Math Book A

305 Pages·2011·14.58 MB·English

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Math in Focus™: Singapore Math by Marshall Cavendish
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Courses 1–3 for grades 6 – 8 is a math program from Singapore o
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created for U.S. classrooms, aligned with Common Core State u
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Standards. Marshall Cavendish math programs have contributed to ™
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Singapore’s consistent top performance in international studies S
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since 1995. g
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In the Student Book r
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• Learn introduces concepts through modeling in an engaging
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and easy to understand format. t
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• Guided Practice allows the teacher to work through
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exercises with students and assess understanding. M
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• Practice provides independent opportunities for reinforcing rs
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and enhancing concepts. a
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• Hands-On and Technology Activities reinforce ideas, C
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concepts, and problem-solving strategies through interactive v
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learning. n
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• Math Journal opportunities are found within the Practice to s
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reflect, explain, construct arguments, and justify reasoning.
• Brain @ Work provides opportunities at the end of each
chapter for concept application and critical thinking.
• Chapter Wrap Up provides a visual content map for each
chapter. Connections between the key concepts are illustrated.
• Chapter Review/Test offers cumulative practice on the
concepts and skills instructed in each chapter in preparation
for the assessment.
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© 2012 Marshall Cavendish International (Singapore) Private Limited
Published by Marshall Cavendish Education
An imprint of Marshall Cavendish International (Singapore) Private Limited
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Website: www.hmheducation.com/mathinfocus
First published 2012
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Marshall Cavendish and Math in Focus™ are trademarks of Times
Publishing Limited.
Math in FocusTM Course 1 Student Book A
ISBN 978-0-547-55936-0
Printed in United States of America
1 2 3 4 5 6 7 8 1401 17 16 15 14 13 12 11
4500291302 A B C D E
(M)MIF6A_SE_copyright.indd 1 3/11/11 1:19 PM
Course 1A Contents
CHAPTER
Positive Numbers
1
and the Number Line
Chapter Opener How has the number system changed? . . . . . . . . . . . . . . . . . . . . . . 2
Big Idea Whole numbers, fractions, and decimals are numbers that can be
represented in several ways .
Recall Prior Knowledge • Finding factors of a whole number • Finding
multiples of a whole number • Identifying prime numbers • Using order of
3
operations to simplify a numerical expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 The Number Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Learn • Represent numbers on a number line • Write statements of
inequality comparing two whole numbers using the symbols > and <
• Represent fractions, mixed numbers, and decimals on a horizontal number
line • Represent fractions, mixed numbers and decimals on a vertical number
line • Write statements of inequality for two fractions or two decimals using
the symbols > and < • Compare numbers in different forms
In Student Book A and Student Book B, look for
Practice and Problem Solving Assessment Opportunities
• Practice in every lesson • Quick Check at the beginning of every
• Real-world and mathematical problems in chapter to assess chapter readiness
every chapter • Guided Practice after every Learn to
assess readiness to continue lesson
• in every chapter
• Chapter Review/Test in every chapter to
• exercises
review or test chapter material
• Cumulative Reviews four times during
the year
iii
1.2 Prime Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Learn • Identify composite numbers • Write a composite number as a
product of its prime factors
1.3 Common Factors and Multiples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Learn • Identify the common factors of two whole numbers • Find the
greatest common factor of two whole numbers • Use the greatest common
factor with the distributive property • Find the common multiples of two
numbers • Find the least common multiple of two whole numbers
Hands-On Activity Find the Common Factors and the Greatest Common
Factor of Two Numbers
1.4 Squares and Square Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Learn • Find a square of a whole number • Find a square root of a perfect
square
1.5 Cubes and Cube Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Learn • Find a cube of a whole number • Find a cube root of a perfect cube
• Evaluate numerical expressions that contain exponents
Brain @ Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Chapter Wrap Up • Concept Map • Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
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CHAPTER
Negative Numbers
2
and the Number Line
Chapter Opener How cold is an iceberg? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Big Idea Negative numbers are the opposites of positive numbers. For every positive
number, there is a corresponding negative number .
Recall Prior Knowledge • Representing positive numbers on a number line
• Writing statements of inequality for two given positive numbers using the
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symbols > and < . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Negative Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Learn • Recognize the use of positive and negative numbers in real-world
situations • Represent negative numbers on a number line • Write statements
of inequality using the symbols > and < • Interpret and explain statements of
order for positive and negative numbers in real-world situations
Hands-On Activity Represent Negative Numbers on a Number Line and
Compare Two Negative Numbers Using > and <
2.2 Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Learn • Write the absolute value of a number • Use absolute value to
interpret real-world situations
Brain @ Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Chapter Wrap Up • Concept Map • Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
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CHAPTER
Multiplying and Dividing
3
Fractions and Decimals
Chapter Opener How much do you know about the construction of your home? . . . . 62
Big Idea Whole number concepts can be extended to fractions and decimals when
more precise calculations are needed .
Recall Prior Knowledge • Adding and subtracting decimals • Expressing
improper fractions as mixed numbers • Expressing mixed numbers as improper
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fractions • Multiplying fractions by fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Dividing Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Learn • Divide a whole number by a unit fraction • Dividing a whole number
by a proper fraction • Divide a fraction by a fraction • Divide a fraction by an
improper fraction or a mixed number
Hands-On Activities • Dividing Whole Numbers by a Fraction • Dividing
Fractions • Dividing Fractions with a Remainder • Division Involving Whole
Numbers and Fractions
3.2 Multiplying Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Learn • Multiply tenths by a whole number • Multiply hundredths by a whole
number • Multiply tenths by tenths • Multiply decimals by decimals with one
decimal place • Multiply decimals with one or more decimal places
Hands-On Activity Finding the Factors of a Decimal
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3.3 Dividing Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Learn • Divide a whole number by a decimal with one decimal place • Divide
a whole number by hundredths • Divide tenths by tenths • Divide hundredths
by hundredths • Divide hundredths by tenths
3.4 Real-World Problems: Fractions and Decimals . . . . . . . . . . . . . . . . . . . . 94
Learn • Multiply decimals to solve real-world problems • Divide decimals
to solve real-world problems • Divide a whole number by a fraction to solve
two-step problems • Divide a whole number by a fraction to solve multi-step
problems • Decide whether to round up or down to solve real-world problems
• Divide a fraction by a whole number to solve real-world problems
• Divide a fraction by a fraction to solve real-world problems
Brain @ Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Chapter Wrap Up • Concept Map • Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Cumulative Review Chapters 1 – 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
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CHAPTER
4
Ratio
Chapter Opener How can math help you cook? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Big Idea You can use a ratio to compare two quantities, and you can use ratios to
solve problems .
Recall Prior Knowledge • Expressing fractions as equivalent fractions by
multiplication • Expressing fractions as equivalent fractions by division
• Writing equivalent fractions • Writing fractions in simplest form • Converting
measurements given in one unit of measure to another • Interpreting a comparison
bar model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.1 Comparing Two Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Learn • Understand the meaning of ratio • Use a part-part or a part-whole
model to show ratios • Write and interpret ratios as fractions • Use ratios to
find how many times one number or quantity is as great as another
4.2 Equivalent Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Learn • Equivalent ratios show the same comparisons of numbers and
quantities • Use the greatest common factor to write ratios in simplest form
• Equivalent ratios have the same ratio in simplest form • Find equivalent
ratios by multiplication • Find equivalent ratios by division • Find the missing
term of a pair of equivalent ratios • Work with tables of ratios
4.3 Real-World Problems: Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Learn • Draw models to solve problems involving ratios • Draw models to
solve problems involving ratios of three quantities • Draw models to solve
problems involving two sets of ratios • Draw models to solve before-and-after
problems
Brain @ Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Chapter Wrap Up • Concept Map • Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
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CHAPTER
5
Rates
Chapter Opener Who is the better goal scorer? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
Big Idea You can use a rate to compare one quantity to another quantity, and use
rates to solve problems .
Recall Prior Knowledge • Multiplying whole numbers • Multiplying
fractions or mixed numbers by a whole number • Multiplying fractions • Dividing
with fractions and whole numbers • Dividing fractions • Finding the quantity
155
represented by a number of units • Finding ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 Rates and Unit Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Learn • Meaning of rates • Express and compute unit rates in terms of time
and other quantities • Find a unit rate • Find and compare unit rates • Find
the speed or rate of travel of a moving object
5.2 Real-World Problems: Rates and Unit Rates . . . . . . . . . . . . . . . . . . . . . . 168
Learn • Solve simple word problems involving rates and unit rates • Read a
table to find the information to solve multi-step rate problems • Solve multi-
step word problems involving comparison of unit rates • Find the distance
given the speed and time • Find the time given the distance and speed • Find
average speed to solve real-world problems
Brain @ Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Chapter Wrap Up • Concept Map • Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
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