California math triumphs place value and basic number skills volume 1b

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Authors Basich Whitney • Brown • Dawson • Gonsalves • Silbey • Vielhaber

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California Math Triumphs

Volume 1 Place Value and Basic Number Skills

Volume 2 Fractions and Decimals

Volume 3 Ratios, Rates, and Percents

Volume 4 The Core Processes of Mathematics

Volume 5 Functions and Equations

Graphs and Functions

Volume 6 Measurement

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Authors 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

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California 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

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California 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

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Volume 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 +

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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

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

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)

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3 Addition and Subtraction

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.

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x

Chapters 1, 2, and 3 are contained in Volume 1A Chapters 4, 5, and 6 are contained in Volume 1B.

Chapter

4 Multiplication

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

Progress Check 4 60

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

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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.

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3NS2.6 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

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HUNT

SCAVENGER

HUNT

Let’s Get Started

Use the Scavenger Hunt below to learn where things are

located in each chapter

found on page 107 The URL is ca.mathtriumphs.com

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You know how to add

Examples: 2 + 2 + 2 = 6

10 + 10 + 10 + 10 = 40

300 + 300 + 300 = 900 TRY IT!

Multiples of 4 are the numbers you

say when you skip-count by 4

2 + 3 = 5 3 + 2 = 5These sentences show

the Commutative Property of

Addition

Lessons 4-4 through 4-13

5 × 4 = 20 4 × 5 = 20These sentences show

the Commutative Property of

Multiplication

Changing the order in which you multiply numbers does not change the product

STEP 1 Quiz Are you ready for Chapter 4? Take the Online Readiness

Quiz at ca.mathtriumphs.com to find out

STEP 2 Preview Get ready for Chapter 4 Review these skills and compare

them with what you’ll learn in this chapter

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Lesson

4-1

VOCABULARY product

the answer or result of a multiplication problem; it also refers to expressing

a number as the product

of its factors

factor

a number that divides into a whole number evenly; also a number that is multiplied by another number factors product

2 × 3 = 6

array

an arrangement of objects or symbols in rows of the same length and columns of the same length; the length of a row might be different from the length of a column

multiplication

an operation on two numbers to find their product; it can be thought

of as repeated addition Example: 4 × 3 is the same as the sum of four 3s, which is 3 + 3 + 3 +

The symbols × and · are used for multiplication Five times

two can be written as 5 × 2, 5 · 2, or 5(2)

You can model multiplication with an array

2 × 5 is 2 groups of 5, or 5 × 2 is 5 groups of 2

0OFGBDUPSJTUIF OVNCFSPGSPXT

5IFPUIFSGBDUPSJTUIF OVNCFSPGDPMVNOT

The product is the total number of rectangles in the array

The product using either method is 10

The Commutative Property of Multiplication states that the

order in which you multiply the numbers does not matter

So, 2 × 5 = 5 × 2

3NS2.2 Memorize to automaticity the multiplication table for numbers between

1 and 10.

4NS4.1 Understand that many whole numbers break down in different ways.

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Example 1

Draw an array to model the expression

6 × 3 Then write and model the

Count the number

Count the number of rectangles The

product of 3 and 6 is equal to the product

of 6 and 3, which is 18

YOUR TURN!

Draw an array to model the expression

7 × 2 Then write and model the commutative fact

1 Identify the first number in the expression 7

2 Identify the second number in the expression 2

Count the number of rectangles

Use a number line to model the expression 2 × 3

This is the number of times the group is repeated

This is the group size

3 Draw a number line Mark off 2 groups of 3

The product is 6

GO ON

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3 Write 2 + 2 + 2 + 2 as a multiplication expression

Step 3 Write the multiplication fact

YOUR TURN!

Use a number line to model the expression 3 × 5

3 Draw a number line

Mark off 3 groups of 5

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Write each repeated addition fact as a multiplication expression Then

write the commutative fact.

4 5 + 5 + 5 3 × 5 = 15; 5 × 3 = 15 5 9 + 9 2 · 9 = 18; 9 · 2 = 18

6 4 + 4 + 4 + 4 + 4 5 × 4 = 20; 4 × 5 = 20 7 3 + 3 + 3 + 3 4 · 3 = 12; 3 · 4 = 12

Solve.

8 INTERIOR DESIGN Natalie and her mom are tiling a

rectangular kitchen floor Each tile is 1 foot by 1 foot The

length of the kitchen is 8 feet and the width is 14 feet How

many tiles will they need to cover the floor?

Understand Read the problem Write what you know

The rectangular floor is 8 ft by 14 ft

Each tile is a 1 foot square.

Plan Pick a strategy One strategy is to draw a diagram

You need to find how many tiles are needed to cover the whole floor

Solve Draw a rectangle Divide it so it has 8 rows and

14 columns

0OFGBDUPS

JTUIF OVNCFS PGSPXT

0OFGBDUPSJTUIFOVNCFSPGDPMVNOT

Write a multiplication fact for the array 8 × 14

Write the expression as repeated addition

How many tiles will Natalie and her mom need?

112Check Count the squares in the diagram to verify your answer

✓ Draw a diagram.

Use logical reasoning.

Solve a simpler problem Work backward.

Use an equation.

GO ON

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9 HEALTH Lakeesha takes a multivitamin each morning and a

vitamin C tablet each night Write a multiplication expression to

show how many vitamins Lakeesha needs for a 30-day supply of

vitamins How many vitamins is this? 2 · 30; 60 vitamins

Check off each step

✔ Understand

✔ Plan

✔ Solve

✔ Check

10 MUSIC At Caroline’s middle school, the music teacher teaches

music to each grade two times a week If there are three grades at

Caroline’s middle school, how many times does the music teacher

teach each week? Write a multiplication expression to show how

you found the answer

11 Use graph paper and draw as many different rectangular

arrays for the number 12 as possible

Skills, Concepts, and Problem Solving

Use a number line to model each expression Then write and model

the commutative fact

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GO ON

Draw an array to model each expression Then write and model the

commutative fact.

14 4 · 5 4 · 5 = 20; 5 · 4 = 20 15 5 × 3 5 × 3 = 15; 3 × 5 = 15

Write the multiplication expression as repeated addition

Then write the commutative fact.

18 8 × 3 3+3+3+3+3+3+3+3 19 6 × 5 5 + 5 + 5 + 5 + 5 + 5

Write the repeated addition as a multiplication expression

24 PACKAGING There are two different-sized packages of cinnamon

rolls One package has 8 rolls across and 2 rolls down The other

package has 3 rolls across and 4 rolls down Which package holds

more rolls? How much more?

The first package holds 4 more.

25 PUZZLES Gloria and her sister Cherise worked together on a

puzzle Gloria measured the length of the puzzle to be 10 inches

and the width to be 9 inches If each piece of the puzzle is about

1 inch square, about how many pieces are in their puzzle? Write an

addition sentence to find the answer

9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 = 90

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Vocabulary Check Write the vocabulary word that completes each

sentence.

26 The product of two numbers indicates what operation? multiplication

27 Writing 4 × 6 = 6 × 4 is an example of the Commutative

Property of Multiplication

28 The numbers being multiplied in an expression are called factors .

29 Writing in Math How can you verify the Commutative Property

of Multiplication?

Sample answer: Make an array for a given multiplication expression Then

interchange the order of factors Create the array for the second expression

The number of rectangles in both arrays is the same.

Spiral Review

Solve (Lesson 2-6, p 85)

30 MONEY Look at the deposit slip shown at

the right What is the amount of total deposits

rounded to the nearest ten thousand?

31 FOOD The cafeteria served thirty-five thousand, two

hundred ninety-three cookies during the entire school year

What is this amount rounded to the nearest hundred?

35,300

Write each number in word form (Lesson 2-5, p 80)

32 2,503,250 two million, five hundred three thousand, two hundred fifty

33 1,770,609 one million, seven hundred seventy thousand, six hundred nine

34 3,900,000 three million, nine hundred thousand

Write the counting numbers between the following numbers. (Lesson 1-1, p 4)

35 9 and 14 10,11,12,13 36 3 and 7 4,5,6

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Lesson

4-2

VOCABULARY Identity Property of Multiplication

if you multiply a number

by 1, the product is the same as the given number

Example: 8 × 1 = 8 =

1 × 8.

Zero Property of Multiplication

if you multiply a number

by zero, the product

is zero Example: 0 × 5 = 0.

expanded form

the representation of a number as a sum that shows the value of each digit

Example: 536 can be written as 500 + 30 + 6.

3 Multiply 2 times the digit in

the ones column 2 · 1 = 2

101

× 2

2

4 Multiply 2 times the digit

in the tens column 2 · 0 = 0

Write the product in the

tens column

101

× 2

02

in the hundreds column

2 · 1 = 2 Write the product in the hundreds column

The Zero Property of Multiplication states that any number

times zero is zero

5 × 0 = 0 because five groups of zero is zero.

The Identity Property of Multiplication states that any

number times 1 is equal to that number

5 × 1 = 5 because five groups of one is five

The multiples of 10 are:

1 and 10.

3NS2.4 Solve simple problems involving multiplication of multidigit numbers by one-digit numbers 3NS2.6 Understand the special properties of 0 and 1 in multiplication and division.

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4 Multiply 7 times the

hundreds place value

in the ones column

4 · 0 = 0

110

× 4

0

in the tens column

in the hundreds column

4 · 1 = 4 Write the product in thehundreds column

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Circle correct answer(s) Cross out incorrect answer(s)

Step 2 Rewrite the problem in vertical format

1 0 1

× 8 8

8 × 1 = 8

1 0 1

× 8 08

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Find each product

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Solve

23 FASHION Emma plans to buy several shirts that are on

sale for $10 each Emma wants to know if she has enough

money to buy 2, 3, or 4 shirts What is the price of 2, 3, and

4 shirts?

Emma wants to buy shirts that are $10 each.

Plan Pick a strategy One strategy is to look for a pattern

Solve List the multiples of 10: 1 × 10 = 10 ,

2 × 10 = 20 , 3 × 10 = 30 .

Look for the pattern Notice the ones digit is a

0 ,while the tens digit is the other factor

Find the pattern What is the price of 1 shirt? $10

2 shirts? $20 3 shirts? $30 4 shirts? $40Check Does the answer make sense? Look over your

solution Did you answer the question?

24 NATURE Suri planted a sapling that grows 10 inches a month

How many inches will it grow in 6 months? 60 inches

Check off each step

✔ Understand

✔ Plan

✔ Solve

✔ Check

25 COMMUNITY SERVICE The fifth graders collected 7 bags of

canned goods to donate to a charity If each bag held 10 cans, how

many cans did they collect in all? 70

26 Explain how to multiply using the expanded form of the

factors in a multiplication problem

Write one factor in expanded form Then find the product of each of the place

values and the other factor The sum of the products is the final product.

Problem-Solving Strategies

Draw a diagram.

Solve a simpler problem Work backward.

✓ Look for a pattern.

GO ON

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16 Chapter 4 Multiplication

Find each product Estimate first.

39 FOOD How many hot dogs are in five packages?

5 × 10 = 50 There are 50 hot dogs in the five

packages.

40 MONEY There are ten pennies in each dime If you have six

dimes, how many pennies do you have?

6 · 10 = 60 You have 60 pennies.

FOOD Hot dogs are packaged in groups of 10.

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sentence

41 The Identity Property of Multiplication says that when you

multiply a number by 1, the product is the same as the given

number

42 The property that states if you multiply a number by zero, the

product is zero is called the Zero Property of Multiplication .

43 Writing in Math Write the fact family for 1 × 9 Explain how you

know the facts in a family

There are two multiplication facts, the given fact and its

commutative fact There are two division facts,

the inverse statement for each multiplication fact.

Spiral Review

Solve (Lesson 2-4, p 91)

44 COMPUTERS Amado needs to create a password for his

computer He wants to use the digits 4, 9, 6, and 2 He also wants

the number to be odd and round to 2,000 What four-digit number

should he use as his password?

2,469

45 SAVINGS The amount of money that Tamika has invested in

savings bonds rounds to $3,000 and has the digits 8, 1, 4, 2 How

much has Tamika invested if the amount is an even number?

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18 Chapter 4 Multiplication

Chapter

4 Progress Check 1 (Lessons 4-1 and 4-2)

Use a number line to model each expression Then write and model

1 2 · 3 = 6 3 · 2 = 6

Draw an array to model each expression Then write the

2 3 · 8 = 24 8 · 3 = 24

Write the repeated addition as a multiplication expression Then write

14 GAMES How many 1 × 1 squares are on the checkerboard

shown? 64 Half of the 1 × 1 squares are black How many

is that? 32

15 COOKING To make one pizza, Tyrone uses 10 ounces of flour,

8 ounces of pepperoni, 5 ounces of pizza sauce, and 4 ounces

of cheese How much of each ingredient will Tyrone need to

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Lesson

4-3

VOCABULARY double or twice

two times a number; words that indicate to multiply by two are double

a number or twice a number

multiple

a multiple of a number is

the product of that

number and any whole number

Example: 30 is a multiple of 10 because

There are several phrases that mean multiplying 9 by 2

• the product of two and nine

• two times nine

• double the number nine

• twice the number nine

Multiply by 2

Example 1

Find the product of 8 and 2 by using repeated addition Then write

the multiplication fact and its commutative fact.

1 What is the first factor? 8

What is the second factor? 2

2 Write an equation as repeated addition Use the first factor as the

number being added and the second factor as the number of times

you add the number 8 + 8 = 16

3 Write the multiplication fact 8 × 2 = 16

4 Write the commutative fact 2 × 8 = 16

You should practice memorizing the multiplication facts of 2 According

to the Commutative Property, the product is the same, whether the

factor 2 is the first factor or the second factor

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.

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YOUR TURN!

Find the product of 5 and 2 by using repeated addition Then write

the multiplication fact and its commutative fact.

1 What is the first factor? 5 What is the second factor? 2

2 Write an equation as repeated addition Use the first factor as the

number being added and the second factor as the number of times

you add the number 5 + 5 = 10

3 Write the multiplication fact 5 × 2 = 10

Example 2

Use an array to find the missing number that

would make the equation true

4 × ? = 8

1 How many rectangles should be inside

the array? 8

2 The factor already in the equation is 4

The array will have four rows

3 Continue making columns until there are

8 rectangles in the array The number of

columns is the missing number How

many columns do you make? 2

2 columns of 4 rows make 8 rectangles

4 The missing number is 2

The completed equation is 4 × 2 = 8

2 The factor already in the equation is

6 The array will have six rows.

3 Continue making columns until there are

12 rectangles How many columns

do you make? 2

2 columns of 6 rows

make 12 rectangles

4 The missing number is 2

The completed equation is

6 × 2 = 12.

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Circle correct answer(s) Cross out incorrect answer(s)

Guided Practice

Find each product by using repeated addition.

Draw an array to model each expression Find the product

How many columns do you use? 6

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Build the array with 2 rows and a total of 18 squares

How many columns are there? 9

19 The Hilltop Miniature Golf Center has a course with 18

holes The par for each hole is two strokes If a player gets

a par score on each hole, what would be the score for the

18-hole course?

There are 18 holes on the course

The score for each hole is 2 strokes.

Plan Pick a strategy One strategy is to draw a diagram

Solve Draw an array that is 18 by 2

Count the number of squares

The par score for the 18-hole course is 36 strokes

Check You can skip-count by two 18 times

✓ Draw a diagram.

Solve a simpler problem.

Work backward.

Look for a pattern.

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GO ON

20 GAMES Marjorie and Helen have one bag of 18 marbles

They each take a marble from the bag until the bag is

empty How many marbles does each girl get? 9

Check off each step

✔ Understand

✔ Plan

✔ Solve

✔ Check

21 BOOKS Over the summer, two students each read 7 books

How many books did they read total? 14

22 How do you multiply by 2?

Add the number to itself

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37 PACKAGING Paper towels come in packages of 2 How many rolls

are there in 8 packages? 16

38 MONEY A dime is worth 2 nickels If you have five dimes,

how many nickels would have the same value?

5 · 2 = 10 Five dimes have the same value as 10 nickels.

39 FASHION Kraig bought 3 pairs of shoes How many shoes does he

have? 6

sentence

40 In the expression 2 · 3, 2 and 3 are factors

41 When you double a number, you multiply the number by 2.

42 Writing in Math Write three different phrases that describe the

expression 2 · 4

Sample answer: the product of 2 and 4, double the number 4,

twice the number 4, 2 times 4

Spiral Review

43 SLEEP On Saturday night Henry slept for 9 hours On Sunday night,

Henry slept 8 hours How many hours did he sleep on those two

nights?

17 hours (Lesson 3-3, p 145)

Write each number in expanded form (Lesson 2-3, p 85)

44 8,905 8,000 + 900 + 5 45 6,780 6,000 + 700 + 80

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Lesson

4-4

VOCABULARY factor

a number that divides into a whole number evenly; also a number that is multiplied by another number

(Lesson 4-1, p 4)

fact family

a group of related facts using the same numbers Example: 5 × 3 = 15,

20 ÷ 5 = 4 ← related division facts → 20 ÷ 4 = 5

You can find 18 × 5 in several ways:

You should practice memorizing the multiplication facts of 5

According to the Commutative Property, the product is the same

whether the factor 5 is the first factor or the second factor.

Example 1

Find the product of 5 and 7 by using

repeated addition Then write the

multiplication fact and its commutative fact.

2 Write an equation as repeated addition Use

the first factor as the number being added

and the second factor as the number of

times you add the number

7 + 7 + 7 + 7 + 7 = 35

3 Write the multiplication fact 5 × 7 = 35

YOUR TURN!

Find the product of 5 and 9 by using repeated addition Then write the multiplication fact and its commutative fact.

2 Write an equation as repeated addition Use the first factor as the number being added and the second factor as the number of times you add the number

× 5 90

GO ON

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.

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Write the tens digit above the tens

column and the ones digit in the

product under the ones column

1 43

× 5

5

4 Multiply 5 times the

digit in the tens column

5 × 4 = 20

Addone 10 for 21

1 43

× 5

215

5 The product is 215 Compare to your

estimate for reasonableness

Trang 39

Step 2 Rewrite the problem in vertical format

Step 3 Multiply 5 times the digit in the ones column

4,535

Compare to your estimate for reasonableness

GO ON

Trang 40

Find each product Estimate first.

19 PARKS There are five benches in the park Each bench

has three children sitting on it How many children are

sitting on the benches altogether?

There are 5 benches

3 children are on each bench.

Plan Pick a strategy One strategy is to draw a picture

Read the problem Each rectangle represents a bench Each circle represents a child

Solve

number of benches · number of children on each bench = total children

5 · 3 = 15 Check Count the circles in the picture Does the count

match your answer?

Solve a simpler problem.

Work backward.

Look for a pattern.

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