29.5 3 107
Write each number in
scientific notation.
C 295 3 106 D 2.95 3 108
A: 71,000
Move the decimal point so that only one digit is to
the left of the decimal. Remember, the factor
needs to be greater than or equal to 1 and less
than 10.
B: 49,000,000
295,000,000.
Count the number of decimal places that the
decimal point was moved. This tells you how
many powers of 10 you will need.
2.95000000
Write the factor without any zeros on the end.
Multiply by the correct power of 10.
2.95 3 108
Choice D is the correct answer.
AZ7 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW.
Example 3
The 2006 U.S. Census Bureau estimated the
population of New York to be more than
19.3 million people. Write 19.3 million in
scientific notation.
Build A Bridge 3
Write 214.5 million in
scientific notation.
First, write 19.3 million in standard form.
19.3 million is written 19,300,000.
Write the factor as a decimal greater than or
equal to 1 and less than 10. Then, write the power
of 10 the decimal point moved.
The factor is 1.93. The decimal moved 7 places.
So the power of 10 is written as 107.
19.3 million is 1.93 3 107 in scientific notation.
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Guided PractiCE
1 What is the purpose of writing a number in scientific notation?
2 How is a number expressed in scientific notation?
3 Describe the conditions on the factor of a number written in scientific notation.
4 What does the exponent tell you in a number written in scientific notation?
5 609,000,000,000 6 4,702,000,000 For Numbers 7 and 8, write each number in standard form.
7 7.53 3 108
8 9.018 3 106
9 A retailer reports that teenagers spend $6,320,000,000 on clothes each year.
Which shows this number in scientific notation?
A 63.2 3 108
B 6.32 3 109
C 632 3 107
D 6.32 3 108
AZ7 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW.
For Numbers 5 and 6, write each number in scientific notation.
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Practice
For Numbers 1–4, write each number in scientific notation.
1 514,000 2 3,921,000,000 3 280,000,000 4 76,040,000,000,000 For Numbers 5–8, write each number in standard form.
5 1.3 3 107 6 4.68 3 1010 7 8.02 3 105 8 9.275 3 108 9 A lake holds about 2.4 3 104 cubic kilometers of water. Which shows this
amount in standard form?
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A 24,000,000
B 240,000
C 24,000
D 2,400
10 New York City’s public transit system transports 8.5 million people every day.
Which shows this number in scientific notation?
A 8.5 3 107
B 8.5 3 106
C 8.5 3 105
D 85 3 106
11 Liam visited the Dorrance Planetarium at the Arizona Science Center. He
learned about constellations that are 27,000 light-years away from Earth.
Which shows this measurement in scientific notation?
A 2.7 3 105
B 27 3 103
C 2.7 3 103
D 2.7 3 104
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