Copyright © by The McGraw-Hill after numbers to the right of the number on the number line Counting Numbers Less Than 100 Counting numbers are the set of numbers used to count objects
Trang 1Authors Basich Whitney • Brown • Dawson • Gonsalves • Silbey • Vielhaber
Trang 2Copyright © 2008 by The McGraw-Hill Companies, Inc All rights reserved Except as
permitted under the United States Copyright Act, no part of this publication may be
reproduced or distributed in any form or by any means, or stored in a database or
retrieval system, without prior permission of the publisher.
Send all inquiries to:
Cover, i Jupiter Images; iv (tl)File Photo, (tc tr)The McGraw-Hill Companies,
(cl c)Doug Martin, (cr)Aaron Haupt, (bl bc)File Photo; v (L to R 1 2 3 4 6 7 8 9
11 12)The McGraw-Hill Companies, (5 10 13 14)File Photo; vii Dynamics
Graphics Group/Creatas/Alamy; viii Digital Vision/PunchStock; ix, x CORBIS;
xi Digital Vision/PunchStock; xii Digital Vision/Getty Images; 2–3 Mike Watson
Images/CORBIS; 8 Gary Bbouys/AFP/Getty Images; 32 Mark Ransom/
RansomStudios; 59 Rex Stucky/Getty Images; 68–69 Getty Images; 69 Michael
Houghton/StudiOhio; 102 Pixtal/SuperStock; 119 JTB Photo Communications,
Inc./Alamy; 128–129 David Madison/NewSport/CORBIS; 129 Christopher
Stevenson/CORBIS; 141 Getty Images; 148 James Marshall/CORBIS;
156 CORBIS; 170 image100/Alamy; 188 Rubberball/Getty Images;
189 Brand X/JupiterImages
Trang 3California Math Triumphs
1A Chapter 1 Counting
1A Chapter 2 Place Value
1A Chapter 3 Addition and Subtraction
1B Chapter 4 Multiplication
1B Chapter 5 Division
1B Chapter 6 Integers
2A Chapter 1 Parts of a Whole
2A Chapter 2 Equivalence of Fractions
2B Chapter 3 Operations with Fractions
2B Chapter 4 Positive and Negative Fractions and Decimals
3A Chapter 1 Ratios and Rates
3A Chapter 2 Percents, Fractions, and Decimals
3B Chapter 3 Using Percents
3B Chapter 4 Rates and Proportional Reasoning
4A Chapter 1 Operations and Equality
4A Chapter 2 Math Fundamentals
4B Chapter 3 Math Expressions
4B Chapter 4 Linear Equations
4B Chapter 5 Inequalities
5A Chapter 1 Patterns and Relationships
5A Chapter 2 Graphing
5B Chapter 3 Proportional Relationships
5B Chapter 4 The Relationship Between
Graphs and Functions
6A Chapter 1 How Measurements Are Made
6A Chapter 2 Length and Area in the Real World
6B Chapter 3 Exact Measures in Geometry
6B Chapter 4 Angles and Circles
Trang 4Authors and Consultants
iv
AUTHORS
Frances Basich Whitney
Project Director, Mathematics K–12
Santa Cruz County Offi ce of Education
Capitola, California
Kathleen M Brown
Math Curriculum Staff Developer Washington Middle School Long Beach, California
Dixie Dawson
Math Curriculum Leader Long Beach Unifi ed Long Beach, California
CONSULTANTS
Assessment
Donna M Kopenski, Ed.D.
Math Coordinator K–5
City Heights Educational Collaborative
San Diego, California
Instructional Planning and Support
Beatrice Luchin
Mathematics Consultant League City, Texas
ELL Support and Vocabulary
ReLeah Cossett Lent
Author/Educational Consultant Alford, Florida
Dinah-Might Activities, Inc.
San Antonio, Texas
Trang 5California Advisory Board
v
Carol Cronk
Mathematics Program Specialist
San Bernardino City Unifi ed
School District
San Bernardino, California
Audrey M Day
Classroom Teacher Rosa Parks Elementary School San Diego, California
Jill Fetters
Math Teacher Tevis Jr High School Bakersfi eld, California
Grant A Fraser, Ph.D.
Professor of Mathematics California State University, Los Angeles
Los Angeles, California
Eric Kimmel
Mathematics Department Chair
Frontier High School
Bakersfi eld, California
Donna M Kopenski, Ed.D.
Math Coordinator K–5 City Heights Educational Collaborative San Diego, California
Michael A Pease
Instructional Math Coach Aspire Public Schools Oakland, California
Chuck Podhorsky, Ph.D.
Math Director City Heights Educational Collaborative San Diego, California
Arthur K Wayman, Ph.D.
Professor Emeritus
California State University, Long
Beach
Long Beach, California
Frances Basich Whitney
Project Director, Mathematics K–12 Santa Cruz County Offi ce of Education
Capitola, CA
Mario Borrayo
Teacher Rosa Parks Elementary San Diego, California
Melissa Bray
K–8 Math Resource Teacher Modesto City Schools Modesto, California
CALIFORNIA ADVISORY BOARD
Glencoe wishes to thank the following professionals for their invaluable
feedback during the development of the program They reviewed
the table of contents, the prototype of the Student Study Guide, the
prototype of the Teacher Wraparound Edition, and the professional
Bonnie Awes
Teacher, 6th Grade Math Monroe Clark Middle School San Diego, California
Kathleen M Brown
Math Curriculum Staff Developer Washington Middle School Long Beach, California
Trang 6California Reviewers
vi
CALIFORNIA REVIEWERS
Each California Reviewer reviewed at least two chapters of the Student
Study Guides, providing feedback and suggestions for improving the
effectiveness of the mathematics instruction
Bobbi Anne Barnowsky
Monica S Patterson
Educator Aspire Public Schools Modesto, California
Rechelle Pearlman
4th Grade Teacher Wanda Hirsch Elementary School Tracy, California
Armida Picon
5th Grade Teacher Mineral King School Visalia, California
Anthony J Solina
Lead Educator Aspire Public Schools Stockton, California
Trang 7Volume 1A Place Value and Basic Number Skills
1NS1.3 Represent equivalent forms
of the same number through the use of physical models, diagrams, and number expressions (to 20) (e.g., 8 may be represented as 4 + 4, 5 + 3, 2 + 2 +
Trang 8viii
Giant Redwoods, Sequoia National Park
2-1 Whole Numbers to 1,000 .70
2NS1.1, 2NS1.2
2-2 Round and Compare Whole
Numbers Less Than 1,000 77
2NS1.3, 4NS1.3
Progress Check 1 84
2-3 Whole Numbers Less Than 10,000 85
3NS1.3, 3NS1.5
2-4 Round and Compare Whole
Numbers Less Than 10,000 91
4NS1.2, 4NS1.3
Progress Check 2 98
2-5 Read and Write Whole Numbers in the Millions 99
4NS1.1
2-6 Round and Compare Whole
Numbers in the Millions 105
4NS1.2, 4NS1.3
2-7 Order and Compare Numbers
to Two Decimal Places 111
2NS1.2 Use words, models, and expanded forms (e.g., 45 = 4 tens + 5)
to represent numbers (to 1,000).
2NS1.3 Order and compare whole numbers to 1,000 by using the symbols <,=, >.
3NS1.3 Identify the place value for each digit in numbers to 10,000.
3NS1.5 Use expanded notation
to represent numbers (e.g., 3,206 = 3,000 + 200 + 6).
4NS1.1 Read and write whole numbers in the millions.
4NS1.2 Order and compare whole numbers and decimals to two decimal places.
4NS1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand.
4NS1.6 Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., 1
2 = 0.5 or 0.50; 7
4 = 1 3
4 = 1.75)
Trang 9ix
Cacti growing in Baja California Peninsula
Chapter
3-1 Addition Facts for 0 to 5 .130
1NS2.5 Show the meaning of addition (putting together, increasing) and subtraction (taking away, comparing,
fi nding the difference).
1NS2.6 Solve addition and subtraction problems with one- or two-digit numbers (e.g., 5 + 58 = ).
1NS2.7 Find the sum of three one-digit numbers.
2NS2.2 Find the sum or difference of two whole numbers up to three digits long.
2NS2.3 Use mental arithmetic to fi nd the sum or difference of two two-digit numbers.
3NS1.3 Identify the place value for each digit in numbers to 10,000.
3NS2.1 Find the sum or difference of two whole numbers between
0 and 10,000.
4NS1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand.
4NS3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers.
Trang 10x
Chapters 1, 2, and 3 are contained in Volume 1A Chapters 4, 5, and 6 are contained in Volume 1B.
Chapter
4-1 Introduction to Multiplication 3NS2.2, 4NS4.1 4
4-2 Multiply with 0, 1, and 10 3NS2.2, 3NS2.4, 3NS2.6 11
Progress Check 1 18
4-3 Multiply by 2 3NS2.2, 3NS2.4 19
4-4 Multiply by 5 3NS2.2, 3NS2.4 25
Progress Check 2 32
4-5 Multiply by 3 3NS2.2, 3NS2.4, 4NS3.2 33
4-6 Multiply by 4 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 39
Progress Check 3 46
4-7 Multiply by 6 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 47
4-8 Multiply by 7 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 53
Progress Check 4 60
4-9 Multiply by 8 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 61
4-10 Multiply by 9 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 67
Progress Check 5 74
4-11 Multiply by 11 and 12 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 75
4-12 Perfect Squares 3NS2.2, 4NS4.1 81
Progress Check 6 88
4-13 Multiply Large Numbers 3NS2.4, 3NS2.6, 4NS3.2 89
Assessment Study Guide 95
Chapter Test 102
Standards Practice 104
Standards Addressed
in This Chapter
2NS3.1 Use repeated addition, arrays, and counting by multiples to do multiplication.
2NS3.3 Know the multiplication tables
of 2s, 5s, and 10s (to “times 10”) and commit them to memory.
3NS2.2 Memorize to automaticity the multiplication table for numbers between 1 and 10.
3NS2.4 Solve simple problems involving multiplication of multidigit numbers by one-digit numbers (3,671 × 3 = ).
3NS2.6 Understand the special properties of 0 and 1 in multiplication and division.
4NS3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by
a one-digit number; use relationships between them to simplify computations and to check results.
4NS4.1 Understand that many whole numbers break down in different ways (e.g., 12 = 4 × 3 = 2 × 6 = 2 × 2 × 3).
Poppy meadow in the Santa Ynez Mountains
Trang 113NS2.6 Understand the special properties of 0 and 1 in multiplication and division
4NS3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by
a one-digit number; use relationships between them to simplify computations and to check results.
Trang 123NS2.6 Understand the special properties of 0 and 1 in multiplication and division.
4NS1.8 Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in “owing”).
5NS1.5 Identify and represent
on a number line decimals, fractions, mixed numbers, and positive and negative integers.
5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results.
6NS2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.
7NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole- number powers.
Big Sur Coast
Trang 13Let’s Get Started
Use the Scavenger Hunt below to learn where things are
located in each chapter
p 58?
you where you can take the Online Readiness Quiz
Trang 14You count and compare numbers,
or objects, every day.
The United States government has official counters who count the nation’s people every 10 years to identify population trends
Trang 15Copyright © by The McGraw-Hill Companies, Inc.
3
You know that if you have
2 ten-dollar bills and 4 one-dollar bills, you have $24
Lessons 1-1 and 1-6
Counting numbers are the set of
numbers used to count objects
Place value tells you the value of
each digit, like the 2 and 4 in 24
An equation states that two
expressions are equal
A number pattern is a regular,
repeating sequence of numbers
The pattern is to add 10 to each number
STEP 1 Quiz Are you ready for Chapter 1? Take the Online Readiness
Quiz at ca.mathtriumphs.com to find out
STEP 2 Preview Get ready for Chapter 1 Review these skills and compare
them with what you’ll learn in this chapter
Trang 16Copyright © by The McGraw-Hill
after
numbers to the right of the number on the number line
Counting Numbers Less Than 100
Counting numbers are the set of numbers used to count
objects (1, 2, 3, 4, 5, …) The first counting number is 1
Counting numbers before will be to the left of the number on
the number line
Counting numbers after will be to the right of the number on
the number line
Counting numbers between two numbers are the numbers
to the ri
to the right of the lesser number and to the left of the greater
number
When you are asked to write the counting numbers between
1 and 5, for example, you do not include 1 and 5 So the
counting numbers between 1 and 5 are 2, 3, and 4
Example 1
Use a number line to graph the counting
numbers between 13 and 19.
1 On the number line, locate the
counting numbers given
10 11 12 13 14 15 16 17 18 19 20
2 Find the counting numbers to the
right of the least number, 13, and to
the left of the greatest number, 19
They are 14, 15, 16, 17, and 18
3 Place dots on 14, 15, 16, 17, and 18
2 Find the counting numbers to the right
of the least number, 4, and to the left of the greatest number, 8 They are 5, 6, and 7
3 Place dots on the counting numbers between 4 and 8
1NS1.1 Count, read, and write whole numbers to 100.
Trang 17Copyright © by The McGraw-Hill Companies, Inc.
3 Start with 34 Write all of the counting
numbers until you get to 37
GO ON
Trang 18Copyright © by The McGraw-Hill
Step 2 The counting numbers to the right of the least
number, 45, are 46, 47, 48, and 49 Stop when you get to the greater number, 50
Step 3 Place a dot on the numbers
that are between 45 and 50
Use a number line to graph the following.
9 the counting number after 67
Trang 19Copyright © by The McGraw-Hill Companies, Inc.
Solve.
weekend He forgot her address, but remembers that she
lives between Mrs McGee and Mr Scofield
Mrs McGee lives on Seond Avenue, and Mr Scofield lives
on Fourth Avenue On what street is Dewayne’s
grandmother’s house?
Understand Read the problem Write what you know
Dewayne’s grandmother lives between
Plan Pick a strategy One strategy is to draw a picture
1 First Avenue
2 Second Avenue
3 Third Avenue
1 Fourth Avenue
Draw an X on the street where Mrs McGee lives.
Draw an X on the street where Mr Scofield lives.
Solve The number is between 2 and 4
Dewayne’s grandmother lives on Avenue
Check Count from 1 to 10 Does 3 come between 2 and 4?
✓ Draw a picture
Look for a pattern.
Guess and check.
Act it out.
Solve a simpler problem.
GO ON
Trang 208 Chapter 1 Counting
with 5 wins Germany has won it 3 times The number
of Italy’s wins is between Brazil’s and Germany’s
How many times has Italy won the World Cup?
Check off each step
Understand
Plan
Solve
Check
I know that he is one year younger than my
grandfather My grandfather is 89 years old
How old is Mr Rodriquez?
16 What does before mean? Write a sentence using
the word before
Skills, Concepts, and Problem Solving
Write the missing counting numbers.
Trang 21Copyright © by The McGraw-Hill Companies, Inc.
20 Sunday Monday Tuesday Wednesday Thursday Friday Saturday
Write true or false for each statement.
33 The first counting number is 0
34 The numbers between 46 and 52 are 47, 48, 49, 50 and 51
35 The number before 9 is 10
Use a number line to graph the following.
36 the counting number before 42
37 the counting number after 96
90 91 92 93 94 95 96 97 98 99 100 GO ON
Trang 22Copyright © by The McGraw-Hill
38 the counting numbers between 19 and 22
Solve
locker is 42 and Cruz’s is 45 What could be Pam’s locker number?
thirty-five I have one digit that is a zero What number am I?
Vocabulary Check Write the vocabulary word that completes each
sentence.
41 The counting numbers that come will be to the right of
the number on the number line
42 The counting numbers that come will be to the left of
the number on the number line
43 Writing in Math Jim graphed the counting numbers between
5 and 8 below Explain Jim’s mistake
44 AGE Write your age in the square Outside the square on the left,
write the number that is before your age On the right side of the
square, write the number that is after your age What two numbers
is your age between?
Solve.
They bought three tickets together Ruby lost her ticket Janet and
Ramon are in seats 15 and 16 What two seats could Ruby be in if
their seats are together?
Trang 23Copyright © by The McGraw-Hill Companies, Inc.
greater than
numbers to the right of the number on the number line
KEY Concept
Whole Numbers Less Than 100
Whole numbers are zero and the counting numbers {0, 1, 2,
3, 4, 5 …} The only difference between counting numbers and
whole numbers is the number 0
Whole numbers that are less than are to the left of the
number on the number line
Whole numbers that are greater than are to the right of the
number on the number line
0, 1, 2, and 3
are less than 4.
Zero is a whole number.
5, 6, 7, 8, 9, and 10
are greater than 4.
1NS1.1 Count, read, and write whole numbers to 100.
To graph whole numbers on a number line, place
a dot on the number line for the numbers
Example 1
Use the number line to graph the whole
numbers less than 6
1 You are graphing whole numbers
2 Identify the whole numbers less than 6
Less than means go to the left, so the whole
numbers left of 6 are 5, 4, 3, 2, 1, and 0
3 Place a dot on the numbers you want to
Trang 24Copyright © by The McGraw-Hill
2 The first number after 23 is 24
3 The number before 32 is 31
4 Start with 24 and write all of the whole
numbers until you get to 31
24, 25, 26, 27, 28, 29, 30, and 31
The whole numbers between 23 and 32 are
24, 25, 26, 27, 28, 29, 30, and 31 Be sure not
2 What is the first number after 93?
3 What is the number before 98?
4 Write the numbers between 93 and 98
1 Write the first five whole numbers
2 What is the first whole number?
Compare the whole numbers Use the words greater than or less than.
5 4 3
2
1
Trang 25Copyright © by The McGraw-Hill Companies, Inc.
5 Use a number line to graph the whole numbers that are
greater than 6, but less than 11.
Step 1 You are graphing numbers 6 and 11
Step 2 Which direction from 6 are the whole numbers
more than 6?
List the numbers on the number line
Step 3 Place a dot on the whole numbers you identified
Use a number line to graph the following whole numbers.
Use the number line to complete each statement.
11 The graph below shows whole numbers between
Trang 26Copyright © by The McGraw-Hill
Solve.
Team Yellow has 2 wins Team Blue has fewer wins than
both Team Red and Team Green, but more wins than Team
Yellow How many wins could they have?
Understand Read the problem Write what you know
number of Team Blue’s wins greater than or less than Team Red’s wins?
number of Team Blue’s wins greater than or less
the number of Team Blue’s wins greater than or less than Team Yellow’s wins?
Plan Pick a strategy One strategy is to make a table
Identify and list the whole numbers, or wins, that Team Blue could have
Solve Draw a table with four columns as shown List the
wins for each team and the possible wins that Team Blue could have
Are Team Blue’s wins greater than or less than this team’s
9 4 2
Team Red Team Green Team Yellow
Less Than 0, 1, 2, 3, 4, 5, 6, 7, 8
1, 2, 3
3, 4, 5, 6, 7, 8, 9
Less Than Greater Than
Then identify the whole numbers, or wins, that are possible for Team Blue in all three situations
Team Blue could have wins
Check Does the answer make sense? Are the number of
Team Blue’s wins less than both Team Red’s and Team Green’s wins? Are the number of Team Blue’s wins greater than Team Yellow’s 2 wins?
✓Make a table.
Look for a pattern.
Guess and check.
Solve a simpler problem.
Work backward.
Trang 27Copyright © by The McGraw-Hill Companies, Inc.
has more stickers than Kaya Explain why Pia is wrong Use the
number line to explain your answer Check off each step
Understand
Plan Solve Check
friend’s team has 6 players Your team has 5 players Which team
has more players?
16 Suppose you have a whole number that is x Explain how
to identify a whole number that is more than x on the
number line
Skills, Concepts, and Problem Solving
Write true or false for each statement.
17 The first whole number is 0
Whole numbers include zero.
The first counting number is 1.
18 The whole numbers less than 5 are 0, 1, 2,
3, 4, and 5
19 The first counting number is 1
Trang 28Copyright © by The McGraw-Hill
I have one digit that is 0 What number am I?
I am less than 12 What number am I?
Vocabulary Check Write the vocabulary word that completes the sentence.
36 numbers are zero and the counting numbers
Trang 29Copyright © by The McGraw-Hill Companies, Inc.
37 Jason was asked to graph the whole numbers less than 5 Explain
his mistake
38 A friend claims that 29 is greater than 41 because 9 is greater than
4 or 1 Explain why the friend is wrong
39 Writing in Math Explain the difference between whole numbers
and counting numbers
Each pulls a number and waits for a turn to order Mary has
number 46, and Isaiah has number 41 Who will be helped first?
Trang 30Copyright © by The McGraw-Hill
Chapter
1
Use a number line to graph whole numbers and counting numbers
1 counting number before 67
Write the following numbers
5 counting numbers between 43 and 50
6 whole numbers less than 10
7 counting numbers less than 10
Solve
won 4 ribbons Mika won 2 If their teammate, Benita, did not
perform as well as either of them, how many ribbons could Benita
have won?
pocket Asád has more money than Cris, but less money than
Marco How many cents could Asád have in his pocket?
Trang 31Copyright © by The McGraw-Hill Companies, Inc.
equation
a mathematical sentence that contains an equal sign, =, indicating that the left side has the same value as the right side
equal
having the same value
KEY Concept
1NS1.3 Represent equivalent forms of the same number through the use of physical models, diagrams, and number expressions (to 20).
4AF1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations.
Equal Expressions
A numerical expression is a phrase that represents a number
The number 5 can be represented by:
An equation is a mathematical sentence that states that two
expressions are equal
2 + 3 = 5
2 + 3 = 4 + 1
Equal means that each expression has the same value
3 + 2 = 4 + 1The symbol used to represent equal is =.
Use the number line to identify different expressions that represent
a given number
Example 1
Write the missing number to make the equation true
1 Which side of the equation has a missing
number? the left side
2 Place 8 tiles on the left side of the equal sign
Place 12 tiles on the right side How many more
tiles do you need on the left to make both sides
have the same number of tiles? 4
Trang 32Copyright © by The McGraw-Hill
2 Draw 4 tiles on the left side of the equal sign
Draw 7 tiles on the right side How many more
tiles do you need on the left to make both sides
have the same number of tiles?
3 Complete the equation + 4 = 7
Example 2
Write five expressions to represent the number 6 Then write one
equation using two of the expressions.
1 Graph the number you want to represent The
5 + 1 represents 6 From the 5, you have to go one
space to the right to get to the number 6
3 Repeat the process until you have five expressions 5 + 1 = 4 + 2
3 + 3 = 2 + 4
1 + 5 = 0 + 6
Take two of the expressions and put them together
with an equal sign
YOUR TURN!
Write five expressions to represent the number 16 Then write
one equation using two of the expressions.
1 Graph the number you want to represent
8 9 10 11 12 13 7
5
Write the first expression by writing the number
plus 0
2 What is the whole number before 16? The number 16 is
one space away Write this as an expression
3 Repeat the process until you have five expressions Take two of
the expressions and put them together with an equal sign
Trang 33
Copyright © by The McGraw-Hill Companies, Inc.
4 Write two expressions to represent the number 10
Step 1 Graph the number you want to represent
Step 2 The first expression can be the number plus zero
+ 0
Step 3 What is the whole number before 10?
Step 4 The number before is one space away
Write this as an expression + 1
Step 5 Write both expressions
Trang 34Copyright © by The McGraw-Hill
1 9 10 11 12 13 14 15 16 17 18 19 20 0
Solve.
One piece was 7 feet How long was the other piece? Write
the equation to represent the rope
Understand Read the problem Write what you know
The total length of the rope is feet
One piece was feet
Plan Pick a strategy One strategy is to act it out Place a
rope next to a number line
9 ft
Solve Cut the rope so that one piece is 7 feet
Count the units on the number line to find the length of the other piece
Write the equation 7 + = 9
Check Do both sides of the equation have the same
value?
Look for a pattern.
Guess and check.
✓ Act it out
Solve a simpler problem.
Work backward.
Trang 35Copyright © by The McGraw-Hill Companies, Inc.
8 feet The other was 7 feet How long are the pieces together?
Write an equation to represent the ribbon Check off each step
Understand Plan
Solve Check
Saturday’s basketball game Leigh scored 10 points Did Tana score
more or fewer points than Leigh? Write the equation to represent
the points Leigh and Tana scored
11 If you know the value of the right side of an equation, do
you also know the value of the left side? Explain
Skills, Concepts, and Problem Solving
Write true or false for each statement If a statement is false,
change the statement to make it true.
12 An expression is a mathematical sentence that has an
equal sign
13 An equation is a mathematical sentence stating that two
expressions are equal
Write expression or equation for each of the following.
Trang 36Copyright © by The McGraw-Hill
Write five expressions to represent each number Use the number line.
17 4
3 4 5 6 7 8 2
1 9 10 11 12 13 14 15 16 17 18 19 20 0
18 14
3 4 5 6 7 8 2
1 9 10 11 12 13 14 15 16 17 18 19 20 0
Solve.
Write an equation to represent the CDs that Aiden has left
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
four numbers
Vocabulary Check Write the vocabulary word that completes each sentence.
21 A phrase that represents numbers is called a(n)
22 A mathematical sentence stating that two expressions are equal is
23 Writing in Math Write an example of an expression and an
equation Explain the difference between expressions and equations
Spiral Review
24 Use a number line to graph the whole
numbers between 47 and 55 (Lesson 1-2, p 11)
Solve (Lesson 1-1, p 4)
3 Main Street and 5 Main Street Circle the store
Trang 37Copyright © by The McGraw-Hill Companies, Inc.
Even numbers are any whole numbers that have been
multiplied by 2 The last digit of the number will be a
0, 2, 4, 6, or 8 Zero is an even number Even numbers
are shown in red above
Odd numbers are not multiples of 2 The last digit
of the number will be a 1, 3, 5, 7, or 9 Odd numbers are
shown in blue above
A number pattern is a regular, repeating sequence of
1 Locate 8 on the number line Circle it to
remind yourself that you are graphing
numbers less than 8
2 Name a number less than 8 Notice that
the number is to the left of 8 on the
number line
3 There is an even number before and after
every odd number
From 8, moving left, skip over a number,
and place a point above 6 Place dots on
the numbers 4, 2, and 0.
2 What is a number less than 8?
Is it to the left or right of 8 on the number line?
3 There is an odd number before and after every even number
From 8, place a dot on every odd number less than 8
GO ON
1NS1.2 Compare and order whole numbers to 100 by using
the symbols for less than, equal
to, or greater than (<, =, >).
Trang 38Copyright © by The McGraw-Hill
Example 2
Complete the number pattern
11, 14, 17, , 23
Explain the pattern.
1 Graph the numbers on a number line
13 14 15 16 17 18 12
11 19 20 21 22 23 24 25
10
2 To get from 11 to 14, count to the right
right three numbers to get from 14 to 17
3 Graph the missing point in the pattern
4 Complete the pattern
11, 14, 17, 20 , 23
5 Explain the pattern
Add 3 to each number
YOUR TURN!
Complete the number pattern.
19, 16, 13, _, 7 Explain the pattern.
1 Graph the numbers on a number line
8 9 10 11 12 13 7
5
2 How many numbers are there from
19 to 16?
Did you count to the right or left of 19?
How many numbers are there from
Trang 39Copyright © by The McGraw-Hill Companies, Inc.
Guided Practice
1 Numbers that end in 1, 3, 5, 7, and 9 are called numbers
2 Whole numbers that end in 0, 2, 4, 6, and 8 are called
numbers
For each number, write even or odd.
7 Graph the even whole numbers less than 7 on the number line
Step 1 Locate on the number line
Step 2 Numbers less than 7 are to the on the
number line
Step 3 The number is even and closest to 7
Step 4 Graph the even numbers to the left of 7 on the
number line
Graph the even whole numbers on the number line.
of 2 Odd numbers are not.
GO ON
Trang 40Copyright © by The McGraw-Hill
Solve.
and greater than 3 What number am I?
Understand Read the problem Write what you know
The number is greater than The number is less than
Plan Pick a strategy One strategy is to draw a graph
Create a number line Label it from 0 to 8
Solve Locate 6 on the number line Draw an arrow from
the 6 pointing to the numbers that are less than 6
Locate 3 Draw an arrow from the 3 pointing to the numbers that are greater than 3
The number 4 solves the puzzle
20 What number am I? Check off each step
Understand
Plan
Solve
Check
more than 38 My last digit is a 0 What number am I?