Math in focus b Singapore Math by Marshall Cavendish

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by

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Marshall Cavendish


© 2012 Marshall Cavendish International (Singapore) Private Limited

© 2014 Marshall Cavendish Education Pte Ltd

Published by Marshall Cavendish Education
Times Centre, 1 New Industrial Road, Singapore 536196
Customer Service Hotline: (65) 6213 9444
US Office Tel: (1-914) 332 8888 I Fax: (1-914) 332 8882
E-mail:
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Houghton Mifflin Harcourt

222 Berkeley Street

Boston, MA 02116
Tel: 617-351-5000
Website: www.hmheducation.com/mathinfocus
Cover: © Stephane Marechal/Photolibrary
First published 2013
All rights reserved. No part of this publication may be reproduced, stored in
a retrieval system or transmitted, in any form or by any means, electronic,
mechanical, photocopying, recording or otherwise, without the prior written
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copies is strictly prohibited.
Marshall Cavendish and Moth in Focus' are registered trademarks of
Times Publishing Limited.
Singapore Mathۥ is a trademark of Singapore Math lnc. 0 and
Marshall Cavendish Education Pte Ltd.
Math in Focus·, Course 1 Student Book B
ISBN 978-0-547-56012-0
Printed in United States of America
13 14 15
4500703012

1401

20 19 18

BCDE

CHAPTER

Ch@!P)'il:e1r OpetrDell" Going on a vacation? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

Equations and inequalities can be used to describe situations and solve
real-world problems.
e

write algebraic expressions

O

Comparing numbers with symbols
Evaluating algebraic expressions

O

O

Using variables to

Plotting

points in a coordinate plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

8.1

5

Solving Algebraic Equations ................................... .
0

Use substitution to solve simple algebraic equations

e

Solve

algebraic equations involving addition or subtraction ° Solve algebraic
equations involving multiplication or division

e

Solve algebraic equations

involving fractions

In Student Book A and Student Book B, look for

e

Practice in every lesson

0

Real-world and mathematical problems in
every chapter

e
e

chapter to assess chapter readiness
o

in every chapter

Ma.:t:/-vJourn.td exercises

Guided Practice after every Learn to
assess readiness to continue lesson

° Chapter Review/Test in every chapter to
review or test chapter material

°

Cm.. uiative Reviews four times during
the year


8.2

Writing Linear Equations . ...................................... .

13

Learn • Write a linear equation to represent a given situation • Use tables
and graphs to represent linear equations

Solving Simple Inequalities ................................... :_ .
Learn ° Determine solutions of inequalities of the form x > c and x < c
0

22

Determine solutions of inequalities of the form x ~ c and x::;; c

Hands-On Activity Writing Inequalities

8.4

Real-World Problems: Equations and Inequalities . .............. .
:.,,earn

8

Write algebraic equations to solve real-world problems

8

29

Write

algebraic inequalities to solve real-world problems

34
Key Concepts ......................... .

35

Ch@pter Revuew /il'est ................................................. .

36

• Concept Map

°


CHAPTER

The

,,Jj El

!fgffl

ChE:!lp1i:ef1' Opell'llefl' Have you ever used a street directory? . . . . . . . . . . . . . . . . . . . . . . .

38

Every point on the coordinate plane can be represented by a pair
of coordinates.
0

Identifying and plotting coordinates

negative numbers on the number line

O

Representing

O

Recognizing and writing the absolute value of

a number ° Finding the perimeter of a polygon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

9.1

42

Points cm the Coordinate Plane .................................. .
· cc, ·

° Find the coordinates of points on a coordinate plane

0

Draw and

identify polygons on a coordinate plane

Hands-On Activity Identifying Quadrilaterals Drawn on a Coordinate Plane

9.2

!Length of !Line Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

° Find the lengths of line segments on the x-axis and y-axis ° Find
lengths of line segments parallel to the x-axis and y-axis

0

Plot points on a

coordinate plane for a real-world problem and solve it

9.3

Real-World Problems: Graphing..................................
i.,,ea;·~~£

0

62

Graph an equation on a coordinate plane

66
° Concept Map ° Key Concepts ......................... .

67

C!hi@p'iteir iewiew!Test ................................................. .

68


CHAPTER

Chapter Opener Have you ever made a quilt? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

The area of a polygon can be found by dividing it into smaller shapes, and
then adding the areas of those shapes.

Reitali! IF»rri@rr !K!rft@'l?JSed(gle e Finding the area of a rectangle using a formula
° Finding the area of a square using a formula O Identifying parallelograms,
trapezoids, and rhombuses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

10.1

75

Arrea of Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Learn • Derive the formula for the area of a triangle e Find the area of a
triangle ° Find the height of a triangle given its area and base e Find the base
of a triangle given its area and height
Hands-On Activity Prove the Formula for Finding the Area of a Triangle

10.2 Area of Parallelograms and Trapezoids...........................
Learn e Derive the formula for the area of a parallelogram ° Find the area of
a parallelogram O Derive the formula for the area of a trapezoid ° Find the
area of a trapezoid

O

88

Apply the formula for the area of a trapezoid

10.3 Area of Other Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
team ° Find the areas of regular polygons

99

10.4 Area of Composite Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

104

Recognize that a plane figure can be divided into other polygons
0
Solve problems involving rectangles and triangles e Solve problems
involving parallelograms, triangles, and rectangles
e

113

°

Concept Map ° Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . .

114

Chapter Reviewfifes'll:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

115


CHAPTER

Chti:llpler Ope!i'iler Have you ever seen a rainbow? . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

118

A circle is a geometric figure that has many useful applications in the
real world.
0

decimals
0

c

Dividing decimals

Adding decimals
a

0

Subtracting decimals

0

Multiplying

Rounding numbers to the nearest whole number

Rounding numbers to the nearest tenth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11.1

Rcu:llius, Diameter, and Circumference of a Cirde . . . . . . . . . . . . . . . . . .
Identify the center and radius of a circle

e

a circle
circle

0

a

Identify the circumference of a circle

119
122

Identify the diameter of

0

° Find the circumference of a

Recognize that half of a circle is a semicircle and a quarter of a circle is

a quadrant

c

Find the lengths of a semicircular arc and the arc of a quadrant

Hands-On Activities

0

Drawing Circles Using a Compass

a

Investigating the

Relationship Between the Circumference and Diameter of a Circle

0

Drawing

Semicircles and Quadrants

11.2

Area of a Cirde. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
e
c

Derive the formula for the area of a circle

Find the area of a semicircle

a

Find the area of a circle

136


11.3

Real-World Problems: Cirdes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
e

Use the formula for circumference to solve real-world problems

e

Use the formula for area of a circle to solve real-world problems

e

Solve real-world problems involving rates and circles

158
e

Concept Map

e

Key Concepts ......................... .

160


CHAPTER

rfac~

I
Clh@pf!:eir Opell'ileir How can math help you make candles? . . . . . . . . . . . . . . . . . . . . . .

168

Area is measured in square units, and the surface area of a prism or
pyramid is the sum of the areas of its faces. Volume is measured in cubic units,
and the volume of a prism is the area of its base times its height.
Identifying special prisms ° Finding the areas of

0

12.1

°

Finding the volumes of rectangular prisms. . . . .

169

Nets of Solids........................ . . . . . . . . . . . . . . . . . . . . . . . . . . . .

172

rectangles, triangles, and trapezoids

0

prism

O

Recognize the net of a cube

O

Recognize the net of a rectangular

Recognize the net of a triangular prism

O

Recognize the net of a

square pyramid

Hands-On Activities

O

Identifying a Cube from a Net

O

Identifying a Prism

from a Net ° Classifying Pyramids

12.2 Surfo1ce Area of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
° Find the surface area of a cube ° Find the surface area of a
rectangular prism ° Find the surface area of a triangular prism ° Find the

181

surface area of a pyramid

12.3 Volume of Prisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
a

Derive the formula for the volume of a rectangular prism a Use a

formula to find the volume of a rectangular prism ° Form cross sections of
prisms a Use a formula to find the volume of any prism

Hands-On Activity Determining the Relationship Between Volume and
Surface Area of Prisms

189


12u4 Real-World Problems: Surface Area and Volume . . . . . . . . . . . . . . . . . .

200

Solve word problems about the volume of rectangular prisms
11 Solve word problems about surface area and volume of non-rectangular
prisms O Solve word problems about prisms with missing dimensions O Solve
word problems about non-rectangular prisms with missing dimensions
11

208
Concept Map ° Key Concepts ........................ .

209

Che.iptew Review/fesiL ................................................ .

210

11


CHAPTER

Ch@p1h~!i' Opeli'iler Do you know why and how statistics are collected?.............

214

Statistics summarizes data so that information or decisions can be gathered
from the data set.
0

13.1

Interpreting data in a line plot .....................

215

Collecting and Tall:nJilating Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
8

Collect and tabulate data

Hands-On Activity Collect, Tabulate, and Interpret Data

13.2 Dot Plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Represent numerical data using a dot plot
set of data 0 Interpret data from a dot plot
0

0

Identifying the shape of a

Hands-On Activity Constructing a Distribution

13.3 Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
Represent numerical data using a histogram e Choose an
appropriate interval to organize data in a histogram 0 Interpret data from
a histogram
0

.........................................................

° Concept Map

e

Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . .

237
238


CHAPTER

easuresof
Central
Chapi:ell' Openell' How do blue jean companies know what customers will buy?. . . . . . 242

Measures of central tendency can be used to summarize data distributions,
and help you make decisions in real-world problems.
Dividing decimals by a whole number ° Finding the
average of each data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

243

14.1

244

Re<1:@~E

!Pirn@fi'

H!ira@wUedlgie

O

Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Learn ° Understand the concept of mean ° Find the mean of a data set using a
dot plot ° Find the total and missing number from the mean
Hands-On Activity Finding Mean and Using Mean to Solve Problems

14.2 Median. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

251

Learn ° Understand the concept of median e Find the median of a data set
using a dot plot ° Compare the mean and median of a data set
Hands-On Activity Collecting and Tabulating Data to Find Median

14.3 Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
Learn ° Understand the concept of mode O Use mode to summarize a data set
Hands-On Activity Finding Mean, Median, and Mode


Ul ..4 Real-World Problems: Mean. Median, and Mode. . . . . . . . . . . . . . . . . .

264

Learn e Decide whether to use mean, median, or mode O Relate the measure
of center to a skewed distribution ° Relate the measure of center to a
symmetrical distribution
Hands-On Activity Finding Possible Values of Mean, Median, and Mode

271

° Concept Map ° Key Concepts. . . . . . . . . . . . . . . . . . . . . . . . . . 272
273
275

Selected Answers ...................................................... 280
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
Table of Measures 0 Form11.11las 1 and Symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

Credits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
Index ................................................................. 313


_ _ Welcome t o - - - - - - - - - - - - - - -

What makes
Math in Focus® different?
0

Singapore Math
by

Marshall Cavendish

This world-class math program comes to you
from the country of Singapore. We are sure that
you will enjoy learning math with the interesting
lessons you will find in these books.

I)>- Two books The textbook is divided into

2 semesters. Chapters 1-7 are in Book A.
Chapters 8-14 are in Book B.
I)>- Longer lessons More concepts are presented

in a lesson. Some lessons may last more than a
day to give you time to understand the math.
I)>- Bar models and visual models will help you

make sense of new concepts and solve realworld and mathematical problems with ease.

About the book

Here are the main features in this book.

Chapter Opener
Introduces chapter concepts and big ideas through a story or
example. There is also a chapter table of contents .

..__, .
[,£,)

__ _

l'il!i

Recall Prior Knowledge

,i;o-,o-.,,,

;;-----.------

c 0.

Assesses previously learned
concepts, definitions, vocabulary,
and models relevant to the chapter.

., . .

C·

Quick Check assesses readiness
for the chapter.

xiv


Look for these features in each lessona
Like terms can be added.,

shows steps that are easy to
follow and understand. It often contains
bar models or other visual models.

a)

Simplify 3x

+ x.

3x

X

~

lxlxlxlxl

Model
mathematics

3x

+

X

=X + X + X + X
= 4x

Guided Practice exercises provide
step-by-step guidance through solutions.

Complete.

Simplify x + Sx.
x

?

?

+ Sx = _]_

Cautions alert you to common mistakes
and misconceptions related to the topics.

When adding and subtracting

algebraic terms with no parentheses,
always work from left to right.
For example:

Structure,
reasoning, and
precision

7 x - Sx - x
9x - 3x

* 7x -

4x

+ 2x * 9x - Sx

Math Notes are helpful hints
Commutative Property of Addition:
Two numbers can be added in
any order.
So, 4

and reminders.

+ a = a + 4.

xv

Simplify each expression. Then state the coefficient of the variable in each expression.
u+u+u+u

Practice and Math Journal
are included in practice sets.

Matn,Jountal Explain how you can use your answers in a) and b) to
show that the following expressions are equivalent.
3x + 6 and 3(x + 2)

Construct viable
arguments

Hands-On Activities and

combine logical thinking with
math skills and concepts to help you meet new problem-solving challenges.

Materials:

• paper
• ruler
• scissors
Work in pairs.
Make the following set of paper strips.
Let the length of the shortest strip be m units. Make and label 5 such strips.

,

......... _/,,.,,..........~~~~/,,........._________ _J

Hands-On or Technology Activities provide opportunities for investigation,
reinforcement, and extension.

Reason, solve
problems, use
tools and models

Find the perimeter of the figure in terms of x, given that all the angles in the
figure are right angles. If x = 5.5, evaluate this expression.
~~/-~..-------',v~.....___----......_,,,.,......._/•··

-....J

problems, found at the end of each chapter, are
challenging and promote critical thinking.

xvi


Chapter Wrap Up
-==-1

1-.

Key concepts, definitions, and formulas are summarized for
easy review.

• • • r ~

The Chapter Wrap Up summaries contain concept maps like
the one shown below.
There may be more than one way to draw a concept map.
With practice, you should be able to draw your own.

The center box contains
the big idea for the chapter.
Other boxes represent key
concepts of the chapter.

Real-life situations
(in word problems)
Numbers
(coefficients)

Variables

are combined

and simplified
to form
can be

Operational signs
+,-,x,+

Structure,
reasoning, and
precision

Evaluated

Expanded

Factored

The lines and arrows show how all the concepts in the
chapter are related to one another and to the big idea.
O·

o:

Chapter Review ITest

o···
0

.···· .. , ..

,-···•·~···~·"~0

•·-·-···,..0 ... -

0

A practice test is found at the
end of each chapter.

C
0-·

O•

:,.

··~•-····-· .,.,

0

,.,....... __ M•••--

·--~-;:-

0"

.

Cumulative Review
Cumulative review exercises
can be found after Chapters 3,
7, 11, and 14.

xvii


CHAPTER

If you travel to another country, you can use linear equations and
inequalities to help you plan your finances. Before you leave,
you might want to change your U.S. dollars into a different currency.

The amount of money you get in the new currency depends on how
many U.S. dollars you start with and also on the currency exchange
rate. To find out how much money you get in the new currency,
you use a linear equation.
(

While on your trip, you may want to set aside money to spend
on souvenirs. You can use a linear inequality to find how many
souvenirs you can buy. Planning finances, travel times, and distances
can all be made easier by using linear equations and inequalities.

L


,,-- Comparing numbers with symbols - - - - - - - - - - - - - - - - - - - - - - - - .
Symbol

Meaning

Example

= 48-.12

=

is equal to

12 x 4

cj:.

is not equal to

6 - 2 -=J:. 2 - 6 - . 6 - 2 is not equal to 2 - 6.

>

is greater than

0 > -9 _ . 0 is greater than -9.

<

is less than

-5

x 4 is equal to 48.

< -1 _ . -5 is less than -1.

Complete with=,>, or<.

25 ?
40 + 8

-26

12+12+12? 3-12

? 8 + 40

-16 ? -7

Using variables to write algebraic expressions - - - - - - - - - - - - - - - - - - - - - Statement

Expression

The sum of x and 7

x+7

The difference "14 less than y"

y- 14

The product of 8 and w

8w

Divide z by 6

-

z

6

Write an algebraic expression for each of the following.

The sum of 15 and p
The product of rand 23

The difference "q less than 10"
@l Divide s by 11.

Chapter 8 Equations and Inequalities

3


Evaluating algebraic expressions - - - - - - - - - - - - - - - - - - - - - - Evaluate 4y + 1 when
a)

y= 7,

a)

= 7,
4y + 1 = (4 · 7) + 1
= 28 + 1
= 29

b)

b)

y

= 10.

When y

= 10,
= (4 · 10) + 1
= 40 + 1
= 41

Substitute.
Multiply inside parentheses.
Add.

When y
4y

+

1

Substitute.
Multiply inside parentheses.
Add.

_ lli( Qukk Check
Evaluate each expression for the given values of the variable.

3x

(W

+ 5 when x

= 9 and x = 12

28 - 4x when x

= 4 and x = 7

Plotting points on a coordinate p l a n e - - - - - - - - - - - - - - - - - - - - - - . . .
y

Plot points A (2, 4) and B (3, 2) on a coordinate plane.
To locate point A (2, 4), move 2 units to the right of the
y-axis and 4 units above the x-axis. Then mark the point
with a dot.

'--3-+------------.-·····

To locate point B (3, 2), move 3 units to the right of the
y-axis and 2 units above the x-axis. Then mark the point

2

with a dot.
----+--1----+---+-----<--+----.x

0

~lf"'t.

~

•

B-

Fh e CKft_

'4di.UD c~ ~

Plot the points on a coordinate plane.

@) K(2, 1), L(3, 3), M(O, 6), and N(7, 5)
4

Chapter 8 Equations and Inequalities

2

3

4

5


Solvi

s

lesson Objective
• Solve equations in one variable.

equation
solution

,,-- Use Sl!llbstitllJlticm to solve simple algebraic eqm:dio1111s.
I
/

a)

The figure shows a balance scale. Find the value of x such that the left side
balances the right side.

represents 1 counter.
represents x counters.

There are (x

+ 5) counters on the left side.

You can think of an
equation as a balance

There are 8 counters on the right side.

scale, where the left
side is always balanced

Since the two sides balance each other,
X

by the right side.

+ 5 = 8.

x+5

= 8 is called an equation.

To solve the equation, you need to find the value of x
that makes x

+5

= 8 true.
Another way to solve an equation

If x

If x

= 1,
= 2,

= 3,

+ 5 = 8 is to ask yourself,

'What number can be added
to 5 to equal 8?' Only 3 can be
added to 5 to equal 8, so the only

x+5=2+5

=7
If x

like x

x+5=1+5
=6

solution of the equation is 3.
(;ic 8)

x+5=3+5
=8

The equation x
x

+5

8 holds true when x

= 3 gives the solution

of the equation x

= 3.
+5

8.

Lesson 8.1 Solving Algebraic Equations

5


b)

Solve the equation 3x
The equation 3x

= 12.

s

= 12 can be represented on a balance scale:
Ill
Ill
Ill

represents 1 counter.
represents x counters.

To solve the equation, you need to find the value of x that makes 3x
If x

1,

If x

2,

3x

=3 · 1
=3

3x

= 4,

3x

(:;t:: 12)

3 •2

=6
If x

(:;t:: 12)

The equation 3x

= 12 has

= 4. The

only one solution, x

=3 •4
= 12

equation does not hold true
for other values of x.

The equation 3x = 12 holds true when x

= 4.

x = 4 gives the solution of the equation 3x

= 12.

Gu,.1ided ~rna1Complete each

? with = or ¢, and each _1_ with the correct value.

For what value of x will x + 3
If x

If x

If x

= 1,
2,

= 4,

= 7 be true?

x+3 =_1_+3
?

? 7)

x+3 =_1_+3
= ?

? 7)

x+3 = _?_+ 3
= ?

x + 3 = 7 is true when x = _1_.

6

= 12 true.

Chapter 8 Equations and Inequalities


Solve each equation using the substitution method.

p

+6

2m

= 13

r+4

=6

4n

= 12

k-10=7
1

= 20

-z=3
5

Solve algebrr1t1ic equations involving addition or subtraction.
a)

Solve the equation x
The equation x

+6

+ 6 = 9.

= 9 can be represented on a balance scale:
represents 1 counter.
represents x counters.

When you remove 6 counters from the left side, the scale becomes unbalanced.

x+6-6<9

To balance the scale, you will need to remove 6 counters from the right side.

x+6-6=9-6

The steps above can be summarized as follows:

x+6=9
x+6-6=9-6
x=3
x

Subtract 6 fron1 both sicles.

= 3 gives the solution of the equation x + 6 = 9.

Compare this with 3

+6

= 9.

Check: Substitute 3 for the value of x into the equation.

3+6-6=9-6
3=9 6

x+6

You can subtract the same number

3+6
=9

When x = 3, the equation x + 6
x = 3 gives the correct solution.

= 9 is true.

from both sides of the equation and
the two sides will remain equal.

Lesson 8.1 Solving Algebraic Equations

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