Smart to the Core Teachers’ Edition - Grade 3 (BEST) by Educational Bootcamp

SMART TO THE CORE

Tel. 305-423-1999

TEACHER’S EDITION

Educational Bootcamp

www.educationalbootcamp.com jandj@educationalbootcamp.com

GRADE 3 EDUCATIONAL BOOTCAMP

grade 3

Teacher’s Edition

TEACHER’S EDITION BOOKLET GRADE 3 Building Depth of Knowledge (DOK)

THIS BOOKLET INCLUDES: Core Skills Activities - the activities within each mission progresses from DOK 1 to DOK 3 to master each standard. Each Core Skills Activity is a set of standards-based basic skills practice questions. Practice Drill Questions - practice problems requiring the application of skills and real-world problem-solving. The Practice Drill Question sets within each mission progress from DOK 1 up to DOK 3.

DIGITAL COMPONENT: Five-Star Challenge - assessments by standard that measure students’ depth of knowledge including their ability to reason abstractly, create models, write arguments and critique strategies.

MATH BOOTCAMP® - SMART TO THE CORE TEACHER’S EDITION - GRADE 3 (FLORIDA) Copyright© 2023 by Educational Bootcamp. First Edition. All rights reserved. Publisher: J&J Educational Boot Camp, Inc. Content Development: Educational Bootcamp J&J Educational Boot Camp, Inc. www.educationalbootcamp.com jandj@educationalbootcamp.com No part of this publication may be reproduced, transmitted, or stored in a retrieval system, in whole or in part, in any form or by any means, electronic or mechanical, including photocopying, recording, or otherwise, without written permission of Educational Bootcamp.

Educational Bootcamp and Math Bootcamp are registered trademarks of J&J Educational Boot Camp, Inc. Printed in the United States of America For information regarding the CPSIA on printed material call: 203-595-3636 and provide reference # LANC 807255

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TABLE OF CONTENTS MISSION

FL CODE

BENCHMARKS FOR EXCELLENT STUDENT THINKING

PAGES

NUMBER SENSE AND OPERATIONS MISSION 1 Reading and Writing Numbers MISSION 2 Composing and Decomposing Four-Digit Numbers

MA.3.NSO.1.1

MA.3.NSO.1.2

MISSION 3 Plotting and Ordering Whole Numbers

MA.3.NSO.1.3

MISSION 4 Rounding Whole Numbers

Read and write numbers from 0 to 10,000 using standard form, expanded form. Compose and decompose four-digit numbers in multiple ways using thousands, hundreds, tens and ones. Demonstrate each composition or decomposition using objects, drawings and expressions or equations.

1-8

9 - 16

Plot, order and compare whole numbers up to 10,000.

17 - 24

MA.3.NSO.1.4

Round whole numbers from 0 to 1,000 to the nearest 10 or 100.

25 – 32

MISSION 5 Adding and Subtracting Multi-Digit Numbers

MA.3.NSO.2.1

Add and subtract multi-digit whole numbers including using a standard algorithm with procedural fluency.

33 - 40

MISSION 6 Multiply a One Digit Whole Number

MA.3.NSO.2.3

Multiply a one-digit whole number by a multiple of 10, up to 90, or a multiple of 100, up to 900, with procedural reliability.

41 - 48

MA.3.NSO.2.4

Multiply two whole numbers from 0 to 12 and divide using related facts with procedural reliability.

49 - 56

MA.3.NSO.2.2

Explore multiplication of two whole numbers with products from 0 to 144, and related division facts.

MISSION 7 Multiplying Two Whole Numbers and Divide

FRACTIONS MISSION 8 Representing and Interpreting Unit Fractions MISSION 9 Representing and Interpreting Fractions Greater than One MISSION 10 Reading and Writing Fractions

MISSION 11 Plotting, Ordering, and Comparing Fractional Numbers MISSION 12 Finding Equivalent Fractions ii

Represent and interpret unit fractions in the form 1/n as the quantity formed by one part when a whole is partitioned into n equal parts.

57 - 64

MA.3.FR.1.2

Represent and interpret fractions, including fractions greater than one, in the form of m/n as the result of adding the unit fraction 1/n to itself m times.

65 - 72

MA.3.FR.1.3

Read and write fractions, including fractions greater than one, using standard form, numeral-word form and word form.

73 - 80

MA.3.FR.2.1

Plot, order and compare fractional numbers with the same numerator or the same denominator.

81 - 83

MA.3.FR.2.2

Identify equivalent fractions and explain why they are equivalent.

89 - 96

MA.3.FR.1.1

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP

TABLE OF CONTENTS MISSION MISSION 13 Applying the Properties of Multiplication MISSION 14 Solving Real-World Problems MISSION 15 Evaluating Equations MISSION 16 Determining Unknown Whole Numbers

MISSION 17 Identifying Even and Odd Whole Numbers MISSION 18 Determining Multiples MISSION 19 Finding Numerical Patterns

FL CODE

BENCHMARKS FOR EXCELLENT STUDENT THINKING

MA.3.AR.1.1

ALGEBRAIC REASONING Apply the distributive property to multiply a one-digit number and two-digit number. Apply properties of multiplication to find a product of one-digit whole numbers.

MA.3.AR.1.2

MA.3.AR.2.2 MA.3.AR.2.3

PAGES

97 - 104

Solve one- and two-step real-world problems involving any of four operations with whole numbers.

105 - 112

Determine and explain whether an equation involving multiplication or division is true or false.

113 - 120

Determine the unknown whole number in a multiplication or division equation, relating three whole numbers, with the unknown in any position.

121 – 128

MA.3.AR.2.1

Restate a division problem as a missing factor problem using the relationship between multiplication and division.

MA.3.AR.3.1

Determine and explain whether a whole number from 1 to 1,000 is even or odd.

129 - 136

MA.3.AR.3.2

Determine whether a whole number from 1 to 144 is a multiple of a given one-digit number.

137 - 144

MA.3.AR.3.3

Identify, create and extend numerical patterns.

145 - 152

MEASUREMENT MISSION 20 Using Measuring Tools

MA.3.MD.1.1

Select and use appropriate tools to measure the length of an object, the volume of liquid within a beaker and temperature.

153 - 160

MISSION 21 Solving Real-world Problems

MA.3.MD.1.2

Solve real-world problems involving any of the four operations with whole-number lengths, masses, weights, temperatures or liquid volumes.

161 - 168

MISSION 22 Telling and Writing Time to the Nearest Minute

MA.3.MD.2.1

Using analog and digital clocks tell and write time to the nearest minute using a.m. and p.m. appropriately.

169 - 176

MISSION 23 Finding Elapsed Time

MA.3.MD.2.2

Solve one- and two-step real-world problems involving elapsed time.

iii

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177 - 184

TABLE OF CONTENTS GEOMETRIC

REASONING

MISSION 24 Identifying Points, Lines, and Line Segments

MA.3.GR.1.1

Describe and draw points, lines, line segments, rays, intersecting lines, perpendicular lines and parallel lines. Identify these in two-dimensional figures.

185 - 192

MISSION 25 Identifying and Drawing Quadrilaterals

MA.3.GR.1.2

Identify and draw quadrilaterals based on their defining attributes. Quadrilaterals include parallelograms, rhombi, rectangles, squares and trapezoids.

193 - 200

MISSION 26 Drawing Lines of Symmetry

MA.3.GR.1.3

Draw line(s) of symmetry in a two-dimensional figure and identify line-symmetric two-dimensional figures.

201 - 208

MA.3.GR.2.1

Explore area as an attribute of a two-dimensional figure by covering the figure with unit squares without gaps or overlaps. Find areas of rectangles by counting unit squares.

209 - 216

MA.3.GR.2.2

Find the area of a rectangle with whole-number side lengths using a visual model and a multiplication formula.

217 - 224

MA.3.GR.2.3

Solve mathematical and real-world problems involving the perimeter and area of rectangles with whole-number side lengths using a visual model and a formula.

225 - 232

MA.3.GR.2.4

Solve mathematical and real-world problems involving the perimeter and area of composite figures composed of non-overlapping rectangles with whole-number side lengths.

233 - 240

MISSION 27 Exploring Area as an Attribute of TwoDimensional Figures

MISSION 28 Determining the Area of a Rectangle MISSION 29 Solving Problems Involving Area and Perimeter MISSION 30 Finding Perimeter and Area of Composite Figures

DATA ANALYSIS & PROBABILITY MISSION 31 Collecting and Representing Data

MA.3.DP.1.2

Interpret data with whole-number values represented with tables, scaled pictographs, circle graphs, scaled bar graphs or line plots by solving one– and two-step problems.

MA.3.DP.1.1

Collect and represent numerical and categorical data with whole-number values using tables, scaled pictographs, scaled bar graphs or line plots. Use appropriate titles, labels and units.

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, Inc.

241- 248

READING AND WRITING NUMBERS

MA.3.NSO.1.1 Read and write numbers from 0 to 10,000 using standard form, expanded form and word form. Use a place value table to write multi-digit numbers in expanded or word form.

Example: 8,472 THOUSANDS

HUNDREDS

TENS

ONES

8 × 1,000

4 × 100

7 × 10

2×1

8,000

400

8,472 in expanded form is 8,000 + 400 + 70 + 2.

8,472 in word form is eight thousand four hundred seventy-two. To read multi-digit numbers, knowing the place value of each digit is important. Starting at the rightmost digit and moving left, the place values of each digit are ones, tens, hundreds, and thousands. Use baseten blocks to visualize these place values. Read the number based on the place value of each digit.

Example: 2,536 STANDARD FORM

THOUSANDS

HUNDREDS

TENS

ONES

two thousand

five hundred

thirty

six

2 × 1,000 = 2,000

5 × 100 = 500

3 × 10 = 30

6×1=6

BASE-TEN BLOCKS

WORD FORM

EXPANDED FORM

2,000 + 500 + 30 + 6 1

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DIRECTIONS: Write these numbers in expanded form.

3,482

3,000 + 400 + 80 + 2

1,958

1,000 + 900 + 50 + 8

4,672

4,000 + 600 + 70 + 2

8,053

8,000 + 50 + 3

6,581

6,000 + 500 + 80 + 1

DIRECTIONS: Write these numbers in word form.

7,356

Seven thousand three hundred fifty-six

1,463

One thousand four hundred sixty-three

2,967

Two thousand nine hundred sixty-seven

6,374

Six thousand three hundred seventy-four

4,087

Four thousand eighty-seven

DIRECTIONS: Write these numbers in standard form.

2,000 + 400 + 10 + 6

2,416

Six thousand five hundred eighty-seven

6,587

1,000 + 900 + 20 + 4

1,924

Five thousand fifty-eight

5,058

7,000 + 300 + 40

7,340

Three thousand four hundred eighty-five

3,485

8,000 + 600 + 40 + 4

8,644

Nine thousand five hundred thirteen

9,513

2,000 + 20 + 8

2,028

Six thousand six hundred seventy-four

6,674

COPYING IS STRICTLY PROHIBITED BY LAW

DIRECTIONS: Write these numbers in expanded form. 7,390

7,000 + 300 + 90

6,315

6,000 + 300 + 10 + 5

2,766

2,000 + 700 + 60 + 6

4,201

4,000 + 200 + 1

9,038

9,000 + 30 + 8

DIRECTIONS: Write these numbers in word form. 2,538

Two thousand five hundred thirty-eight

3,281

Three thousand two hundred eighty-one

4,785

Four thousand seven hundred eighty-five

4,556

Four thousand five hundred fifty-six

2,209

Two thousand two hundred nine

DIRECTIONS: Write these numbers in standard form.

5,000 + 100 + 40 + 3

5,143

Three thousand five hundred eighty-seven

3,587

7,000 + 200 + 50 + 8

7,258

Eight thousand forty-one

8,041

3,000 + 800 + 20

3,820

Two thousand five hundred seventy-seven

2,577

9,000 + 900 + 20 + 3

9,923

Five thousand nine hundred eleven

5,911

7,000 + 90 + 6

7,096

Four thousand eight hundred fifty-two

4,852

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1 The number 5,075 can also be written as which of the following? Fifty thousand seventy-five Five thousand seven hundred fifty Five thousand seven hundred five Five thousand seventy-five

2 Which of these numbers is different from the rest? 2,840 Two thousand eight hundred four 2,000 + 800 + 4 2,804

3 Which of the following is the expanded form of 4,058? 4,000 + 50 + 8 4,000 + 500 + 8 4,000 + 500 + 80 4+0+5+8

4 What is the expanded form of nine thousand seven hundred twenty? 9 + 1,000 + 7 + 100 + 20 9 + 1,000 + 700 + 20 9,000 + 700 + 2 9,000 + 700 + 20

5 How do you write 5,000 + 60 + 8 in standard form? 5,068

5,608

5,680

568,000 COPYING IS STRICTLY PROHIBITED BY LAW

DIRECTIONS: Write these numbers in expanded form. 8,137

8,000 + 100 + 30 + 7

6,413

6,000 + 400 + 10 + 3

1,187

1,000 + 100 + 80 + 7

3,131

3,000 + 100 + 30 + 1

7,428

7,000 + 400 + 20 + 8

DIRECTIONS: Write these numbers in word form. 4,482

Four thousand four hundred eighty-two

6,925

Six thousand nine hundred twenty-five

9,210

Nine thousand two hundred ten

2,514

Two thousand five hundred fourteen

5,309

Five thousand three hundred nine

DIRECTIONS: Write these numbers in standard form.

2,000 + 700 + 60 + 2

2,762

One thousand one hundred fifty-five

1,155

8,000 + 100 + 50 + 1

8,151

Seven thousand ninety-two

7,092

6,000 + 800 + 70

6,870

Eight thousand eight hundred four

8,804

5,000 + 100 + 70 + 9

5,179

Six thousand seven hundred twenty-nine

6,729

5,000 + 70 + 3

5,073

Nine thousand three hundred sixty

9,360

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1 How do you write 3,000 + 700 + 4 in word form? Three thousand seven hundred four Three thousand seven hundred forty Three thousand seven hundred forty-four Three thousand seventy-four

2 Which of these numbers is different from the rest? 7,186 Seven thousand one hundred eighty-six 7,000 + 100 + 80 + 6 Seven thousand one hundred sixty-eight

3 The number 2,405 can also be written as which of the following? Two thousand four hundred five Two thousand forty-five Two thousand four hundred fifty Twenty four thousand five

4 Which of these numbers is different from the rest? 3,000 + 700 + 4 Three thousand seven hundred four 3,704 Three thousand seventy-four

5 The number 1,000 + 600 + 90 + 3 is the same as which of the following? 1,639

1,693

1,936

1,963 COPYING IS STRICTLY PROHIBITED BY LAW

1 The number eight thousand one hundred two can also be written as which of the following? 8,000 + 100 + 2 8,000 + 100 + 20 8 + 1,000 + 100 + 2 8 + 1,000 + 100 + 20

2 The number four thousand six hundred five is the same as which of the following? 4,650 4,065 4,000 + 600 + 5 4,000 + 600 + 50

3 Which of the following is the expanded form of 6,902? 6,000 + 90 + 2 6,000 + 900 + 2 6,000 + 900 + 20 6+9+0+2

4 What is the expanded form of four thousand three hundred nineteen? 4 + 1,000 + 3 + 100 + 19 4 + 3,000 + 100 + 90 4,000 + 300 + 10 + 9 4,000 + 3 + 19

5 The number five thousand sixty is the same as which of the following?

5,006

5,060

5,066

5,660

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6 How do you write 5,000 + 900 + 10 + 1 in word form? Five thousand nine hundred one Five thousand nine hundred eleven Five thousand nine hundred ten Five thousand ninety-one

7 Which of these numbers is different from the rest? 6,252 Sixty-two hundred and fifty-two 6,000 + 200 + 5 + 2 Six thousand two hundred fifty-two

8 The number 1,703 can also be written as which of the following? One thousand seventy-three One thousand seven hundred three Seventeen hundred and three Seventy thousand three

9 Which of these numbers is different from the rest? Two thousand forty-seven 2,000 + 400 + 7 2,407 Two thousand four hundred seven

10 The number 9,000 + 300 + 60 + 1 is the same as which of the following? 9,136

9,316

9,613

9,361

COPYING IS STRICTLY PROHIBITED BY LAW

COMPOSING AND DECOMPOSING FOUR-DIGIT NUMBERS

MA.3.NSO.1.2 Compose and decompose four-digit numbers in multiple ways using thousands, hundreds, tens and ones. Demonstrate each composition or decomposition using objects, drawings and expressions or equations. Use a place value table to compose a four-digit number and combine each digit’s values in their respective place values. Each digit in a multi-digit number, starting from the rightmost digit and moving left, represents ones, tens, hundreds, and thousandths. By adding these values together, you can create a complete number. Example: Compose a number that has 5 thousands, 62 tens, and 4 ones. THOUSANDS

HUNDREDS

TENS

ONES

5 × 1,000

0 × 100

62 × 10

4×1

5,000

620

Regrouping: •

10 ones = 1 ten

•

10 tens = 1 hundred

5,000 + 620 + 4 = 5,624 Adding the value of each digit, we can compose the number as: 5,000 + 620 + 4 = 5,624

When decomposing a four-digit number, remember that each digit represents a specific place value. Starting from the rightmost digit and moving left, each digit represents ones, tens, hundreds, and thousandths. You can also regroup each digit to represent different place values. Example: Decompose the number 8,736. The number 8,736 can be interpreted as having 8 thousands, 7 hundred, 3 tens, and 6 ones. THOUSANDS

HUNDREDS

TENS

ONES

8 × 1,000

7 × 100

3 × 10

6×1

8,000

700

Regrouping: •

10 ones = 1 ten

•

10 tens = 1 hundred

By adding the value of each digit, we can decompose the number as: 8 thousands + 7 hundreds + 3 tens + 4 ones 9

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DIRECTIONS: Decompose the number 3,475 in five different ways using regrouping. 3 thousands + 4 hundreds + 7 tens + 5 ones 3 thousands + 4 hundreds + 75 ones 3 thousands + 47 tens + 5 ones 34 hundreds + 7 tens + 5 ones 3,475 ones

DIRECTIONS: Decompose the number 6,083 in five different ways using regrouping. 6 thousands + 8 tens + 3 ones 6 thousands + 83 ones

6,083 ones 60 hundreds + 8 tens + 3 ones 608 tens + 3 ones

DIRECTIONS: Check (

) the number that is different from the rest.

7 thousands + 5 hundreds + 1 ten + 4 ones

64 hundreds + 5 tens + 9 ones

7,514 ones

6 thousands + 4 hundreds + 5 ten + 9 ones

75 thousands + 1 ten + 4 ones

6,459 ones

7 thousand + 51 tens + 4 ones

6 thousand + 5 tens + 9 ones

2 thousands + 86 hundreds + 3 ones

3 thousands + 5 hundreds + 7 ten + 8 ones

28 hundreds + 6 tens + 3 ones

3 thousand + 57 tens + 8 ones

2 thousands + 8 hundreds + 63 ones

35 thousands + 7 tens

2 thousands + 8 hundreds + 6 tens + 3 ones

35 thousands + 78 tens

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DIRECTIONS: Decompose the number 8,194 in five different ways using regrouping.

8 thousands + 1 hundreds + 9 tens + 4 ones 8 thousands + 1 hundreds + 94 ones 8 thousands + 19 tens + 4 ones 81 hundreds + 9 tens + 4 ones 8,194 ones

DIRECTIONS: Decompose the number 2,706 in five different ways using regrouping.

2 thousands + 7 hundreds + 6 ones 2 thousands + 706 ones 2,706 ones 27 hundreds + 6 ones 270 tens + 6 ones

DIRECTIONS: Check (

) the number that is different from the rest.

5 thousands + 2 hundreds + 8 tens + 1 one

6,309 ones

52 hundreds + 8 tens + 1 one

6 thousands + 3 hundreds + 9 tens

5,281 ones

63 hundreds + 9 tens

5 thousands + 2 hundreds + 81 tens

639 tens

3 thousands + 5 hundreds + 9 tens + 6 ones

1 thousand + 9 hundreds + 37 ones

359 tens + 6 ones

19 hundreds + 3 tens + 7 ones

35 thousands + 9 tens + 6 ones

1 thousand + 93 tens + 7 ones

3 thousands + 59 tens + 6 ones

1 thousand + 93 hundreds + 7 ones

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1 Jack is thinking of a number that has 50 tens and 11 ones. What is the number that Jack is thinking? 5,011

5,110

511

7,025

7,250

3,142

3,214

2,850

8,520

2 Which of the following base-ten block sets show 1,390?

3 Which of these numbers has 70 hundreds? 5,270

5,702

4 Which of these numbers has 14 tens?

1,423

2,314

5 Which of these numbers has 85 ones? 2,085

2,805

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DIRECTIONS: Decompose the number 2,354 in five different ways using regrouping.

2,354 ones 2 thousands + 3 hundreds + 54 ones 23 hundreds + 5 tens + 4 ones 235 tens + 4 ones 2 thousands + 3 hundreds + 5 tens + 4 ones

DIRECTIONS: Decompose the number 7,118 in five different ways using regrouping.

71 hundreds + 18 ones 7 thousands + 1 hundred + 1 ten + 8 ones 7,118 ones 71 hundreds + 1 ten + 8 ones 7 thousands + 1 hundred + 18 ones

DIRECTIONS: Check (

) the number that is different from the rest.

1 thousands + 3 hundreds +7 tens + 9 ones

9,529 ones

1 thousand + 37 hundreds + 9 ones

9 thousands + 5 hundreds + 9 tens + 2 ones

13 hundreds + 7 tens + 9 ones

95 hundreds + 92 ones

1,379 ones

952 tens + 2 ones

47 hundreds + 1 ten + 9 ones

2 thousands + 9 hundreds + 3 tens + 7 ones

471 tens + 9 ones

2 thousands + 937 ones

4 thousands + 7 hundreds + 1 ten + 9 ones

2 thousands + 93 hundreds + 7 ones

4 thousands + 719 tens

293 tens + 7 ones

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1 Which of these numbers is the same as 34 hundreds + 182 tens? 3,492

3,582

5,220

7,182

2 A number is shown using base-ten blocks. What number is shown?

286

386

2,176

2,186

3 Which of these numbers is the same as 1 thousand + 12 hundreds + 6 tens? 1,126

1,720

2,126

2,260

4 Which of these numbers is the same as 144 tens + 36 ones? 1,436

1,476

1,800

1,836

5 A number is shown using base-ten blocks. What number is shown?

1,162

1,172

1,262

COPYING IS STRICTLY PROHIBITED BY LAW

1,272

1 Peter’s lucky number has 2 thousands, 64 hundreds, and 18 ones. What is Peter’s lucky number? 2,648

2,658

8,418

8,580

2 Which of the following is the correct way to decompose 269 using base-ten blocks?

3 Emily wrote a number that has 2 ones, 172 tens, and 3 thousands. What number did Emily write? 2,175

2,372

4,722

3,174

5,857

7,250

9,417

9,174

4 Which of these numbers has 57 hundreds? 4,570

5,702

5 Which of these numbers has 17 ones? 1,947 15

1,794

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6 Which of these numbers is the same as 42 hundreds + 139 tens? 5,590

4,290

4,213

1,390

7 A number is shown using base-ten blocks. What number is shown?

240

386

354

254

8 Which of these numbers is the same as 3 thousand + 13 hundreds + 8 tens? 4,083

4,380

4,308

4,038

9 Which of these numbers is the same as 372 tens + 58 ones? 3,887

3,787

3,877

3,778

10 A number is shown using base-ten blocks. What number is shown?

1,237

1,272

1,262

COPYING IS STRICTLY PROHIBITED BY LAW

1,273

PLOTTING AND ORDERING WHOLE NUMBERS MA.3.NSO.1.3 Plot, order and compare whole numbers up to 10,000. To plot, order, and compare multi-digit numbers, use a number line with an appropriate scale. If the numbers are too close in value, use a smaller interval in scale. If the numbers are too far apart in value, use a bigger interval in scale. Ensure that the smallest number on the number line is smaller than the least number and that the largest number on the number line is greater than the greatest number. Remember, the number to the right is always greater than the number to the left.

Example: Plot 3,544, 3,872, and 3,250 on a number line and order the numbers from least to greatest. The numbers are too far apart (difference of hundreds), so using 100s as intervals is best. Also, the least number is 3,250, so use 3,200 as the smallest number on the number line. The greatest number is 3,872, so use 3,900 as the largest number on the number line. 3,200

3,300

3,400

3,500

3,600

3,700

3,800

3,900

Plot the numbers: 3,250 is 1 between 3,200 and 3,300, 3,544 is about less than halfway 4 3 between 3,500 and 3,600, and 3,872 is about 4 between 3,800 and 3,900. 3,250 3,200

3,544 3,300

3,400

3,500

3,872 3,600

3,700

3,800

3,900

Therefore, 3,544 is greater than 3,250, and 3,872 is greater than 3,544. A place value table can be used to compare and order multi-digit numbers. Begin by comparing the digits, starting with the leftmost digit and moving to the right.

Example: Order the numbers 3,544, 3,872, and 3,250 from least to greatest. THOUSANDS HUNDREDS

TENS

ONES

The three numbers have the same thousands digit. So, compare the hundreds digits. Since 8 > 5 > 2, then it means 3,872 is greater than 3,544, and 3,544 is greater than 3,250.

Therefore, 3,250 < 3,544 < 3,872. 17

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DIRECTIONS: Compare each pair of numbers. Use >, <, or = to show the relationship of each pair.

1,984

1,894

4,823

4,822

9,806

9,860

5,025

5,250

2,004

3,654

3,651

DIRECTIONS: Use the number line to compare the relationships of the pair of points given. Use >, <, or = to show the relationship.

A 2,000

B 2,500

C 3,000

E F

3,500

4,000

G 4,500

H 5,000

5,500

Point A

Point B

Point F

Point C

Point G

Point D

Point E

Point F

Point B

Point G

Point D

Point H

DIRECTIONS: List the numbers in order from least to greatest. 4,106 4,167 4,160

4,106 < 4,160 < 4,167

5,400 5,040 5,004

5,004 < 5,040 < 5,400

6,385 6,384 6,856

6,384 < 6,385 < 6,856

7,896 7,698 7,986

7,698 < 7,896 < 7,986

3,284 3,482 3,428

3,284 < 3,428 < 3,482 COPYING IS STRICTLY PROHIBITED BY LAW

DIRECTIONS: Compare each pair of numbers. Use >, <, or = to show the relationship of each pair.

3,279

3,729

1,036

1,035

1,718

4,851

4,815

5,090

5,009

7,194

7,193

Use the number line to compare the relationships of the pair of points

DIRECTIONS: given. Use >, <, or = to show the relationship.

500

1,500

2,500

3,500

4,500

G 5,500

H 6,500

Point B

Point A

Point F

Point C

Point H

Point E

Point G

Point B

Point D

Point E

Point A

DIRECTIONS: List the numbers in order from least to greatest.

7,500

7,261 7,621 7,126

7,126 < 7,261 < 7,621

1,905 1,950 1,095

1,095 < 1,905 < 1,950

4,198 3,189 5,819

3,189 < 4,198 < 5,819

2,515 2,551 2,155

2,155 < 2,515 < 2,551

9,992 9,993 9,949

9,949 < 9,992 < 9,993 MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 A number is shown on the number line. All of these numbers are less than the number shown on the number line except which one? 950

1,000

985

1,005

1,050

1,020

1,060

1,420

1,240

2 Which of these numbers makes the statement true?

1,444 > ? > 1,410 1,320

1,140

3 Rose arranged the numbers 856, 834, and 852 in ascending order as 834, 856, and 852. Did she arranged the numbers correctly? No, because 856 should come before 834 because it is less than 834. No, because 834 should come after 852 because it is greater than 852. No, because 852 should come before 856 because it is less than 856. Yes, she correctly arranged the numbers in ascending order.

4 Which of the following statements is true? 6,352 > 6 thousands + 3 hundreds + 2 tens + 5 ones 6,352 = 6 thousands + 3 hundreds + 2 tens + 5 ones 6,352 < 6 thousands + 3 hundreds + 2 tens + 5 ones None of the statements are true.

5 Which of the following lists the numbers 4,685, 4,856, and 4,568 in ascending order?

4,568,

4,856,

4,685

4,685,

4,856,

4,568

4,856,

4,568,

4,685

4,568,

4,685,

4,856 COPYING IS STRICTLY PROHIBITED BY LAW

Compare each pair of numbers. Use >, <, or = to show

DIRECTIONS: the relationship of each pair. 3,854

3,845

1,793

1,972

9,400

9,040

7,317

7,137

8,624

8,642

4,810

4,801

DIRECTIONS: Use the number line to compare the relationships of the pair of points given. Use >, <, or = to show the relationship.

1,000

1,500

Point A

Point C

D 2,000

Point C

Point H

E F

G 3,500

2,500

3,000

4,000

Point B

Point G

Point F

Point D

Point H

Point G

Point D

Point C

DIRECTIONS: List the numbers in order from least to greatest.

1,007 1,700 1,070

1,007 < 1,070 < 1,700

1,435 1,249 1,762

1,249 < 1,435 < 1,762

5,715 5,709 5,789

5,709 < 5,715 < 5,789

2,957 2,936 2,148

2,148 < 2,936 < 2,957

7,130 7,124 7,120

7,120 < 7,124 < 7,130 MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

4,500

1 Which of the following numbers is the greatest? 2,058

2,508

2,805

2,850

2 Which of the following statements best justifies why 2,309 < 2,903? The hundreds digit of 2,309 is less than the hundreds digit of 2,903. The thousands digit of 2,309 is less than the hundreds digit of 2,903. The hundreds digit of 2,309 is less than the hundreds digit of 2,903. The tens digit of 2,309 is less than the ones digit of 2,903.

3 Which of the following lists the numbers 4,440, 4,044, and 4,404 in descending order?

4,440,

4,404,

4,044

4,044,

4,440,

4,404

4,404,

4,044,

4,440

4,440,

4,044,

4,404

4 Which of the following numbers has the least value? 5,085

5,805

5,508

5,058

5 A number is shown on the number line. 5,100 5,150 5,200 5,250 5,300 5,350 5,400 5,450 5,500 5,550 5,600

Which of these numbers is greater than the number shown on the number line? 5,000

5,340

5,120

5,280

COPYING IS STRICTLY PROHIBITED BY LAW

1 A number is shown on the number line. 4,800 4,810 4,820 4,830 4,840 4,850 4,860 4,870 4,880 4,890 4,900

Which of these numbers is less than the number shown on the number line? 4,845

4,795

4,905

4,925

2 Which of these number lines correctly shows the location of 5,700 on the number line? 5,500

6,000

6,500

5,500

6,000

6,500

5,500

6,000

6,500

5,500

6,000

6,500

3 Which of the following signs makes the statement true?

2,074 ? 2,407 >

It cannot be determined.

4 Which of the following lists the numbers 3,546, 3,981, and 3,275 in ascending order? 3,275,

3,981,

3,546

3,275,

3,546,

3,981

3,981,

3,275,

3,546

3,981,

3,546,

3,275

5 Which of the following numbers has the least value? 6,419 23

6,149

6,194

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

6,491

6 Which of the following numbers is the greatest? 7,208

7,280

7,802

7,820

7 Which of the following statements best justifies why 5,609 > 5,307? The hundreds digit of 5,609 is less than the hundreds digit of 5,307. The hundreds digit of 5,609 is greater than the hundreds digit of 5,307. The thousands digit of 5,609 is less than the hundreds digit of 5,307. The thousands digit of 5,609 is greater than the thousands digit of 5,307.

8 Which of the following lists the numbers 3,142, 3,412, and 3,124 in descending order? 3,142,

3,124,

3,412

3,412,

3,124,

3,142

3,412,

3,142,

3,124

3,124,

3,142,

3,412

9 Which of the following statements is true? 1,527 = 1 thousands + 5 hundreds + 2 tens + 7 ones 1,527 > 1 thousands + 5 hundreds + 7 tens + 2 ones 1,527 < 1 thousands + 2 hundreds + 5 tens + 7 ones None of the statements are true.

10 Hailey arranged the numbers 742, 796, and 769 in ascending order as 742, 769, and 796. Did she arrange the numbers correctly?

No, because 856 should come before 834 because it is less than 834. No, because 834 should come after 852 because it is greater than 852. No, because 852 should come before 856 because it is less than 856. Yes, she correctly arranged the numbers in ascending order. COPYING IS STRICTLY PROHIBITED BY LAW

ROUNDING WHOLE NUMBERS MA.3.NSO.1.4 Round whole numbers from 0 to 1,000 to the nearest 10 or 100. Use a number line to round numbers to the nearest 10. Use benchmark tens as endpoints of the number line, and plot the number needed to be rounded off. Check which benchmark ten the number is closer to.

Example: Round 356 to the nearest 10. The number 356 falls between the benchmark tens 350 and 360, so use these numbers as endpoints of the number line. 350

351

352

353

354

355

356

357

358

359

360

Plot the number 356 on the number line and check which benchmark ten it is closer to.

6 units 350

351

352

353

4 units 354

355

356

357

358

359

360

Since 356 is closer to 360 (it is 4 units away from 360 and 6 units away from 350), 356 rounded to the nearest 10 is 360. Use a number line to round numbers to the nearest 100. Use benchmark hundreds as endpoints of the number line, and plot the number needed to be rounded off. Check which benchmark hundreds the number is closer to.

Example: Round 356 to the nearest 100. The number 356 falls between the benchmark hundreds 300 and 400, so use these numbers as endpoints of the number line. 300

310

320

340

350

360

370

380

390

400

Plot the number 356 on the number line and check which benchmark ten it is closer to.

56 units 300

310

320

330

44 units 340

350

356 360

370

380

390

400

Since 356 is closer to 400 (it is 44 units away from 400 and 56 units away from 300), 356 rounded to the nearest 100 is 400. One more thing to remember when rounding numbers: When the number is exactly at the halfway point of two possible answers, the number is always rounded up. 25

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

DIRECTIONS: Round these numbers to the nearest 10.

486 = 123 = 645 = 724 =

490 120 650 720

217 = 945 = 521 = 877 =

220 950 520 880

DIRECTIONS: Round these numbers to the nearest 100.

486 = 123 = 645 = 724 =

500 100 600 700

217 = 945 = 521 = 877 =

200 900 500 900

DIRECTIONS: Select all numbers that satisfy each condition. Rounds to 350 when rounded to the nearest 10.

342

358

355

352

347

686

682

248

352

716

832

Rounds to 680 when rounded to the nearest 10.

672

679

676

Rounds to 300 when rounded to the nearest 100.

298

256

304

Rounds to 800 when rounded to the nearest 100.

816

728

845

COPYING IS STRICTLY PROHIBITED BY LAW

DIRECTIONS: Round these numbers to the nearest 10.

897

318

127

736

900 320 130 740

149 = 182 = 271 = 468 =

150 180 270 470

DIRECTIONS: Round these numbers to the nearest 100.

378 = 325 = 751 =

100 400 300 800

123 = 517 = 571 = 841 =

100 500 600 800

DIRECTIONS: Select all numbers that satisfy each condition. Rounds to 100 when rounded to the nearest 10.

101

106

516

529

851

829

462

419

Rounds to 520 when rounded to the nearest 10.

518

524

526

Rounds to 900 when rounded to the nearest 100.

849

951

949

Rounds to 500 when rounded to the nearest 100.

512 27

587

481

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Which of the following numbers does not round to 540 when rounded to the nearest 10? 538

534

541

544

2 What is 759 rounded to the nearest 100? 700

750

760

800

3 Which of the following numbers rounds to 600 when rounded to the nearest 100? 510

530

545

598

4 Which of the following numbers does not round to 200 when rounded to the nearest 100? 178

265

228

244

5 Last year Ayala took a total of 285 photos on her phone. To the nearest hundred, about how many photos did Ayala take last year on her phone? 200 photos

280 photos

290 photos

300 photos COPYING IS STRICTLY PROHIBITED BY LAW

DIRECTIONS: Round these numbers to the nearest 10.

122

278

397

428

120 280 400 430

912

834

267

194

709

194

462

628

910 830 270 190

DIRECTIONS: Round these numbers to the nearest 100.

178

329

909

580

200 300 900 600

700 200 500 600

DIRECTIONS: Select all numbers that satisfy each condition. Rounds to 160 when rounded to the nearest 10.

163

151

166

156

159

678

671

137

378

346

Rounds to 680 when rounded to the nearest 10.

684

673

680

Rounds to 100 when rounded to the nearest 100.

124

167

Rounds to 300 when rounded to the nearest 100.

291 29

242

326

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Kim needs to read a book that has 348 pages. To the nearest hundred, about how many pages does the book have? 300 pages

340 pages

350 pages

400 pages

2 What is 86 rounded to the nearest 10? 70

100

3 What does 945 round to when rounded to the nearest 10? 900

940

950

1000

4 Which of the following numbers does not round to 40 when rounded to the nearest 10? 39

5 What is 492 rounded to the nearest 100?

400

490

895

500

COPYING IS STRICTLY PROHIBITED BY LAW

1 Which of the following numbers rounds to 800 when rounded to the nearest 100? 778

854

862

898

2 Which of the following numbers does not round to 700 when rounded to the nearest 100? 664

742

715

754

3 Lorenzo says 452 rounds to 450. Gabriel says 452 rounds to 500. Who is correct? Lorenzo Gabriel Both of them, depending on whether you are rounding to the nearest 10 or nearest 100 Neither of them are correct

4 Which of the following numbers rounds to 300 when rounded to the nearest 100? 210

230

279

245

5 Last year Josephine took a total of 439 photos with her camera. To the nearest hundred, about how many photos did Josephine take last year with her camera?

400 photos

440 photos

490 photos

500 photos

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

6 Yuri needs to read a book that has 183 pages. To the nearest hundred, about how many pages does the book have? 290 pages

200 pages

180 pages

100 pages

7 What is 64 rounded to the nearest 10? 60

100

8 What does 997 round to when rounded to the nearest 10? 900

940

950

1,000

9 Which of the following numbers does not round to 60 when rounded to the nearest 10? 56

10 What is 819 rounded to the nearest 100? 910

800

820

900

COPYING IS STRICTLY PROHIBITED BY LAW

ADDING AND SUBTRACTING MULTI-DIGIT NUMBERS

MA.3.NSO.2.1 Add and subtract multi-digit whole numbers including using a standard algorithm with procedural fluency.

Stack the numbers by place value columns. Add or subtract, starting with the ones column, then the tens column, and then the hundreds column. Regroup when needed.

ADD: 548 + 215

SUBTRACT: 823 - 415

HUNDREDS TENS ONES

Remember when regrouping: • 10 ones = 1 ten • 10 tens = 1 hundred

Remember when regrouping: • 1 hundred = 100 ones • 1 hundred = 10 tens

Write each number in expanded form. Add the ones, tens, and hundreds. Then, add all three sums.

ADD: 548 + 215 SUM OF HUNDREDS

SUM OF TENS

SUM OF ONES

548 = 500

215 = 200

700

13 = 763

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

DIRECTIONS: Use place value tables to find each sum or difference.

234 + 481

568 + 254

HUNDREDS

TENS

ONES

HUNDREDS

TENS

ONES

786 - 345

916 - 689

HUNDREDS

TENS

ONES

HUNDREDS

TENS

ONES

DIRECTIONS: Write each number in expanded form and then find the sum.

532 + 241

532 241

= 500 + 30 + 2 = 200 + 40 + 1 700 + 70 + 3 = 773

238 + 645

238 645

= 200 + 30 + 8 = 600 + 40 + 5 800 + 70 + 13 = 883

417 + 496

417 496

= 400 + 10 + 7 = 400 + 90 + 6 800 + 100 + 13 = 913

365 + 197

365 197

= 300 + 60 + 5 = 100 + 90 + 7 400 + 150 + 12 = 562

186 + 249

186 249

= 100 + 80 + 6 = 200 + 40 + 9 300 + 120 + 15 = 435 COPYING IS STRICTLY PROHIBITED BY LAW

DIRECTIONS: Use place value tables to find each sum or difference.

367 + 572

155 + 365

HUNDREDS

TENS

ONES

HUNDREDS

TENS

ONES

968 - 563

643 - 467

HUNDREDS

TENS

ONES

HUNDREDS

TENS

ONES

DIRECTIONS: Write each number in expanded form and then find the sum.

716 + 162

716 162

= 700 + 10 + 6 = 100 + 60 + 2 800 + 70 + 8 = 878

594 + 336

594 336

= 500 + 90 + 4 = 300 + 30 + 6 800 + 120 + 10 = 930

248 + 734

248 734

= 200 + 40 + 8 = 700 + 30 + 4 900 + 70 + 12 = 982

711 + 243

711 243

= 700 + 10 + 1 = 200 + 40 + 3 900 + 50 + 4 = 954

634 + 199

634 199

= 600 + 30 + 4 = 100 + 90 + 9 700 + 120 + 13 = 833

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Liam read 364 pages in his book last month. He read 348 pages this month. How many pages did he read in all? 792

721

712

702

2 Sophia made 527 cookies during her shift at the bake shop. Customers purchased 208 cookies. How many cookies does Sophia have left? 309

319

291

206

3 Find the value of 694 + 493. 1,078

1,178

1,287

1,187

4 A toy shop sold 520 toy cars in January and 640 toy cars in February. How many toy cars did the shop sell in January and February? 1,160

1,040

1,060

960

5 Noah has 931 green marbles in a box. He has 726 blue marbles in another box. How many marbles does he have in all? 1,645

1,657

1,755

1,575 COPYING IS STRICTLY PROHIBITED BY LAW

DIRECTIONS: Use place value tables to find each sum or difference.

476 + 263 HUNDREDS

149 + 176 TENS

ONES

HUNDREDS

TENS

ONES

847 - 625

754 - 396

HUNDREDS

TENS

ONES

HUNDREDS

TENS

ONES

DIRECTIONS: Write each number in expanded form and then find the sum.

364 + 532

364 532

= 300 + 60 + 4 = 500 + 30 + 2 800 + 90 + 6 = 896

834 + 121

834 121

= 800 + 30 + 4 = 100 + 20 + 1 900 + 50 + 5 = 955

539 + 332

539 332

= 500 + 30 + 9 = 300 + 30 + 2 800 + 60 + 11 = 871

512 + 425

512 425

= 500 + 10 + 2 = 400 + 20 + 5 900 + 30 + 7 = 937

716 + 194

716 194

= 700 + 10 + 6 = 100 + 90 + 4 800 + 100 + 10 = 910

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Emma scored 710 points in her first word game and 328 points in her second word game. How many more points did she make in the first game than in the second game? 382

328

392

482

2 There were 1,204 toys in a shop. During Christmas season, 817 were sold. How many toys were left? 873

738

387

378

3 Find the value of 978 + 311. 1,286

1,289

1,267

1,298

4 A factory produced 420 bicycles in one month and 394 in another month. How many bicycles did it produce in total? 841

148

481

814

5 Billy has 712 baseball cards in a box. He has 582 baseball cards in another box. How many cards does he have in all? 1,249

1,194

1,294

1,429 COPYING IS STRICTLY PROHIBITED BY LAW

1 Hugh read 319 pages in his book last month. He read 499 pages this month. How many pages did he read in all? 881

188

281

818

2 A baker made 215 muffins for his bakery. His customers ate 176 muffins. How many muffins does the bakery have left? 39

3 Find the value of 683 ̶ 177. 560

605

506

650

4 A store sold 489 video games in November and 567 video games in December. How many video games did the store sell in all? 1,605

1,056

1,046

1,506

5 Gary ordered 331 pairs of shorts for his store. He ordered 897 shirts. How many shorts and shirts did he order in all?

1,822

1,282

1,288

1,228

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

6 Olivia scored 545 points in round one of her video game and 351 points in the second round. How many more points did she score in the first round than in the second round? 941

194

149

491

7 There were 2,490 cars at the dealership. By the end of the year, 1,563 were sold. How many cars were left? 927

297

972

792

8 Find the value of 777 ̶ 119. 586

685

568

658

9 A small factory printed 150 books in one month and 129 in another month. How many books did it produce in total? 972

279

729

297

10 Kim has 243 small blocks in a box. She has 324 blocks in another box. How many more blocks does she have in the second box? 18

19 COPYING IS STRICTLY PROHIBITED BY LAW

MULTIPLY A ONE DIGIT WHOLE NUMBER MA.3.NSO.2.3 Multiply a one-digit whole number by a multiple of 10, up to 90, or a multiple of 100, up to 900, with procedural reliability. Use skip counting by multiples on a number line to find the product of a one-digit whole number by a multiple of 10 or a multiple of 100.

Multiply: 3 × 20 3 “jumps” of 20

100

600

700

800

900

1,000

Therefore, 3 × 20 = 60.

Multiply: 4 × 200 4 “jumps” of 200

100

200

300

400

500

Therefore, 4 × 200 = 800. Use base-ten blocks to find the product of one-digit whole number by a multiple of 10 or a multiple of 100.

Multiply: 3 × 20

Multiply: 4 × 200

Draw three groups of 20.

Draw four groups of 200.

Therefore, 3 × 20 = 60. 41

Therefore, 4 × 200 = 800.

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

DIRECTIONS: Find the product for each of the following.

3 × 40

2 × 80

7 × 30

5 × 50

8 × 90

9 × 20

6 × 60

DIRECTIONS: Check (

120 160 210 250 720 180 360

2,800 3 × 800 = 2,400 9 × 300 = 2,700 6 × 500 = 3,000 4 × 900 = 3,600 5 × 200 = 1,000 8 × 600 = 4,800 7 × 400 =

) all multiplication sentences that are correct.

4 × 30 = 70

7 × 50 = 350

6 × 30 = 180

8 × 50 = 400

2 × 300 = 5,000

2 × 50 = 70

5 × 300 = 1,500

4 × 500 = 900

7 × 300 = 2,100

3 × 500 = 1,500

9 × 70 = 630

2 × 90 = 180

5 × 70 = 120

3 × 90 = 270

8 × 700 = 5,600

5 × 90 = 450

3 × 700 = 1,000

6 × 900 = 1,500

4 × 700 = 2,800

8 × 900 = 1,700 COPYING IS STRICTLY PROHIBITED BY LAW

DIRECTIONS: Find the product for each of the following.

5 × 80

3 × 90

4 × 70

9 × 40

6 × 90

7 × 80

6 × 30

DIRECTIONS: Check (

400 270 280 360 540 560 180

2,400 9 × 500 = 4,500 2 × 900 = 1,800 4 × 800 = 3,200 3 × 700 = 2,100 5 × 800 = 4,000 5 × 300 = 1,500 8 × 300 =

) all multiplication sentences that are correct.

9 × 20 = 180

2 × 40 = 90

5 × 20 = 120

9 × 40 = 360

6 × 200 = 1,200

4 × 400 = 1,600

7 × 200 = 1,400

6 × 400 = 2,500

9 × 200 = 1,900

7 × 400 = 2,800

5 × 30 = 160

2 × 80 = 160

6 × 30 = 180

5 × 80 = 260

4 × 300 = 1,400

8 × 80 = 680

7 × 300 = 2,100

7 × 800 = 5,600

9 × 300 = 2,700

9 × 800 = 7,200

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 What is the product of 60 and 3? 90

900

180

1,800

2 What is the product of 600 and 2? 1,200

120

1,800

180

3 The local library received a donation of 9 boxes of books. If each box contained 50 books, how many books did the local library receive? 9,000 books

4,500 books 900 books 450 books

4 Which of the following multiplication sentences is correct? 30 × 9 = 540 30 × 9 = 360 30 × 9 = 270 30 × 9 = 180

5 Edward needs to sell 3 booklets of tickets for the fair. There are 500 tickets in each booklet. How many tickets does Edward need to sell?

150 tickets 500 tickets 1,500 tickets 5,000 tickets COPYING IS STRICTLY PROHIBITED BY LAW

DIRECTIONS: Find the product for each of the following.

9 × 30

5 × 80

7 × 60

3 × 80

4 × 90

2 × 60

7 × 70

DIRECTIONS: Check (

270 400 420 240 360 120 490

3,500 5 × 200 = 1,000 3 × 600 = 1,800 4 × 400 = 1,600 5 × 500 = 2,500 7 × 900 = 6,300 8 × 600 = 4,800 7 × 500 =

) all multiplication sentences that are correct.

4 × 40 = 160

7 × 50 = 300

3 × 40 = 120

4 × 50 = 200

2 × 400 = 600

1 × 500 = 500

8 × 400 = 3,000

8 × 500 = 4,000

9 × 400 = 3,600

9 × 500 = 4,300

2 × 70 = 120

2 × 60 = 110

9 × 70 = 620

5 × 60 = 300

6 × 700 = 4,200

8 × 60 = 480

5 × 700 = 3,500

7 × 600 = 4,400

4 × 700 = 2,800

9 × 600 = 5,400

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Which of the following multiplication sentences is correct? 500 × 6 = 120 500 × 6 = 1,200 500 × 6 = 300 500 × 6 = 3,000

2 What is the product of 40 and 9? 150

360

480

1,560

3 What is the product of 700 and 4? 1,400

2,000

2,800

3,600

4 Which of the following multiplication sentences is correct? 20 × 7 = 700 20 × 7 = 350 20 × 7 = 210 20 × 7 = 140

5 Which of the following multiplication sentences is correct? 600 × 4 = 240

600 × 4 = 2,400 600 × 4 = 360 600 × 4 = 3,600

COPYING IS STRICTLY PROHIBITED BY LAW

1 Which of the following can help you find the product of 70 and 6? 70 × 6 is the same as 7 tens × 6, which is equal to 42 tens or 420. 70 × 6 is the same as 7 tens × 6, which is equal to 42 tens or 4,200. 70 × 6 is the same as 7 tens × 6, which is equal to 13 tens or 130. 70 × 6 is the same as 7 tens × 6, which is equal to 13 tens or 1,300.

2 Which of the following can help you find the product of 8 and 400? 8 × 400 is the same as 8 × 4 hundreds, which is equal to 24 hundreds or 240 8 × 400 is the same as 8 × 4 hundreds, which is equal to 24 hundreds or 2,400. 8 × 400 is the same as 8 × 4 hundreds, which is equal to 32 hundreds or 320.

8 × 400 is the same as 8 × 4 hundreds, which is equal to 32 hundreds or 3,200.

3 Which of the following can help you find the product of 7 and 900? 7 × 900 is the same as 7 × 9 hundreds, which is equal to 63 hundreds or 630. 7 × 900 is the same as 7 × 9 hundreds, which is equal to 16 hundreds or 1,600. 7 × 900 is the same as 7 × 9 hundreds, which is equal to 63 hundreds or 630. 7 × 900 is the same as 7 × 9 hundreds, which is equal to 16 hundreds or 160.

4 What is the product of 7 and 90? 70

630

6,300

5 What is the product of 4 and 600?

1,000

240

2,400

4,000 MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

6 Which of the following multiplication sentences is correct? 8 × 900 = 170 8 × 900 = 7,200 8 × 900 = 2,700 8 × 900 = 720

7 What is the product of 50 and 6? 300

560

3,000

8 What is the product of 200 and 8? 1,000

2,600

1,600

4,600

9 Which of the following multiplication sentences is correct? 60 × 3 = 350 60 × 3 = 280 60 × 3 = 150 60 × 3 = 180

10 Which of the following multiplication sentences is correct? 900 × 4 = 360

900 × 4 = 36 900 × 4 = 360 900 × 4 = 3,600

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MULTIPLYING TWO WHOLE NUMBERS AND DIVIDE

MA.3.NSO.2.4 Multiply two whole numbers from 0 to12 and divide using related facts with procedural reliability. MA.3.NSO.2.2 Explore multiplication of two whole numbers with products from 0 to 144, and related division facts.

Use arrays to represent multiplication facts.

Use equal groups to represent multiplication facts.

Multiply: 6 × 4

6 columns of 4 items

4 rows

4 rows of 6 items 6 columns

6 equal groups of 4

4 equal groups of 6

= 24

Related fact family: 6 × 4 = 24 4 × 6 = 24

24 ÷ 4 = 6 24 ÷ 6 = 4

Use a number line to represent multiplication facts.

Multiply: 6 × 4 6 “jumps” of 4

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

4 “jumps” of 6

Related fact family: 6 × 4 = 24 4 × 6 = 24 49

24 ÷ 4 = 6 24 ÷ 6 = 4

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

DIRECTIONS: Draw an array to find the product.

7×3

9×4

= 36

= 21

DIRECTIONS: Draw equal groups to find the product.

5×6

8×4

= 32

= 30

DIRECTIONS: Use a number line to find the product.

3 × 6 = 18

DIRECTIONS: Pick the number sentence that does not belong to the same fact family.

3 × 4 = 12

8 × 6 = 48

3 × 9 = 27

7 × 6 = 42

2 × 6 = 12

6 × 8 = 48

9 × 3 = 27

6 × 8 = 48

12 ÷ 4 = 3

48 ÷ 6 = 8

9÷3=3

42 ÷ 7 = 6

12 ÷ 3 = 4

40 ÷ 8 = 5

27 ÷ 9 = 3

42 ÷ 6 = 7

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DIRECTIONS: Draw an array to find the product.

5×6

8×5

= 40

= 30

DIRECTIONS: Draw equal groups to find the product.

6×4

7×3

= 21

= 24

DIRECTIONS: Use a number line to find the product.

4 × 4 = 16

DIRECTIONS: Pick the number sentence that does not belong to the same fact family.

5 × 3 = 15

4 × 8 = 36

12 × 3 = 36

7 × 4 = 28

3 × 5 = 15

8 × 4 = 32

3 × 12 = 36

4 × 7 = 28

15 ÷ 3 = 3

32 ÷ 8 = 4

36 ÷ 3 = 12

28 ÷ 7 = 3

15 ÷ 5 = 3

32 ÷ 4 = 8

36 ÷ 12 = 2

28 ÷ 4 = 7

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1 What is the quotient when 36 is divided by 4? 6

2 Which of these numbers will complete the multiplication problem?

7 × ____ = 49 5

3 Which related multiplication fact can help you find the quotient of 9 ÷ 3? 1×3=3 2×3=6 3×3=9 4 × 3 = 12

4 Which related division fact can help you find the product of 12 × 5? 10 ÷ 2 = 5 12 ÷ 6 = 2 50 ÷ 5 = 10 60 ÷ 12 = 5

5 Which of these numbers will complete the division problem?

77 ÷ ____ = 7 7

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DIRECTIONS: Draw an array to find the product.

4×6

5×5

= 25

= 24

DIRECTIONS: Draw equal groups to find the product.

3×5

5×4

= 20

= 15

DIRECTIONS: Use a number line to find the product.

2 × 9 = 18

DIRECTIONS: Pick the number sentence that does not belong to the same fact family.

2 × 8 = 10

4 × 9 = 36

7 × 9 = 63

6 × 4 = 12

8 × 2 = 16

9 × 4 = 32

9 × 7 = 63

4 × 6 = 24

16 ÷ 2 = 8

36 ÷ 4 = 9

63 ÷ 7 = 9

24 ÷ 4 = 6

16 ÷ 8 = 2

36 ÷ 9 = 4

63 ÷ 9 = 6

24 ÷ 6 = 4

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1 Select all answer choices that represent 4 × 5.

2 Mary bought 6 crates of eggs. Each crate has 18 eggs. How many eggs did she purchase in all? 810

180

108

801

3 A classroom has 15 rows of 9 chairs. How many chairs are there in the classroom? 153

135

531

315

4 Anna has 32 oranges to be placed evenly between 8 rows in a crate. How many oranges are there in 1 row? 12

5 Carl had 14 crayons. He divided them equally among his 7 friends. How many crayons did each friend get? 2

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1 What is the quotient when 54 is divided by 9? 6

2 Which of these numbers will complete the multiplication problem?

9 × ____ = 72 5

3 Which related multiplication fact can help you find the quotient of 45 ÷ 5?

4 × 9 = 36 5 × 9 = 45 6 × 9 = 54 7 × 9 = 64

4 Which related division fact can help you find the product of 7 × 8? 56 ÷ 8 = 7 32 ÷ 4 = 8 80 ÷ 10 = 8 49 ÷ 7 = 7

5 Which of these numbers will complete the division problem?

72 ÷ ____ = 6

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6 John bought 7 boxes of chocolates. Each box has 6 chocolates. How many chocolates did he purchase in all? 62

7 A classroom has 5 rows of 8 desks. How many desks are there in the classroom? 30

8 David had 18 markers. He divided them equally among his 3 friends. How many markers did each friend get? 6

9 Julia has 30 apples to be placed evenly between 6 rows in a crate. How many apples are there in 1 row? 7

10 Choose all of the equations that can be represented using the model below.

8×4

4×4

3×6

6×3

4×8

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REPRESENTING AND INTERPRETING UNIT FRACTIONS

MA.3.FR.1.1

1 Represent and interpret unit fractions in the form as the quantity formed by one part when a n whole is partitioned into n equal parts. 1 Use a number line numbered from 0 to 1 to represent a fraction of the form , where the number line is n divided into n equal parts and one part is taken. 1

Example: Use a number line to show 4 . Draw a number line numbered from 0 to 1 and divide it into 4 equal parts.

1 Since 4 means one part of four equal parts taken, then one part of the number line represents 1 . 4 1 4

Use strip diagrams to represent a fraction of the 1 form , where one whole is divided into n equal n parts. 1

Use shapes to represent a fraction of the 1 form , where one whole is divided into n equal n parts. 1

Example: Use a strip diagram to show 4 .

Example: Use a shape to show 4 .

Draw a strip diagram and divide it into 4 equal parts.

Draw a circle or a square and divide it into 4 equal parts.

Since 4 means one part of four equal parts taken, then one part of the strip diagram represents 1 . 4

1 4

Since 4 means one part of four equal parts taken, then one part of the shape represents 1 . 4 1 4

1 4

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DIRECTIONS: Identify the fractions represented on the number lines. 1 8

1 6

1 3 0

1 1 5

DIRECTIONS: Label the fractions for the shaded portion represented on the strip diagrams. 1 2

1 5

1 10

1 6

DIRECTIONS: Write a fraction for the shaded portions of the shapes below.

1 5

1 3

1 8

1 4

1 6 1 2

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DIRECTIONS: 3 4 0

2 5 1

1 5 9

3 6 0

DIRECTIONS: Label the fractions for the shaded portion represented on the strip diagrams. 1 4

1 5

1 9

1 7

DIRECTIONS: Write a fraction for the shaded portions of the shapes below.

1 8

1 6

1 10

2 12

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3 15

1 12

1 What fraction can represent the shaded portion of the circle? 1 2

1 3

2 3

1 4

2 A set of fruits is shown below.

What fraction of the set is an orange? 1 4

1 5

1 6

1 8

3 A number line is shown below.

What fraction does the point on the number line represent? 3 4

2 3

1 4

1 3

Which of the following models shows 1 8 of the circle is shaded?

5 What fraction can represent the shaded portion of the rectangle?

1 4

1 5

1 6

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1 8 60

DIRECTIONS: 3 5

1 4 1

6 7 0

4 8 1

DIRECTIONS: Label the fractions for the shaded portion represented on the strip diagrams. 1 3

1 2

1 11

1 8

DIRECTIONS: Label the fractions shown on the shapes. 1 4

1 6 1 3

1 7

1 8

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2 5

1 Which of the following shows that 1 the sets of clothing is a sweater? 2

2 A set of balls used for sports is shown below.

What fraction of the sports equipment is a basketball? 1 4

3 4

1 3

2 3

Which of the following number lines shows the fraction 1 ? 10

4 A number line is shown below.

What fraction does the point on the number line represent? 1 1 1 6 8 10

1 12

5 Which of the following models shows 1 of the rectangle is shaded? 4

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1 What fraction can represent the shaded portion of the square? 1 2

1 4

1 1

1 3

2 A number line is shown below.

What fraction does the point on the number line represent? 1 1 1 2 4 3

1 5

3 Which of the following shows 1 of the items is a pair of socks? 3

Which of the following models shows 1 of the circle is shaded? 6

5 What fraction can represent the shaded portion of the rectangle?

1 4 63

1 5

1 6

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4 6

6 Which of the following shows 1 of the set of birds is a pigeon? 4

7 A set of athletic equipment is shown below.

What fraction of the set is a soccer ball? 1 4

3 4

1 3

2 3

Which of the following number lines shows the fraction 1 ? 9

9 A number line is shown below.

What fraction does the point on the number line represent? 1 1 1 6 8 10

1 12

10 Which of the following models shows 1 of the rectangle is shaded? 8

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REPRESENTING AND INTERPRETING FRACTIONS GREATER THAN ONE MA.3.FR.1.2 Represent and interpret fractions, including fractions greater than one, in the form of m as the n result of adding the unit fraction 1 to itself m times.

Use a number line to compose and decompose a fraction of the form into m unit fractions of the n 1 form n . 6

Example: Use a number line to show 4 . Draw and divide each unit of the number line into 4 equal parts.

Since each part of this number line represents 1 , then taking six 1 parts is equivalent to 6 . 4 4 4 1

six 4 parts = 4 + 4 + 4 + 4 + 4 + 4 = 4 1 4

1 4

Use strip diagrams to compose and decompose a m into m unit fractions of fraction of the form n 1 the form .

1 4

Use shapes to compose and decompose a m into m unit fractions of fraction of the form n 1 the form .

Example: Use a strip diagram to show 4 .

Example: Use a shape to show 4 .

Draw strip diagrams and divide each strip diagram into 4 equal parts.

Draw circles and divide each circle into 4 equal parts.

Since each part of the strip diagram shows 1 , 4 then taking six 1 parts is equivalent to 6 .

Since each part of the circle shows 4 , then 1 taking six 4 parts is equivalent to 6 .

1 4 1 4

1 4

1 1 1 4 4 4 1 1 1 1 1 1 6 4 + 4 + 4 + 4 + 4 + 4 = 4 65

1 4 1 4

1 1 1 1 1 1 6 4 + 4 + 4 + 4 + 4 + 4 = 4

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DIRECTIONS: Identify the fractions represented on the number lines.

5 8

4 3

3 2 0

4 5 1

DIRECTIONS: Identify the fractions represented on the strip diagrams. 8 5

5 3

10 6

14 10

DIRECTIONS: Identify the fractions shown on the shapes.

8 5

4 3

11 8

9 6

7 6

7 4

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DIRECTIONS: Identify the fractions represented on the number lines. 5 2 0

8 5 3

5 4 0

2 2 3

DIRECTIONS: Identify the fractions represented on the strip diagrams. 6 4

12 7

6 5

16 9

DIRECTIONS: Identify the fractions shown on the shapes.

7 5

11 7

8 6

21 12

10 9

14 10

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1 The rectangle below is divided into equal parts. 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 What fraction of the whole rectangle is shaded? 1 12 7 5

1 12

7 12 5 7

2 Which of the following fraction models shows

3 ? 5

3 Which of the following shows 5 as a sum of unit fractions? 8 5 5 5 5 5 5 5 5 1 + 2 + 3 + 4 + 5 + 6 +7 + 8 1 2 3 4 5 8+8+8+8+8 1 1 1 1 1 1 1 1 5+5+5+5+5+5+5+5 1 1 1 1 1 8+8+8+8+8

4 A number line is shown below.

What fraction is shown on the number line? 4 6

4 6

4 10

1 10

Three

Seven

Ten

How many 1 are there in 7 ? 3 3 One

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DIRECTIONS: Identify the fractions represented on the number lines.

5 3 0

5 6 2

1 7 4

6 9 0

DIRECTIONS: Identify the fractions represented on the strip diagrams. 18 11

10 5

18 12

21 15

DIRECTIONS: Identify the fractions shown on the shapes.

26 18

14 8

13 8

35 20

13 11

24 14

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1 The rectangle below is divided into equal parts. 1 1 1 1 1 5 5 5 5 5 What fraction of the whole rectangle is shaded? 1 1 4 5 5 4

4 5

2 Which of the following fraction models shows 4 ? 6

3 Which of the following shows 6 as a sum of unit fractions? 5 1 2 3 4 5 6 5+5+5+5+5+5 1 1 1 1 1 6+6+6+6+6 1 1 1 1 1 1 5+5+5+5+5+5 6 6 6 6 6 1+2+3+4+5

4 A number line is shown below.

What fraction is shown on the number line? 1 3 8 8

1 3

3 5

One

Eight

How many 1 are there in 8 ? 4 4 Twelve

Four

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1 The rectangles below are each divided into equal parts. 1 1 1 1 1 1 1 6 6 6 6 6 6 6 What fraction is shaded in the model? 9 12 9 6

1 6

3 12 3 6

2 Which of the following fraction models shows

2 ? 8

3 Which of the following shows 7 as a sum of unit fractions? 2 1 2 3 4 5 6 7 2 + 2 + 2 + 2 + 2 + 2 +7 7 7 1+1 1 1 1 1 1 1 1 2+2+2+2+2+2+2 7 7 1+2

4 A number line is shown below.

What fraction is shown on the number line? 5 9

3 9

1 9

6 9

Four

Five

Ten

How many 1 are there in 8 ? 5 5 Eight 71

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6 The rectangle below is divided into equal parts. 1 1 1 1 1 1 6 6 6 6 6 6 What fraction of the whole rectangle is shaded? 1 1 6 6 5 6

4 6

7 Which of the following fraction models shows 6 ? 10

8 7 as a sum of unit fractions? 3 1 1 1 1 1 1 1 3 + 3 + 3 + 3 + 3 + 3 +3

Which of the following shows

1 1 1 1 1 3+3+3+3+3 1 1 1 1 1 1 3+3+3+3+3+3 3 3 3 3 3 1+2+3+4+5

9 A number line is shown below.

What fraction is shown on the number line? 1 6 8 8

1 5

5 8

Nine

Eight

10 How many 1 are there in 6 ? 9 9 Three

Six

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READING AND WRITING FRACTIONS MA.3.FR.1.3 Read and write fractions, including fractions greater than one, using standard form, numeral-word form and word form. Use a chart or a table to correctly read and write fractions in the form m using the standard form,

numeral-word form, and word form, and to properly visualize the fraction. Understand that a fraction of m means taking m parts that are each 1 in size. the form

STANDARD FORM

1 3

2 3

3 3

4 3

NUMERALWORD FORM

1 third

2 thirds

3 thirds

4 thirds

WORD FORM

one-third

two-thirds

three-thirds

four-thirds

1 3

2 3

3 3

4 3

FRACTION MODEL

When reading fractions, it is important to remember the vocabulary terms associated with each 1 m fraction. Understand that a fraction in the form means taking m parts that are each n in size.

In a fraction of the form n , when

•

n = 2, then one whole is divided into 2 equal parts, and each part is a half.

•

n = 3, then one whole is divided into 3 equal parts, and each part is a third.

•

n = 4, then one whole is divided into 4 equal parts, and each part is a fourth.

•

n = 5, then one whole is divided into 5 equal parts, and each part is a fifth.

•

n = 6, then one whole is divided into 6 equal parts, and each part is a sixth. MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

DIRECTIONS: Write the numeral-word form and word form of each fraction. STANDARD FORM

NUMERAL-WORD FORM

WORD FORM

7 halves

Seven-halves

5 sixths

Five-sixths

9 eighths

Nine-eighths

3 fourths

Three-fourths

7 2 5 6 9 8 3 4

DIRECTIONS: Write the word form and standard form of each fraction. NUMERAL-WORD FORM

WORD FORM

STANDARD FORM

7 thirds

Seven-thirds

9 fourths

Nine-fourths

3 halves

Three-halves

3 tenths

Three-tenths

7 3 9 4 3 2 3 10

DIRECTIONS: Write the standard form and numeral-word form of each fraction. WORD FORM

STANDARD FORM

Eight-fifths

Seven-twelfths Six-fourths Four-tenths

8 5 7 12 6 4 4 10

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NUMERAL-WORD FORM

8 fifths

7 twelfths 6 fourths 4 tenths 74

DIRECTIONS: Write the numeral-word form and word form of each fraction. STANDARD FORM

NUMERAL-WORD FORM

WORD FORM

8 thirds

Eight-thirds

1 third

One-third

6 eighths

Six-eighths

9 fifths

Nine-fifths

8 3 1 3 6 8 9 5

DIRECTIONS: Write the word form and standard form of each fraction. NUMERAL-WORD FORM

WORD FORM

STANDARD FORM

4 eighths

Four-eighths

3 fifths

Three-fifths

2 ninths

Two-ninths

5 halves

Five-halves

4 8 3 5 2 9 5 2

DIRECTIONS: Write the standard form and numeral-word form of each fraction. WORD FORM

One-seventh

Three-ninths Eight-thirds Seven-elevenths 75

STANDARD FORM

1 7 3 9 8 3 7 11

NUMERAL-WORD FORM

1 seventh

3 ninths 8 thirds 7 elevenths

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1 What is 2 written in word form? 3 Half-third

Two-thirds

Two-threes

Three-halves

2 How many thirds are there in 5 ? 3 2

3 What is four-eighths written in standard form?

4 3

4 8

1 4

8 4

2 What is 6 written in numeral-word form? 2 sixths

2 eighths

6 eighths

6 halves

5 Which of the following fractions is different from the rest? 7 2

7 halves

Seven-halves

2 7

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DIRECTIONS: Write the numeral-word form and word form of each fraction. STANDARD FORM

NUMERAL-WORD FORM

WORD FORM

2 fourths

Two-fourths

4 fifths

Four-fifths

6 halves

Six-halves

1 eighth

One-eighth

2 4 4 5 6 2 1 8

DIRECTIONS: Write the word form and standard form of each fraction. NUMERAL-WORD FORM

WORD FORM

STANDARD FORM

3 ninths

Three-ninths

5 sixths

Five-sixths

7 sixths

Seven-sixths

9 eighths

Nine-eighths

3 9 5 6 7 6 9 8

DIRECTIONS: Write the standard form and numeral-word form of each fraction. WORD FORM

Nine-fifths

Eleven-fifteenths Seven-twelfths Four-eighths 77

STANDARD FORM

9 5 11 15 7 12 4 8

NUMERAL-WORD FORM

9 fifths 11 fifteenths 7 twelfths 4 eighths

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 What is 4 written in word form? 5 Four-fifths

Fourth-fives

Five-fourths

Fourth-fifths

2 How many halves are there in 3 ? 2 1

3 Which of the following fraction models shows six-eighths?

4 What is 3 written in numeral-word form? 8 8 thirds

8 threes

3 eights

3 eighths

5 Which of the following fractions is different from the rest? 2 3

2 threes

Two-thirds

2 thirds

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1 What is 8 written in word form? 4 Eight-fourths

Four-eighths

Eight-fours

Four-eights

2 Which of the following fraction models shows 4 sixths?

3 What is six-tenths written in standard form? 4 6 10 6

6 4 6 10

4 How many sevenths are there in 9 ? 7 2

5 Which of the following fractions is different from the rest?

4 6

6 quarters

Six-quarters

6 4

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6 What is 3 written in word form? 7 Third-sevenths

Three-sevenths

Three-sevens

Third-sevens

7 How many halves are there in 5 ? 2 1

8 What is 4 eighths written in standard form?

8 8

4 8

8 4

4 4

9 What is 2 written in numeral-word form? 9 2 ninths

1 threes

7 eights

3 eighths

10 Which of the following fractions is different from the rest? 8 5

8 fifths

Eight fives

Eight-fifths

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PLOTTING, ORDERING, AND COMPARING FRACTIONAL NUMBERS MA.3.FR.2.1 Plot, order and compare fractional numbers with the same numerator or the same denominator. Plot fractional numbers on the number lines. Use the locations of the fractional numbers on the number lines to compare their values. The farther the fractional number is from 0, the greater the number. 5

Example: Plot 4 and 3 on the number lines to compare their values. 5 4

5 3

Since 3 is farther from 0 than 4 , then 3 is greater than 4 . 6

Example: Plot 4 and 4 on the number lines to compare their values. 6 4

7 4

Since 4 is farther from 0 than 4 , then 4 is greater than 4 . Use models like strip diagrams or shapes to compare fractional numbers. The bigger the model, the greater the fraction. 2

Use fraction models to compare 3 and 4 . 2 3 2 4

1 3 1 4

1 3 1 4 2

1 4

Since the strip diagram for 3 is bigger than the strip diagram for 2 , then 2 is 4 3 2 greater than 4 . 81

Use shapes to compare 6 and 6 . 2 6

1 6

4 6

1 6

Since the shaded portion of the shape is 2 4 bigger for 6 than 6 , this means that 2 4 is 6 greater than 6 .

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

each pair of fractions. Use >, <, or = to show the DIRECTIONS: Compare relationship of each pair.

5 6

5 8

7 2

4 2

9 2

9 3

2 4

3 4

4 5

4 6

8 3

6 3

8 4

8 2

5 8

4 8

3 5

3 4

List these fractions in order from least to greatest.

DIRECTIONS: Use the comparison symbols to show the ordering.

2 4

1 4

3 4

3 5

3 6

9 3

5 3

8 3

5 2

5 6

5 4

4 5

6 5

8 5

7 5

7 3

7 8

9 8

5 8

7 8

1 4 < 3 6 < 5 3 < 5 6 < 4 5 < 7 8 < 5 8 <

2 3 < 4 4 3 3 5 < 4 8 9 < 3 3 5 5 4 < 2 6 8 < 5 5 7 7 5 <3 7 9 < 8 8

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each pair of fractions. Use >, <, or = to show the DIRECTIONS: Compare relationship of each pair.

7 3

7 5

4 7

4 5

2 3

2 6

3 5

5 3

6 7

3 4

7 2

9 3

9 4

8 3

2 4

2 3

8 4

8 6

DIRECTIONS: List these fractions in order from least to greatest. Use comparison symbols to show the ordering.

7 2

3 5

9 7

1 7

3 8

3 5

9 6

6 9

5 6

8 4

2 3

9 7

7 3

8 5

7 4

3 2

3 3

3 4

5 7

8 7

2 7

3< 9< 7 5 7 2 1 3 3 < < 7 8 5 6 5 9 < < 9 6 6 2 9 8 < < 3 7 4 8 7 7 < < 5 4 3 3 3 3 < < 4 3 2 2 5 8 < < 7 7 7

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Which of the following fractions has the least value? 19 5

15 5

13 5

17 5

2 Which of the following fractions lies to the right of 6 on a number line? 4 5 3 4 4 1 4

7 4

3 Which of the following signs makes the statement true?

7 4

7 8

It cannot be determined.

4 Which of the following correctly orders the fractions from greatest to least? 3 7 5 2, 2, 2

3 5 7 2, 2, 2

5 7 3 2, 2, 2

7 5 3 2, 2, 2

5 Which of the following fractions has the greatest value? 24 8

25 8

6 28

7 28

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Compare each pair of fractions. Use >, <, or = to show

DIRECTIONS: the relationship of each pair.

3 9

7 6

6 3

9 5

3 4

9 4

8 5

8 6

5 2

5 3

2 7

3 9

4 5

4 6

9 2

9 7

6 7

6 4

DIRECTIONS: List these fractions in order from least to greatest. Use comparison symbols to show the ordering.

3 6

5 6

2 6

7 5

6 7

7 6

5 2

2 3

3 2

8 5

6 4

9 5

3 7

8 9

4 8

5 8

6 9

4 7

4 2

6 4

8 6

2 3 5 < < 6 6 6 6 7 7 < < 7 6 5 2< 3< 5 3 2 2 6 < 8<9 4 5 5 3 4 8 < < 7 8 9 4 5 6 < < 7 8 9 8 6 4 < 4< 2 6

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Which of the following fractions has the least value? 44 45 6 6 43 6

42 6

2 Which of the following fractions lies to the left of 5 on a number line? 5 5 5 4 6 5 3

5 2

3 Which of the following statements is true? 1 3 1 The fraction 3 2 is to the right of 2 on the number line, so 2 is greater than 2 . 1 3 1 The fraction 3 2 is to the right of 2 on the number line, so 2 is less than 2 . 3 is to the left of 1 on the number line, so 3 is greater than 1. The fraction 12 12 2 2 3 1 3 1 The fraction 2 is to the left of 2 on the number line, so 2 is less than 2.

Which of the following fractions lies to the right of 6 on a number line? 5 6 6 4 8 6 10

6 12

5 Which of the following correctly orders the fractions from least to greatest? 2 2 2 4, 6, 8

2 2 2 8, 6, 4

2 2 2 6, 8, 4

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1 Which of the following signs makes the statement true? 8 3

8 4

It cannot be determined.

2 Which of the following fractions lies to the right of 7 on a number line? 10 9 5 1 10 10 10

3 Which of the following shows the location of 4 3 on a number line?

2 3

1 1

4 Which of the following fractions has the least value? 33 9

34 5

33 5

33 6

5 Which of the following fractions has the greatest value?

52 6

52 5

52 2

52 3 MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

3 10

6 Which of the following fractions has the least value? 17 11 9 9 18 9

12 9

7 Which of the following fractions lies to the left of 3 on a number line? 5 5 5 4 6 5 5

2 5

8 Which of the following statements is true? 5 6 6 The fraction 5 2 is to the right of 2 on the number line, so 2 is greater than 2 . The fraction 3 is to the right of 1 on the number line, so 3 is less than 1 2. 2 2 2 6 6 4 The fraction 4 7 is to the left of 10 on the number line, so 10 is greater than 7 . 3 1 3 1 The fraction 2 is to the left of 2 on the number line, so 2 is less than 2 .

Which of the following fractions lies to the right of 8 on a number line? 5 7 9 3 8 3 2

4 11

10 Which of the following correctly orders the fractions from greatest to least? 4 4 4 4, 9, 8

4 4 4 8, 6, 4

4 4 4 6, 8, 4

4 4 4 4, 6, 8 COPYING IS STRICTLY PROHIBITED BY LAW

FINDING EQUIVALENT FRACTIONS MA.3.FR.2.2 Identify equivalent fractions and explain why they are equivalent. Plot the fractions on number lines, and use the number lines to determine equivalent fractions. 1

Example: Determine fractions that are equivalent to 2 . 1 2

1 3

2 3

1 4

2 4

1 5

3 4

2 5

1 3

1 1

3 5

2 6

4 5

3 6

4 6

1 5 6

These fractions are all equivalent to 2 . Use fraction models, such as strip diagrams to determine equivalent fractions. 1

Example: Determine fractions that are equivalent to 2 . 1 2

2 2

1 3

2 3

1 4

2 4

1 5 1 6

3 3 3 4

2 5

3 5

2 6

3 6

4 4 4 5

4 6

5 5 5 6

6 6

The fractions equivalent to 2 are 4 and 6 because these fractions are the same size. 89

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DIRECTIONS: Identify whether each pair of fractions is equivalent or not equivalent.

2 and 3 3 4

8 and 4 6 3

Equivalent

Not equivalent

1 and 2 3 6

4 and 2 6 3

Equivalent

Not equivalent

1 and 3 4 8

6 and 3 8 5

Equivalent

Not equivalent

DIRECTIONS: Circle the fractions that are equivalent to the model.

8 6

4 3

10 6

3 5

2 3

1 2

2 3

3 6

5 2

5 3

3 2

4 3

9 6

6 5

8 6

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DIRECTIONS: Identify whether each pair of fractions is equivalent or not equivalent.

7 and 4 2 3

5 and 8 6 9

Equivalent

Not equivalent

1 and 3 3 9

1 and 4 2 8

Equivalent

Not equivalent

9 and 6 4 4

3 and 6 4 8

Equivalent

Not equivalent

DIRECTIONS: Circle the fractions that are equivalent to the model.

5 2

5 4

5 6

8 4

3 5

8 10

10 12

12 14

11 6

6 8

11 8

4 10

9 8

6 10

22 16

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1 Which of these fractions is equivalent to 3 4? 1 1 3 4

5 6

9 12

i and iii only

i, ii, and iii

2 Which of these fractions are equivalent? i.

ii.

iii.

i and ii only

ii and iii only

3 Which of the following statements is true? The fractions 2 and 2 are not equivalent because the two fractions do not represent the 5 8 same part of a whole. The fractions 2 and 2 are equivalent because both fractions have the same numerator. 5 8 The fractions 2 and 2 are not equivalent because their denominators are different. 5 8 The fractions 2 and 2 are equivalent because both fractions represent two wholes. 5 8

4 Which of these fractions is not equivalent to the rest?

5 Use these two number lines to determine which pair of fractions are not equivalent.

0 0

1 8 1 12

2 3 8 and 12

2 8 2 12

3 12

3 8 4 12

4 8 5 12

6 12

4 6 8 and 12

5 8 7 12

6 8 8 12

9 12

10 12

6 9 8 and 12

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7 8 11 12

1 7 10 8 and 12 92

DIRECTIONS: Identify whether each pair of fractions is equivalent or not equivalent.

8 and 6 4 3

3 and 6 4 8

Equivalent

Not equivalent

1 and 2 4 8

2 and 4 5 8

Equivalent

Not equivalent

5 and 6 4 5

9 and 6 3 2

Equivalent

Not equivalent

DIRECTIONS: Circle the fractions that are equivalent to the model.

8 4

7 4

8 5

6 4

7 5

4 5

4 3

8 6

6 4

6 8

9 5

7 5

4 5

9 6

7 6

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1 Which of these fractions is equivalent to 10 ? 12 5 6

6 8

1 6

1 5

i and iii only

i, ii, and iii

2 Which of these fractions are equivalent? i.

ii.

iii.

i and ii only

ii and iii only

3 Which of the following statements is true? 2 3 The fractions 8 and 12 are not equivalent because their numerators are different. 2 3 The fractions 8 and 12 are equivalent because both fractions represent two-thirds. 2 The fractions 8 and 3 are not equivalent because their denominators are different. 12 3 The fractions 2 8 and 12 are equivalent because both fractions represent one-fourth.

4 Which of these fractions is not equivalent to the rest?

5 Use these two number lines to determine which pair of fractions is not equivalent.

0 0

1 6 1 12

2 4 6 and 12

2 12

2 6 3 12

4 12

3 6 5 12

6 12

3 5 6 and 12

4 6 7 12

8 12

5 6 9 12

10 12

4 8 6 and 12

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11 12

1 5 10 6 and 12 94

1 Which of these fractions is equivalent to 6 8? 1 1 6 8

3 4

10 12

i and iii only

i, ii, and iii

2 Which of these fractions are equivalent? i.

ii.

iii.

i and ii only

ii and iii only

3 Which of the following statements is true? The fractions 7 and 8 are not equivalent because the two fractions do not represent the 12 12 same part of a whole. The fractions 7 and 8 are equivalent because both fractions have the same numerator. 12 12 7 and 8 are not equivalent because their numerators are different. The fractions 12 12 The fractions 7 and 8 are equivalent because the two fractions represent the same part 12 12 of a whole.

4 Which of these fractions is not equivalent to the rest?

5 Use these two number lines to determine which pair of fractions is not equivalent.

0 0

1 8 1 12

1 2 8 and 12 95

2 8 2 12

3 12

3 8 4 12

4 8 5 12

6 12

4 6 8 and 12

5 8 7 12

6 8 8 12

9 12

7 8 10 12

11 12

6 9 8 and 12

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2 3 8 and 12

6 Which of these fractions is equivalent to 10 ? 12 5 6

6 8

1 6

1 5

i and iii only

i, ii, and iii

7 Which of these fractions are equivalent? i.

ii.

iii.

i and ii only

ii and iii only

8 Which of the following statements is true? 4 6 The fractions 6 and 9 are not equivalent because their numerators are different. 4 6 The fractions 6 and 9 are equivalent because both fractions represent two-thirds. 4 The fractions 6 and 6 are not equivalent because their denominators are different. 9 6 The fractions 4 6 and 9 are equivalent because both fractions represent one-fourth.

9 Which of these fractions is not equivalent to the rest?

10 Use these two number lines to determine which pair of fractions is not equivalent.

0 0

1 6 1 12

2 4 6 and 12

2 12

2 6 3 12

4 12

3 6 5 12

6 12

5 10 6 and 12

4 6 7 12

8 12

5 6 9 12

10 12

4 8 6 and 12

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11 12

1 2 5 6 and 12 96

APPLYING THE PROPERTIES OF MULTIPLICATION MA.3.AR.1.1 Apply the distributive property to multiply a one-digit number and two-digit number. Apply properties of multiplication to find a product of one-digit whole numbers. The associative property states that it does not matter how we group the numbers.

(2 × 4) × 3

The commutative property states that you can swap numbers and still get the same answer.

2 × (4 × 3)

3×4

4×3

Use rectangular arrays to demonstrate the distributive property to find the product of a one-digit number and a two-digit number.

Example: Apply the distributive property using rectangular arrays to find the product of 4 × 12. 12 can be broken down as 10 + 2.

Therefore, you can write 4 × 12 as 4 × (10 + 2) = (4 × 10) + (4 × 2).

4 × 10 = 40 4×2=8

Therefore, 4 × 12 = 40 + 8 = 48.

Use base-ten blocks to demonstrate the distributive property to find the product of a one-digit number and a two-digit number.

Example: Apply the distributive property using base-ten blocks to find the product of 4 × 12. 12 consists of 1 tens and 2 ones

4 × 12 = 4 × (10 + 2) So, 4 × 12 consists of 4 × 1 tens and 4 × 2 ones.

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DIRECTIONS: Use the associative property to write an equivalent multiplication sentence.

7 × (5 × 8) (14 × 3) × 6 5 × (15 × 6) (2 × 18) × 3 4 × (9 × 10)

(7 × 5) × 8 14 × (3 × 6) (5 × 15) × 6 2 × (18 × 3) (4 × 9) × 10

DIRECTIONS: Use the commutative property to write an equivalent multiplication sentence.

3 × 14 15 × 7 12 × 9 4 × 11 8 × 12

14 × 3 7 × 15 9 × 12 11 × 4 12 × 8

DIRECTIONS: Use the distributive property to write an equivalent multiplication sentence and find the product.

8 × 16

(8×10) + (8×6)

80 + 48 = 128

9 × 34

(9×30) + (9×4)

270 + 36 = 306

7 × 28

(7×20) + (7×8)

140 + 56 = 196

5 × 78

(5×70) + (5×8)

350 + 40 = 390

4 × 63

(4×60) + (4×3)

240 + 12 = 252

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DIRECTIONS: Use the associative property to write an equivalent multiplication sentence.

(2 × 7) × 3 + 6 × 5

2 × (7 × 3) + 6 × 5

(8 × 17) × 9

8 × (17 × 9)

6 × (12 × 7) + 9

(6 × 12) × 7 + 9

11 + 5 × (13 × 2)

11 + (5 × 13) × 2

6 × (8 × 13 × 4) × 5

(6 × 8 × 13) × 4 × 5

DIRECTIONS: Use the commutative property to write an equivalent multiplication sentence.

8 × 82

82 × 8

12 × 168

168 × 12

6×8

8 × 6

17 × 78

78 × 17

9 × 102

102 × 9

the distributive property to write an equivalent multiplication sentence DIRECTIONS: Use and find the product.

9 × 19

(9×10) + (9×9)

90 + 81 = 171

5 × 92

(5×90) + (5×2)

450 + 10 = 460

8 × 37

(8×30) + (8×7)

240 + 56 = 296

7 × 64

(7×60) + (7×4)

420 + 28 = 448

3 × 98

(3×90) + (3×8)

270 + 24 = 294

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1 Which of the following multiplication sentences shows the associative property of multiplication? 5 × 36 = 36 × 5 5 × (30 + 6) = (5 × 30) + (5 × 6) 5 × (4 × 9) = (5 × 4) × 9 36 × 1 = 36

2 A multiplication sentence is shown below. Determine the number that makes the multiplication sentence true.

8 × 36 = ? × 8 8

3 A multiplication sentence is shown below. Determine the number that makes the multiplication sentence true.

6 × 24 = 6 × (20 + 4) = (6 × ?) + (6 × 4) 4

4 Which of the following multiplication sentences shows the associative property of multiplication? (3 × 6) × 9 = 3 × (6 × 9) 3 × (6 + 9) = (3 × 6) + (3 × 9) (3 × 6) × 9 = (6 × 3) × 9 3 × (6 × 9) = 3 × 54

5 A multiplication sentence is shown below. Determine the number that makes the multiplication sentence true.

(8 × ?) × 3 = 8 × (5 × 3) 3

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15 100

DIRECTIONS: Use the associative property to write an equivalent multiplication sentence.

(2 + 3) × 8 × (2 × 5)

(2 + 3) × (8 × 2) × 5

5 × (3 × 9) - 7

(5 × 3) × 9 - 7

15 × 5 - 8 × (11 × 6)

15 × 5 - (8 × 11) × 6

(6 × 4) × 2

6 × (4 × 2)

11 + 4 × (3 × 8)

11 + (4 × 3) × 8

DIRECTIONS: Use the commutative property to write an equivalent multiplication sentence.

19 × 65

65 × 19

35 × 44

44 × 35

8 × 96

96 × 8

4 × 479

479 × 4

13 × 71

71 × 13

Use the distributive property to write an equivalent multiplication DIRECTIONS: sentence and find the product.

101

11 × 62

(11×60) + (11×2)

660 + 22 = 682

8 × 51

(8×50) + (8×1)

400 + 8 = 408

5 × 110

(5×100) + (5×10)

500 + 50 = 550

4 × 85

(4×80) + (4×5)

320 + 20 = 340

3 × 150

(3×100) + (3×50)

300 + 150 = 450

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1 Which of the following multiplication sentences shows the distributive property of multiplication? 9×1=9

9 × (3 × 4) = (9 × 3) × 4

9 × 12 = 12 × 9

9 × (10 + 2) = (9 × 10) + (9 × 2)

2 Kevon and Joseph need to find the product of 3, 4, and 6. •

Kevon says that because 3 × 4 = 12, he can use the distributive property to rewrite the equation 3 × 4 × 6 as (12 × 4) + (12 × 6), which is equivalent to 120.

•

Joseph says that because 4 × 6 = 24, he can use the associative property to rewrite the equation 3 × 4 × 6 as 3 × 24, which is equivalent to 72.

Who is correct? Kevon only

Joseph only

Both of them

Neither of them

3 Which of the following multiplication sentences shows the distributive property of multiplication? 7 × 24 = 7 × 2 × 12

7 × (20 + 4) = (7 × 20) + (7 × 4)

(7 × 8) × 3 = 7 × (8 × 3)

3 × (7 × 8) = (7 × 8) × 3

4 Treyvon used the steps below to find the product of (3 × 6) and 2. What property of multiplication did he use to find the product? GIVEN: (3 × 6) × 2 STEP 1: 2 × (3 × 6) STEP 2: 2 × 18 STEP 3: 36

Associative property of multiplication Commutative property of multiplication Distributive property of multiplication Multiplication using a standard algorithm

5 Beth and Patricia need to find the product of 6 and 24. • •

Beth claims 6 × 24 is equal to 6 × (3 × 8) and (6 × 3) + (6 × 8), which is equates to 66. Patricia claims 6 × 24 is equal to 6 × (4 + 20) and (6 × 4) + 20, which equates to 44.

Who is correct? Beth only

Patricia only

Both of them

Neither of them COPYING IS STRICTLY PROHIBITED BY LAW

102

1 Carolina used the following steps to find the product of 8 and 24. What property of multiplication did she use to find the product? GIVEN: 8 × 24 STEP 1: 8 × (20 + 4) STEP 2: (8 × 20) + (8 × 4) STEP 3: 160 + 32 STEP 4: 192

Associative property of multiplication Commutative property of multiplication Distributive property of multiplication Multiplication using a standard algorithm

2 A multiplication sentence is shown below. Use the associative property of multiplication to determine the number that makes the multiplication sentence true.

(9 × 4) × 5 = 9 × (4 × ?) 4

3 Which of the following multiplication sentences shows the distributive property of multiplication?

3 × (15 + 7) = (3 × 15) + (3 × 7)

3 × (15 × 7) = (3 × 15) × 7

3 × 15 = 15 × 3

3×1=3

4 Jen and Kelly need to find the product of 7 and 26. • •

Jen claims 7 × 26 is equal to 7 × (2 × 13) and (7 × 2) + (7 × 13), which is equates to 105. Kelly claims 7 × 26 is equal to 7 × (6 + 20) and (7 × 6) + (7 × 20), which equates to 182.

Who is correct? Jen only

Kelly only

Both of them

Neither of them

5 Allan and Mark need to find the product of 4 and 22. • Allan says he can find the product of 4 × 22 by rewriting the multiplication sentence as 4 × (20 + 2), then rewriting it again using the distributive property as (4 × 20) + (4 × 2), which is equivalent to 88. • Mark says he can find the product of 4 × 22 by rewriting the multiplication sentence as 4 × (2 × 11), then rewriting it again using the associative property as (4 × 2) × 11, which is equivalent to 88. Who is correct?

103

Allan only

Mark only

Both of them

Neither of them

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6 Which of the following multiplication sentences shows the associative property of multiplication? 9×5=5×9 9 × (5 + 8) = (9 × 5) + (9 × 8) 9×1=9 9 × (5 × 8) = (9 × 5) × 8

7 A multiplication sentence is shown below. Determine the number that makes the multiplication sentence true.

12 × 49 = 49 × ? 8

8 A multiplication sentence is shown below. Determine the number that makes the multiplication sentence true.

4 × 15 = 4 × (10 + 5) = (4 × ?) + (4 × 5) 10

9 Which of the following multiplication sentences shows the associative property of multiplication? (13 × 12) × 5 = (12 × 13) × 5 13 × (12 + 5) = (13 × 12) + (13 × 5) (13 × 12) × 5 = 13 × (12 × 5) 13 × (12 × 5) = 13 × 60

10 Which of the following multiplication sentences shows the distributive property of multiplication?

6 × 80 = 7 × 8 × 10 6 × (8 × 10) = (6 × 8) × 10 (6 × 8) × 10 = 6 × (8 × 10) 6 × (8 + 10) = (6 × 8) + (6 × 10) COPYING IS STRICTLY PROHIBITED BY LAW

104

SOLVING REAL-WORLD PROBLEMS MA.3.AR.1.2 Solve one- and two-step real-world problems involving any of four operations with whole numbers. When solving one- and two-step real-world problems involving any of four operations, follow the steps shown below.

Example: Anne had 3 boxes of chocolate cookies, and each box contained 12 cookies. She also had a box of 10 almond cookies. How many cookies did Anne have in all?

STEP 1

Anne had 3 boxes of chocolate cookies, and each Identify the necessary information. Circle the givens in the problem and box contained 12 cookies. She also had a box of 10 underline what needs to be figured almond cookies. How many cookies did Anne have in out. all? ADDITON: in all, sum, altogether, combined, plus, increased by, more than, added to, totaled

STEP 2

SUBTRACTION: less, fewer, left, minus, difference, take away, deduct, remaining, decreased by

Identify keywords in the question. Identifying keywords can help you figure out what to do.

MULTIPLICATION: product, times, of, multiplied by, twice, double, triple, each, per DIVISION: quotient, divide, half, split, share, evenly, equal groups, each, per •

Anne had 3 boxes of chocolate cookies, and each box contained 12 cookies. 3 × 12 = 36 cookies

STEP 3

Use models to visualize the situation given in the questions. Do this one step at a time. You can use • base-ten blocks, number lines, or even draw out a picture.

12 cookies 12 cookies 12 cookies She also had a box of 10 almond cookies. 36 + 10 = 46 cookies 36 cookies

STEP 4

105

Write your final answer.

10 cookies

Therefore, Anne had 46 cookies in all.

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DIRECTIONS: Use models to solve each word problem. On the home screen of Gene's tablet, he had 6 rows of apps, with 8 apps on each row. If he deleted 18 apps, how many would he have left on his home screen? 8 apps 8 apps 8 apps 8 apps 8 apps 8 apps 6 × 8 = 48 apps 48 apps

ANSWER:

30 apps

Remaining apps

18 apps

48 - 18 = 30 apps

Adam had 3 times as many candies as Faye. Adam then split his candy evenly into 5 piles. If Faye had 40 candies, how many candies would be in each of Adam's piles? 40 candies

40 candies

3 × 40 = 120 candies

120 candies

1 pile

ANSWER:

24 candies 1 pile

1 pile

120 ÷ 5 = 24 candies

There are 40 students trying out for the trivia teams. If 19 of them were not picked for the team, and the rest were put into 3 equal groups, how many students would be in each group? 40 students Remaining students

19 students

40 - 19 = 21 students

7 students

21 students 1 group

1 group

ANSWER:

1 group

21 ÷ 3 = 7 students

A clothing company used 9 buttons on jeans and 5 buttons on shirts. If they made 3 shirts and 1 pair of jeans, how many buttons did they use in all? 5 buttons

5 buttons

3 × 5 = 15 buttons

9 buttons

15 + 9 = 24 buttons

ANSWER:

24 buttons 15 buttons

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106

DIRECTIONS: Use models to solve each word problem. Rose has 8 bags of 50 candies each. She gives 90 candies to her classmates. How many candies does she have left?

50 × 8 = 400 candies 50

Remaining candies

ANSWER:

310 candies

400 - 90 = 310 candies Jax had 4 times less strawberries than Phil. Jax then split his entire strawberry harvest into bags of 50. If Phil had 600 strawberries, how many bags did Jax use?

150

600 ÷ 4 = 150 strawberries

150

ANSWER:

150 strawberries

1 bag

3 bags

150 ÷ 50 = 3 bags

1 bag

We use 250g of flour for 1 pizza and 300g of flour for 1 cake. If we make 5 pizzas and 2 cakes, how much flour will we use?

250 g

ANSWER:

250 × 5 = 1,250 g

1,850 g 1250 g

300 g

300 g 1,250 + 2 × 300= 1,850 g

31 students want to play football. They are divided into teams of 6 players. In order to have 6 equal teams, how many students must be added? 6 × 6 = 36 students 6

6 31 students

ANSWER:

6 5

5 students 36 - 31 = 5 students

107

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1 Denver bought 8 boxes of chocolate bars. He gave 3 of the boxes to his brother. If each box contains 6 chocolate bars, how many chocolate bars does Denver have left? 18 chocolate bars

30 chocolate bars

40 chocolate bars

48 chocolate bars

2 Nephtalie and Maria collect dolls. Nephtalie has 4 dolls in her collection, and Maria has 3 times as many dolls as Nephtalie. How many dolls do the two of them have in all? 8 dolls

12 dolls

16 dolls

18 dolls

3 Junior was assigned to arrange chairs in the auditorium. He needed to arrange 72 chairs into 6 equal rows. How many chairs will be in each row? 6 chairs

8 chairs

10 chairs

12 chairs

4 Harry went to a toy store and bought 8 toy cars. Each toy car cost 3 dollars. If Harry paid with a $50 bill, how much change should he get back? 24 dollars

26 dollars

30 dollars

32 dollars

5 Mr. Romero went on a business trip that lasted 4 weeks and 3 days. How many days did Mr. Romero’s business trip last? (Note: There are 7 days in 1 week.) 7 days

28 days

31 days

49 days

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108

DIRECTIONS: Use models to solve each word problem. Sara’s dad bought 5 boxes of chocolate and each has 30 pieces of chocolate. If he gives his daughter 10 pieces a day, how many will he have left after 10 days? 30

5 × 30 = 150

150 pieces of chocolate

ANSWER:

50 pieces

100 pieces of chocolate 150 - 10 × 10 = 50

Remaining

Rick had half as many toys as David. Rick stores his toys evenly in 3 boxes. If David had 60 toys, how many toys are in each of Rick's boxes? 30 toys

30 toys

60 ÷ 2 = 30 toys

ANSWER:

30 toys

10 toys

10 toys 10 toys

30 ÷ 3 = 10 toys

As a gift to his mother and 2 sisters, John decides to make a bouquet of flowers for each of them. He has 7 lilies and wants each bouquet to have 2 lilies. How many lilies will he have left? 2

2 7 lilies

1 Lily

2 × 3 = 6 lilies

ANSWER:

1 lily

6 lilies

7 - 6 = 1 lilies

We use 3m of wood to build a dog house and 1m for 2 birdhouses. If we build 4 dog houses and 4 birdhouses, how many meters of wood will we use?

3m of wood

109

3m of wood

3 × 4 = 12m of wood ANSWER:

12m of wood

1m of

12 + 2 × 1 = 14m of

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14m

1 Rupert shared 48 marbles with four of his friends. If each of his friends received the same number of marbles, how many marbles did he give to each of his friends? 12 marbles

15 marbles

8 marbles

10 marbles

2 An electric company needs to install streetlights along a 7-block street. Six streetlights will be installed in each of the first 4 blocks, and five streetlights will be installed in each of the remaining blocks. How many streetlights will be installed in all? 35 streetlights

39 streetlights

40 streetlights

42 streetlights

3 Emma went to the garden shop. She bought two petunias and seven orchids. Each petunia costs $7, and each orchid costs $9. How much money did Emma spend on the plants? $9

$63

$77

$81

4 Angie prepared 6 batches of chocolate cookies for her party tonight. Each batch consisted of 10 cookies. She also prepared 12 raisin cookies. How many cookies did she prepare in all?

72 cookies

60 cookies

48 cookies

40 cookies

5 The recipe for a pie calls for 8 eggs. The recipe for a cake calls for 5 eggs. If Miriam wants to make 4 pies and 1 cake, how many eggs does she need in all? 32 eggs

37 eggs

40 eggs

42 eggs COPYING IS STRICTLY PROHIBITED BY LAW

110

1 A restaurant uses 8 ounces of meat for their burgers and 12 ounces of meat for their nachos. If Tom ordered 3 burgers and 1 order of nachos, how many ounces of meat does the restaurant use in all? 30 ounces

36 ounces

40 ounces

48 ounces

2 Annette's mother gave her some money for scarves. She bought 6 scarves for 7 dollars each. She was left with 3 dollars. How much money did Annette receive from her mother? 40 dollars

42 dollars

45 dollars

50 dollars

3 Amy worked 30 hours last week, spread equally over 5 days. If she is paid $8 per hour, how much did she earn each day? $30

$36

$40

$48

4 Jeff was assigned to arrange tables in the party hall. He needed to arrange 56 tables into 7 equal rows. How many tables were in each row? 6 tables

8 tables

10 tables

12 tables

5 Martha bought 9 packs of gummy bears. She gave 4 of the packets to her sister. If each pack contains 5 gummy bears, how many gummy bears does Martha have left?

111

14 gummy bears

22 gummy bears

17 gummy bears

25 gummy bears

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6 Harry had 52 playing cards. He dealt them to four of his friends. If each of his friends received the same number of cards, how many cards did he deal to each friend? 11 cards

13 cards

10 cards

26 cards

7 A company needs to install stop signs along a 9-block street. Five stop signs will be installed in the first 6 blocks, and seven signs will be installed in the remaining blocks. How many stop signs will be installed by the company in all? 51 stop signs

57 stop signs

37 stop signs

45 stop signs

8 Ellie went to the bakery. She bought three pastries and eight muffins. Each pastry costs $2, and each muffin costs $4. How much money did Ellie spend on the items? $6

$16

$32

$38

9 Keanu prepared 5 trays of biscuits for his party tonight. Each tray had 15 biscuits on it. Then he prepared an additional 11 sweet biscuits. How many biscuits did he prepare in all? 72 biscuits

60 biscuits

86 biscuits

40 biscuits

10 The recipe for a pie calls for 6 eggs, and the recipe for a cake calls for 10 eggs. If Miriam wants to make 3 pies and 2 cakes, how many eggs does she need in all? 32 eggs

38 eggs

40 eggs

42 eggs

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112

EVALUATING EQUATIONS MA.3.AR.2.2 Determine and explain whether an equation involving multiplication or division is true or false. Understand that the equal sign (=) in a number sentence indicates that the values of each side of the number sentence are equal. Use visual representations like counters, drawings, strip diagrams, or base-ten blocks to show whether the values of each side are equal. LEFT SIDE

RIGHT SIDE

3×4

EXAMPLE

2×6

VISUAL REPRESENTATION

CONCLUSION

The equation 3 × 4 = 2 × 6 is true because the left-hand side is equal to 12, the right-hand side is equal to 12, and 12 = 12.

LEFT SIDE

12 ÷ 3

EXAMPLE VISUAL REPRESENTATION

CONCLUSION

RIGHT SIDE

The equation 12 ÷ 3 = 2 × 4 is false because the left-hand side is equal to 4, the right-hand side is equal to 8, and 4 ≠ 8.

LEFT SIDE EXAMPLE

2×4

RIGHT SIDE

5×2

20 ÷ 2

VISUAL REPRESENTATION

CONCLUSION

113

The equation 5 × 2 = 20 ÷ 2 is true because the left-hand side is equal to 10, the right-hand side is equal to 10, and 10 = 10. MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

a check mark to indicate if the equations DIRECTIONS: Use below are true or false.

EQUATION

TRUE

FALSE

5 × 6 = 10 × 4 12 ÷ 6 = 4 ÷ 2 2 × 3 = 10 ÷ 2 15 ÷ 3 = 1 × 5 7×2=6×3 20 ÷ 5 = 8 ÷ 2 3 × 5 = 18 ÷ 2 6÷3=2×3 6×8=9×4 18 ÷ 6 = 9 ÷ 3 5 × 6 = 20 ÷ 4 12 ÷ 3 = 2 × 2 4×4=3×3 8÷4=4÷2 9 × 3 = 36 ÷ 4 COPYING IS STRICTLY PROHIBITED BY LAW

114

DIRECTIONS: Use a check mark to indicate if the equations below are true or false.

EQUATION

TRUE

3×6=9×2 24 ÷ 3 = 8 ÷ 2 3 × 3 = 18 ÷ 2 10 × 2 = 5 × 5 60 ÷ 5 = 6 × 2 80 ÷ 2 = 100 ÷ 5 8 × 8 = 128 ÷ 2 27 ÷ 9 = 1 × 4 7 × 9 = 21 × 3 20 ÷ 5 = 80 ÷ 20 4 × 8 = 96 ÷ 3 30 ÷ 5 = 2 × 4 11 × 4 = 14 × 3 46 ÷ 23 = 16 ÷ 8 5 × 14 = 200 ÷ 8 115

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FALSE

1 Which of the following multiplication equations is true? 5 × 5 = 15

5 × 5 = 20

25 = 5 × 5

30 = 5 × 5

2 Which of the following division equations is true? 6 = 21 ÷ 3

21 ÷ 3 = 7

8 = 21 ÷ 3

21 ÷ 3 = 9

3 Which of the following number sentences is true? 2 × 5 = 20 ÷ 10

2 × 5 = 20 ÷ 5

2 × 5 = 20 ÷ 4

2 × 5 = 20 ÷ 2

4 A number sentence is given below.

8×2=4 ? 4 Which of the following operations makes the number sentence true?

−

5 Which of the following multiplication equations is true? 3×4=2×6

3×4=2×7

3×4=2×8

3×4=2×9

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116

DIRECTIONS: Use a check mark to indicate if the equations below are true or false.

EQUATION

TRUE

8 × 9 = 12 × 6 21 ÷ 3 = 28 ÷ 4 3 × 9 = 56 ÷ 2 76 ÷ 4 = 2 × 9 4×4=8×2 36 ÷ 2 = 72 ÷ 6 5 × 6 = 90 ÷ 3 20 ÷ 5 = 2 × 2 10 × 10 = 24 × 5 42 ÷ 6 = 84 ÷ 12 3 × 7 = 128 ÷ 6 136 ÷ 4 = 5 × 7 12 × 12 = 25 × 6 25 ÷ 5 = 80 ÷ 16 9 × 9 = 168 ÷ 2 117

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FALSE

1 A multiplication sentence is given below.

5 × 6 = 2 × 10 Which of the following statements is true? The multiplication sentence 5 × 6 = 2 × 10 is true as both the left and right sides of the equal sign are 30. The multiplication sentence 5 × 6 = 2 × 10 is true. The right side of the equal sign is equal to 5, and the left side also contains the factor 5. The multiplication sentence 5 × 6 = 2 × 10 is false because the left side of the equal sign is equal to 30 and the right side is equal to 20. None of the statements are true.

2 Which of the following number sentences is true? 3 × 2 = 12 ÷ 1

3 × 2 = 12 ÷ 2

3 × 2 = 12 ÷ 3

3 × 2 = 12 ÷ 4

3 A division sentence is given below.

6÷3=4÷2 Which of the following statements is true? The division sentence 6 ÷ 3 = 4 ÷ 2 is true. The left side of the equal sign, 6 ÷ 3, is equal to 2, and the right side of the equal sign, 4 ÷ 2, is also equal to 2. The division sentence 6 ÷ 3 = 4 ÷ 2 is false. The left side of the equal sign, 6 × 3, is equal to 18, and the right side of the equal sign, 4 × 2, is equal to 8. The division sentence 6 ÷ 3 = 4 ÷ 2 is false. The left side of the equal sign, 6 ÷ 3, is equal to 3, and the right side of the equal sign, 4 ÷ 2, is equal to 2. None of the statements are true.

4 Which of the following division equations is true? 25 ÷ 5 = 9 ÷ 3

24 ÷ 6 = 9 ÷ 3

21 ÷ 3 = 9 ÷ 3

24 ÷ 8 = 9 ÷ 3

5 Which of the following multiplication equations is true? 5 × 5 = 15

5 × 5 = 20

30 = 5 × 6

30 = 5 × 5 COPYING IS STRICTLY PROHIBITED BY LAW

118

1 A number sentence is given below.

8÷2=4×2 Which of the following statements is true? The number sentence is true because the left side of the equal sign, 8 ÷ 2, is equal to 4, and the right side of the equal sign, 4 × 2, is also equal to 4. The number sentence is true because the left side of the equal sign, 8 ÷ 2, is equal to 4, and the right side also contains the factors 4 and 2. The number sentence is false because the left side of the equal sign, 8 ÷ 2, is equal to 4, and the right side of the equal sign, 4 × 2, is equal to 8. None of the statements are true.

2 Which of the following multiplication equations is true?

9×4=6×5

9×4=6×6

9×4=6×7

9×4=6×8

3 Which of the following division equations is true? 15 ÷ 5 = 8 ÷ 4

20 ÷ 4 = 15 ÷ 5

35 ÷ 5 = 21 ÷ 3

40 ÷ 5 = 12 ÷ 3

4 A number sentence is given below.

9×2=3 ? 6 Which of the following operations makes the number sentence true?

−

5 A number sentence is given below.

12 × 3 = 9 ? 4 Which of the following operations makes the number sentence true?

119

−

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6 Which of the following multiplication equations is true? 7 × 6 = 49

7 × 6 = 42

13 = 7 × 6

30 = 7 × 6

7 Which of the following division equations is true? 6 = 35 ÷ 5

35 ÷ 5 = 5

7 = 35 ÷ 5

35 ÷ 5 = 9

8 Which of the following number sentences is true? 2 × 5 = 20 ÷ 10

2 × 5 = 20 ÷ 5

2 × 5 = 20 ÷ 4

2 × 5 = 20 ÷ 2

9 A number sentence is given below.

16 ÷ 2 = 4 ? 4 Which of the following operations makes the number sentence true?

−

10 Which of the following multiplication equations is true? 5×6=8×6

5×6=4×8

5×6=6×6

5 × 6 = 3 × 10

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120

DETERMINING UNKNOWN WHOLE NUMBERS

MA.3.AR.2.3 Determine the unknown whole number in a multiplication or division equation, relating three whole numbers, with the unknown in any position. MA.3.NSO.2.1 Restate a division problem as a missing factor problem using the relationship between multiplication and division. Understand that fact families relate multiplication and division equations. Remember that multiplication and division are inverse operations. Use rectangular arrays to model the relationship between multiplication and division.

Example: Use a rectangular array to find all multiplication and division equations related to 4 × 6. 4 × 6 can be modeled as 4 rows of 6 6 Based on the model

4 Thus, 4 × 6 = 24.

4 × 6 = 24

Based on the model.

6 × 4 = 24

6 columns of 4

24 ÷ 6 = 4

24 divided into 6 equal columns

24 ÷ 4 = 6

24 divided into 4 equal rows

Use fact families to write a multiplication or division equation to determine the unknown whole number in any position.

121

EQUATION

WHAT IT MEANS

3 × ___ = 6

3 groups of how

___ × 3 = 6

How many groups of

6 ÷ 3 = ___

6 divided into 3 equal

6 ÷ ___ = 3

6 divided into how

VISUAL MODEL

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DIRECTIONS: Fill in the missing fact from each fact family.

7 × 8 = 56

30 ÷ 5 = 6

4 × 9 = 36

8 × 7 = 56

5 × 6 = 30

36 ÷ 9 = 4

56 ÷ 7 = 8

30 ÷ 6 = 5

36 ÷ 4 = 9

56 ÷ 8 = 7

6 × 5 = 30

9 × 4 = 36

15 ÷ 3 = 5

32 ÷ 4 = 8

3 × 7 = 21

5 × 3 = 15

4 × 8 = 32

21 ÷ 7 = 3

15 ÷ 5 = 3

8 × 4 = 32

7 × 3 = 21

3 × 5 = 15

32 ÷ 8 = 4

21 ÷ 3 = 7

Find the missing number in the multiplication or DIRECTIONS: division equations.

5 = 40 8 × _____

5 =6 30 ÷ _____

6 × 3 = 18 _____

28 ÷ 7 = 4 _____

8 = 72 9 × _____

3 =4 12 ÷ _____

7 × 6 = 42 _____

54 ÷ 6 = 9 _____

2 = 18 9 × _____

5 =5 25 ÷ _____

4 × 10 = 40 _____

27 ÷ 3 = 9 _____

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122

DIRECTIONS: Fill in the missing fact from each fact family.

9 × 7 = 63

42 ÷ 6 = 7

6 × 5 = 30

63 ÷ 7 = 9

7 × 6 = 42

30 ÷ 6 = 5

63 ÷ 9 = 7

6 × 7 = 42

5 × 6 = 30

7 × 9 = 63

42 ÷ 7 = 6

30 ÷ 5 = 6

99 ÷ 9 = 11

3 × 9 = 27

48 ÷ 6 = 8

9 × 11 = 99

9 × 3 = 27

48 ÷ 8 = 6

11 × 9 = 99

27 ÷ 9 = 3

6 × 8 = 48

99 ÷ 11 = 9

27 ÷ 3 = 9

8 × 6 = 48

DIRECTIONS: Find the missing number in the multiplication or division equations.

123

9 = 81 9 × _____

5 = 13 65 ÷ _____

7 × 4 = 28 _____

36 ÷ 6 = 6 _____

8 = 40 5 × _____

5 =3 15 ÷ ____

2 × 7 = 14 _____

70 ÷ 10 = 7 _____

5 = 45 9 × _____

7 =7 49 ÷ _____

8 × 12 = 96 _____

55 ÷ 5 = 11 _____

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1 What is the value of a in the equation below? a × 8 = 48 4

2 What is the value of m in the equation below? 9 × m = 63 7

3 What is the value of s in the equation given below?

s ÷ 7 = 13 96

4 Select all of the related facts that can be used to solve this equation: 39 ÷ 3 = b 3 × 13

3×9

13 × 2

17 × 3

13 × 3

5 Select all of the related facts that can be used to solve this equation: 51 ÷ ? = 3

19 × 3

4 × 17

3 × 17

17 × 3

19 × 4 COPYING IS STRICTLY PROHIBITED BY LAW

124

DIRECTIONS: Fill in the missing fact from each fact family.

5 × 7 = 35

6 × 3 = 18

72 ÷ 9 = 8

35 ÷ 7 = 5

18 ÷ 3 = 6

72 ÷ 8 = 9

35 ÷ 5 = 7

3 × 6 = 18

9 × 8 = 72

7 × 5 = 35

18 ÷ 6 = 3

8 × 9 = 72

24 ÷ 6 = 4

13 × 3 = 39

15 × 6 = 90

6 × 4 = 24

3 × 13 = 39

90 ÷ 6 = 15

24 ÷ 4 = 6

39 ÷ 3 = 13

6 × 15 = 90

4 × 6 = 24

39 ÷ 13 = 3

90 ÷ 15 = 6

DIRECTIONS: Find the missing number in the multiplication or division equations.

125

3 = 48 16 × ___

8 =7 56 ÷ _____

2 × 9 = 18 _____

24 ÷ 8 = 3 _____

8 = 72 5 × _____

12 = 8 96 ÷ _____

6 × 7 = 42 _____

84 ÷ 14 = 6 _____

2 = 16 8 × _____

15_ = 9 135 ÷ __

4 ×2=8 _____

44 ÷ 11 = 4 _____

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1 Which of the following multiplication equations can be used to find the quotient of 42 ÷ 6? 6 × ? = 42

3×?=6

6 × ? = 12

2×?=6

2 If 8 × 4 = 32, then 32 ÷ 4 must be equal to which of the following? 4

3 Which of the following multiplication and division sentences is not related to the other facts? 3 × 6 = 18

6÷3=2

6 × 3 = 18

18 ÷ 3 = 6

4 Which of the following multiplication equations can be used to find the quotient of 24 ÷ 4? 2×n=4

2 × n = 24

4×n=4

4 × n = 24

5 If 4 × 5 = 20, then which of the following must be a related division fact? 4÷2=2

8÷4=2

10 ÷ 5 = 2

20 ÷ 4 = 5

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126

1 What is the value of w in the equation below? w × 6 = 42 4

2 What is the value of c in the equation below? 14 × c = 70 6

3 What is the value of h in the equation given below?

h ÷ 5 = 13 55

4 Select all of the related facts that can be used to solve this equation: 72 ÷ 18 = b 4 × 18

7 × 18

18 × 4

16 ×4

4 × 16

5 Select all of the related facts that can be used to solve this equation: 68 ÷ ? = 2

12 × 8

2 × 34

6 × 19

19 × 6

34 × 2 127

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6 If 8 × 6 = 48, then which of the following must be a related division fact? 48 ÷ 6 = 8

8÷2=4

6÷3=2

6÷2=3

7 Paulo and Vincent must find the quotient of 27 ÷ 9. •

Paulo says that since 3 × 9 = 27, then 27 ÷ 9 must be 3.

•

Vincent says that since 9 × 1 = 9, then 27 ÷ 9 must be 1.

Who among them is correct? Paulo only Vincent only Both Paulo and Vincent

Neither Paulo nor Vincent

8 Maya and Fay must find the quotient of 72 ÷ 8 = ◼. •

Maya says that she can rewrite 72 ÷ 8 = ◼ as 2 × ◼ = 8 and determine that the quotient is 4.

•

Fay says that she can rewrite 72 ÷ 8 = ◼ as 4 × ◼ = 8 and determine that the quotient is 2.

Who is correct? Maya only Fay only Both Maya and Fay Neither Maya nor Fay

9 If 8 × 9 = 72, then 72 ÷ 9 must be equal to which of the following? 9

10 Which of the following multiplication and division sentences is not related to the other facts? 8 × 4 = 32

8 × 8 = 64

32 ÷ 4 = 8

32 ÷ 8 = 4 COPYING IS STRICTLY PROHIBITED BY LAW

128

IDENTIFYING EVEN AND ODD WHOLE NUMBERS MA.3.AR.3.1 Determine and explain whether a whole number from 1 to 1,000 is even or odd. Use base-ten blocks to determine whether a number is even or odd. Remember that even numbers can be paired or divided into equal groups of 2 with no leftovers, while odd numbers will always have one left over when paired or divided into equal groups of 2. A block of 10 or a block of 100 can always be divided into equal groups of 2. Therefore, you only have to check the ones blocks.

NUMBER

VISUAL REPRESENTATION

EVEN OR ODD?

Based on the base-ten model, the ones blocks can be paired. So, 76 is even.

127

Based on the base-ten model, the ones blocks cannot be paired. So, 127 is odd.

219

Based on the base-ten model, the ones blocks cannot be paired. So, 219 is odd.

Based on the base-ten model, the ones blocks can be paired. So, 94 is even.

Use a place value table to identify if a number is even or odd by looking at the digits in the ones place. If the digit in the ones place is a multiple of 2 (0, 2, 4, 6, or 8), then the number is even. If it is not, then the number is odd.

NUMBER

129

PLACE VALUE

EVEN OR ODD?

HUNDREDS

TENS

ONES

768

Since the ones digit is a multiple of 2, then the number is even.

944

Since the ones digit is a multiple of 2, then the number is even.

813

Since the ones digit is not a multiple of 2, then the number is odd.

999

Since the ones digit is not a multiple of 2, then the number is odd.

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DIRECTIONS: Use a check mark to indicate if each number is even or odd.

NUMBER

EVEN

ODD

358 643 717 918 645 263 58 96 845 327 731 64 915 804 903 COPYING IS STRICTLY PROHIBITED BY LAW

130

DIRECTIONS: Use a check mark to indicate if each number is even or odd.

NUMBER

EVEN

821 557 236 86 475 114 385 631 324 356 679 991 148 51 232 131

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ODD

1 Select all the odd numbers. 200

441

664

225

729

2 There are an odd number of gallons of water in a water tank. Which of these could be the number of gallons in the water tank? 17

3 A packet of candy has an even number of jellies in it. Which of these could be the number of jellies in the packet? 21

4 Select all the even numbers. 324

520

728

365

173

5 There are an odd number of animals in a zoo. Which of these could be the number of animals in the zoo? 210

364

117

402 COPYING IS STRICTLY PROHIBITED BY LAW

132

DIRECTIONS: Use a check mark to indicate if each number is even or odd.

NUMBER

EVEN

413 250 999 253 174 459 815 458 320 398 315 263 700 107 939 133

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ODD

1 There are an even number of candies in a gift box. Which of these could be the number of candies in the gift box? 35

2 A pencil box has an odd number of pencils in it. Which of these could be the number of pencils in the box? 165

190

110

352

3 There are an even number of trees in a park. Which of these could be the number of trees in the park? 657

461

883

574

4 Select all the odd numbers. 478

287

469

891

766

5 Select all the even numbers. 101

270

852

462

301

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134

1 There are an odd number of T-shirts on a display rack. Which of these could be the number of Tshirts on the rack? 44

2 A box has an even number of marbles in it. Which of these could be the number of marbles in the box? 129

224

437

315

3 There are an odd number of crates in a warehouse. Which of these could be the number of crates in the warehouse? 341

466

720

254

4 Select all the odd numbers. 327

436

539

922

611

5 Select all the even numbers. 102

337

777

572

840

135

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6 Select all the odd numbers. 989

741

440

562

641

7 There are an odd number of people at a party. Which of these could be the number of people at the party? 40

8 A folder has an even number of sheets of paper in it. Which of these could be the number of sheets of paper in the folder? 29

9 Select all the even numbers. 333

789

616

712

492

10 There are an odd number of cars in a parking lot. Which of these could be the number of cars in the parking lot? 68

120

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136

DETERMINING MULTIPLES MA.3.AR.3.2 Determine whether a whole number from 1 to 144 is a multiple of a given one-digit number. Use visual models, addition, or multiplication to generate the multiples of a given number.

Example: Find the first twelve multiples of 3. MODEL

ADDITION

MULTIPLICATION

3=3

1×3=3

3+3=6

2×3=6

3+3+3=9

3×3=9

3 + 3 + 3 + 3 = 12

4 × 3 = 12

3 + 3 + 3 + 3 + 3 = 15

5 × 3 = 15

3 + 3 + 3 + 3 + 3 + 3 = 18

6 × 3 = 18

3 + 3 + 3 + 3 + 3 + 3 + 3 = 21

7 × 3 = 21

3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 24

8 × 3 = 24

3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 27

9 × 3 = 27

3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 30

10 × 3 = 30

3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 33

11 × 3 = 33

3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 36

12 × 3 = 36

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36. 137

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DIRECTIONS: Circle all the numbers that are multiples of the given numbers. GIVEN NUMBER

4 6 7 5 9 8

8 9 14 8 12 10

10 12 16 15 15 16

12 18 18 18 18 20

14 20 24 20 21 24

16 24 28 21 36 40

DIRECTIONS: Write the first five multiples of the given numbers. GIVEN NUMBER

2 4 5 7 8 9

FIRST FIVE MULTIPLES

2, 4, 6, 8, 10 4, 8, 12, 16, 20 5, 10, 15, 20, 25 7, 14, 21, 28, 35 8, 16, 24, 32, 40 9, 18, 27, 36, 45 COPYING IS STRICTLY PROHIBITED BY LAW

138

DIRECTIONS: Circle all the numbers that are multiples of the given numbers. GIVEN NUMBER

3 10 12 13 14 15

4 20 24 23 30 30

6 25 38 26 54 48

9 30 49 39 66 65

13 40 60 51 70 75

DIRECTIONS: Write the first five multiples of the given numbers. GIVEN NUMBER

3 6 10 11 17 18 139

FIRST FIVE MULTIPLES

6, 9, 12, 15, 18 12, 18, 24, 30, 36 20, 30, 40, 50, 60 22, 33, 44, 55, 66 34, 51, 68, 85, 102 36, 54, 72, 90, 108 MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

15 85 74 76 98 95

1 Select all the numbers that are multiples of 11. 11

2 Which of these numbers is a multiple of 7? 22

3 Which of these numbers is a multiple of 3?

4 Which of these sets of numbers show only multiples of 4? 20, 24, 33, 45

35, 40, 50, 55

80, 96, 100, 108

115, 120, 124, 140

5 Which of these sets of numbers show only multiples of 8? 4, 10, 14, 18

8, 16, 30, 44

8, 12, 32, 42

16, 32, 48, 64

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140

all the numbers that are multiples of the DIRECTIONS: Circle given numbers. GIVEN NUMBER

16 19 21 22 23 24

30 38 44 44 46 40

48 58 63 68 69 74

62 76 84 90 90 96

82 96 105 110 116 120

DIRECTIONS: Write the first five multiples of the given numbers. GIVEN NUMBER

25 26 27 28 29 30 141

FIRST FIVE MULTIPLES

50, 75, 100, 125, 150 52, 78, 104, 130, 156 54, 81, 108, 135, 162 56, 84, 112, 140, 168 58, 87, 116, 145, 174 60, 90, 120, 150, 180

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96 114 128 132 136 146

1 Which of these numbers is a multiple of 6? 26

2 Which of these numbers is a multiple of 8? 46

3 Which of these sets of numbers show only multiples of 5? 20, 24, 35, 49

35, 40, 50, 55

80, 98, 102, 110

31, 42, 53, 54

4 Which of these sets of numbers show only multiples of 4? 4, 8, 12, 16

8, 12, 17, 20

6, 12, 16, 24

4, 10, 12, 18

5 Select all the numbers that are multiples of 9. 6

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142

1 Which of these numbers is a multiple of 11? 44

2 Which of these numbers is a multiple of 6? 46

3 Which of these sets of numbers show only multiples of 3? 20, 24, 35, 49

35, 40, 50, 55

21, 30, 51, 63

115, 120, 124, 140

4 Which of these sets of numbers show only multiples of 9? 34, 8, 12, 16

28, 22, 17, 20

16, 12, 16, 24

18, 27, 45, 72

5 Select all the numbers that are multiples of 12. 36

143

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6 Select all the numbers that are multiples of 10. 20

7 Which of these numbers is a multiple of 5? 26

8 Which of these numbers is a multiple of 4?

9 Which of these sets of numbers show only multiples of 2? 20, 24, 36, 46

35, 40, 50, 55

82, 95, 100, 109

115, 120, 124, 140

10 Which of these sets of numbers show only multiples of 6? 4, 10, 14, 18

12, 18, 42, 54

8, 16, 30, 44

16, 32, 48, 64

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144

FINDING NUMERICAL PATTERNS MA.3.AR.3.3 Identify, create and extend numerical patterns. Use skip counting to identify and extend a numerical pattern.

Example: The first three terms in a numerical pattern are 3, 8, and 13. What is the 6th term in this numerical pattern? Step 1: Identify the rule of the numerical pattern.

1st term

2nd term

13, _____, _____, _____ 3rd term

4th term

5th term

6th term

The 2nd term is 5 more than the 1st term: 8 - 3 = 5. The 3rd term is 5 more than the 2nd term: 13 - 8 = 5.

Step 2: Extend the numerical pattern following the rule “Add 5.” +5

13,

18,

23,

1st term

2nd term

3rd term

4th term

5th term

6th term

Therefore, the 6th term in the numerical pattern is 28. Use a 100 chart to identify and extend a numerical pattern.

Example: The first three terms in a numerical pattern are 3, 8, and 13. What is the 6th term in this numerical pattern? The 2nd term is 5 more than the 1st term: 8 - 3 = 5. The 3rd term is 5 more than the 2nd term: 13 - 8 = 5.

Therefore, the 6th term in the numerical pattern is 28.

145

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DIRECTIONS: Identify the rule of each numerical pattern. PATTERN

RULE

Add 3 8, 11, 14, 17, 20 2, 4, 8, 16, 32, 64 Multiply by 2 76, 67, 58, 49, 40 Subtract 9 96, 48, 24, 12, 6, 3 Divide by 2 85, 80, 75, 70, 65, 60 Subtract 5 3, 16, 29, 42, 55, 68 Add 13 DIRECTIONS: Write the next three terms in each numerical pattern.

7 , 15 , 23 , 31 , 39 , 47 3 , 6 , 12 , 24 , 48 , 96 115 , 105 , 95 , 85 , 75 , 65 13 , 23 , 33 , 43 , 53 , 63 48 , 40 , 32 , 24 , 16 , 8 800 , 400 , 200 , 100 , 50 , 25 86 , 69 , 52 , 35 , 18 , 1 COPYING IS STRICTLY PROHIBITED BY LAW

146

DIRECTIONS: Identify the rule of each numerical pattern. PATTERN

7, 12, 17, 22, 27 1, 3, 9, 27, 81 96, 48, 24, 12, 6 81, 74, 67, 60, 53 13, 22, 31, 40, 49 42, 38, 34, 30, 26

RULE

Add 5 Multiply by 3 Divide by 2 Subtract 7 Add 9 Subtract 4

DIRECTIONS: Write the next three terms in each numerical pattern.

5 , 15 , 25 , 35 , 45 , 55 2 , 6 , 18 , 54 , 162 , 486 500 , 425 , 350 , 275 , 200 , 125 243 , 81 , 27 , 9 , 3 , 1 100 , 130 , 160 , 190 , 220 , 250 100 , 85 , 70 , 55 , 40 , 25 32 , 16 , 8 , 4 , 2 , 1 147

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1 Study the set of numbers below. 100, 110, 120, 130, 140 If the set of numbers follows a certain pattern, what is the value of the next term in the pattern? 152

155

150

300

2 Soren was mowing lawns to save money for a video game. He mowed 9 lawns on Thursday, 8 lawns on Friday, 7 lawns on Saturday, and 6 lawns on Sunday. If this pattern continues, how many lawns will he mow on Monday? 2 lawns

3 lawns

4 lawns

5 lawns

3 Sheryl started at 30 and skip counted by fives. Which of the following numbers could be a part of her pattern? 61

4 Charlotte generated a numerical pattern by multiplying the previous term by 2 to get the next term in the pattern. She started her numerical pattern at 4. Which of the following could be Charlotte’s numerical pattern? 4, 6, 8, 10, 12

4, 8, 10, 12, 14

4, 8, 12, 16, 20

4, 8, 16, 32, 64

5 The set of numbers below follows a certain pattern.

12, 24, 36, _____, 60 What is the fourth term in the pattern? 40

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148

DIRECTIONS: Identify the rule of each numerical pattern. PATTERN

RULE

4, 16, 64, 256, 1,024 Multiply by 4 Add 13 30, 43, 56, 69, 82 142, 125, 108, 91, 74 Subtract 17 Multiply by 4 3, 12, 48, 192, 768 Add 22 19, 41, 63, 85, 107 10,000, 1,000, 100, 10, 1 Divide by 10 DIRECTIONS: Write the next three terms in each numerical pattern.

18 , 26 , 34 , 42 , 50 , 58 70 , 58 , 46 , 34 , 22 , 10 480 , 240 , 120 , 60 , 30 , 15 8 , 16 , 32 , 64 , 128 , 256 4 , 28 , 52 , 76 , 100 , 124 555 , 534 , 513 , 492 , 471 , 450 288 , 144 , 72 , 36 , 18 , 9 149

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1 Study the set of numbers below. 7, 14, 28, 56, 112 If the set of numbers follows a certain pattern, what is the value of the sixth term in the pattern? 168

224

448

784

2 John started at 8 and skip counted by fours. Which of the following numbers could be a part of his number pattern? 14

3 Philip started a stamp collection. He bought 24 stamps last May, 30 stamps last June, 36 stamps last July, and 42 stamps last August. If this pattern continues, how many stamps will Philip buy in September? 44 stamps

46 stamps

48 stamps

50 stamps

4 Peter generated a numerical pattern by dividing the previous term by 2. He started his numerical pattern at 800. Which of the following could be Peter’s numerical pattern? 800, 798, 796, 794, 792

800, 750, 700, 650, 600

800, 600, 400, 200, 100

800, 400, 200, 100, 50

5 The set of numbers below follows a certain pattern.

236, 228, _____, 212, 204 What is the value of the missing term in the pattern? 214

216

220

224 COPYING IS STRICTLY PROHIBITED BY LAW

150

1 Jenny started saving some of her lunch money. She started by saving 2 dollars of her lunch money during week one. Then, she saved 3 dollars during week two, 4 dollars during week three, and 5 dollars during week four. If this pattern continues, how much money will she save by the end of week five? 6 dollars

10 dollars

12 dollars

20 dollars

2 Study the set of numbers below. 729, 243, 81, 27, 9 If the set of numbers follows a certain pattern, what is the value of the next term in the pattern? 1

3 Diana started at 75 and skip counted by tens. Which of the following numbers would not be a part of her number pattern? 80

105

4 Clark generated a numerical pattern by dividing the previous term by 2. He started his numerical pattern at 64. Which of the following could be Clark’s numerical pattern? 64, 62, 60, 58, 56

64, 32, 16, 8, 4

64, 32, 16, 14, 7

64, 34, 32, 30, 15

5 The set of numbers below follows a certain pattern.

142, 136, _____, 124, 118 What is the value of the missing term in the pattern?

151

134

132

133

130 MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

6 Study the set of numbers below. 425, 430, 435, 440, 445 If the set of numbers follows a certain pattern, what is the value of the next term in the pattern? 450

455

460

465

7 Sam was shoveling snow to save money for a video game. He shoveled 7 driveways on Thursday, 6 on Friday, 5 on Saturday, and 4 on Sunday. If this pattern continues, how many driveways will he shovel on Monday? 2 driveways

3 driveways

4 driveways

5 driveways

8 Chloe started at 57 and skip counted by sevens. Which of the following numbers could be a part of her number pattern? 14

9 Becky generated a numerical pattern by multiplying the previous term by 3 to get the next term in the pattern. She started her numerical pattern at 2. Which of the following could be Becky’s numerical pattern? 2, 6, 8, 10, 12

2, 6, 18, 19, 22

2, 6, 18, 54, 162

2, 6, 10, 14, 18

10 The set of numbers below follows a certain pattern.

13, 26, 39, _____, 65 What is the fourth term in the pattern? 40

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152

USING MEASURING TOOLS MA.3.M.1.1 Select and use appropriate tools to measure the length of an object, the volume of liquid within a beaker and temperature. Pick the appropriate tool when taking measurements, such as the length of an object, the amount of liquid in a container, or temperature.

When measuring LENGTH

VOLUME

TEMPERATURE

RULER FLASK

BEAKER MEASURING

YARDSTICK OR

THERMOMETER TEST TUBE

Use a ruler, measuring tape, yardstick, or a meter stick to measure the length of an object. To measure the length of an object, place one end of the object on the 0 mark, then read the number on the other end of the object. Make sure one end is on the 0 mark.

Read the number on the other end.

The ruler is 8 inches long. Use a beaker, flask, or test tube to measure the volume of liquids.

Use a thermometer when measuring temperatures.

To measure the volume of liquids, read the number where the top of the liquid reaches.

To measure temperature, read the number where the liquid inside the thermometer reaches.

Read the number where the top of the liquid reaches.

The liquid is 6 fluid ounces. 153

The temperature is 75° F.

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DIRECTIONS: Determine the lengths of the pencils.

LENGTH:

5 inches

LENGTH:

11 inches

LENGTH:

6 inches

LENGTH:

10 inches

DIRECTIONS: Determine the volumes of the liquids.

VOLUME: 50 mL

VOLUME: 20 mL

VOLUME: 90 mL

VOLUME: 60 mL

DIRECTIONS: Determine the temperatures.

TEMPERATURE:

35° F

55° F

95° F

40° F

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154

DIRECTIONS: Determine the lengths of the paintbrushes.

LENGTH:

16 centimeters

LENGTH: 28

centimeters

LENGTH: 20

centimeters

LENGTH: 25

centimeters

DIRECTIONS: Determine the volumes of the liquids.

VOLUME: 3 cups

VOLUME: 4 cups

VOLUME: 4 2 cups

VOLUME: 1 2 cups

DIRECTIONS: Determine the temperatures.

TEMPERATURE:

70° C

80° C

60° C

30° C

155

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1 Peter’s experiment requires him to fill the graduated cylinder with water up to the line across the cylinder. What volume of water should he pour? 250 milliliters 230 milliliters 300 milliliters 320 milliliters

2 Gulliver wants to measure his favorite toothbrush. What is the length of his toothbrush? 9.5 centimeters

9 centimeters

10 centimeters

10.2 centimeters

3 What is the temperature in degrees Fahrenheit of a room after turning on the air conditioner to the nearest degree? 65 degrees Fahrenheit 69 degrees Fahrenheit 71 degrees Fahrenheit 72 degrees Fahrenheit

4 Albert weighed himself in the morning. What is Albert’s weight to the nearest kg? 81 kg

79 kg

90 kg

80 kg

5 Henry wants to measure the diameter of a cooking pot he used to make a recipe. Which of these tools should he use? yardstick

ruler

graduated cylinder

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thermometer 156

DIRECTIONS: Determine the lengths of the objects.

LENGTH:

4 inches

LENGTH: 20

centimeters

LENGTH:

8 inches

LENGTH:

16 centimeters

DIRECTIONS: Determine the volumes of the liquids.

VOLUME: 3 mL

VOLUME: 8 mL

VOLUME: 3 4 cups

VOLUME: 4 4 cups

DIRECTIONS: Determine the temperatures.

TEMPERATURE:

45° F

25° C

85° F

10° C

157

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1 Max wants to measure the milk he needs for his cookie recipe. Which of these tools should he use? yardstick

ruler

graduated cylinder

thermometer

2 Find the measurement of the pencil to the nearest inch. 4 inches

3 inches

5 inches

6 inches

3 Find the measurement of the candy cane to the nearest half inch. 2 and a half inches 3 inches

3 and a half inches 4 inches

4 Find the measurement of the picture of the cookie to the nearest half centimeter. 2 centimeters 3.2 centimeters 3 centimeters 3.5 centimeters

5 The temperature of a winter day in a city is shown on the thermometer. What is the temperature in Celsius to the nearest degree? 70 degrees Celsius

25 degrees Celsius 20 degrees Celsius 30 degrees Celsius COPYING IS STRICTLY PROHIBITED BY LAW

158

1 Spence wants to measure the temperature of a frozen dessert he got from the grocery store. Which of these tools should he use? yardstick

ruler

graduated cylinder

thermometer

2 Find measurement of the pencil to the nearest half inch. 4.5 inches

3.5 inches

2.5 inches

1.5 inches

3 Find the measurement of the candy cane to the nearest inch. 3 and a half inches 4 inches

4 and a half inches 5 inches

4 Find the measurement of the picture of the orange to the nearest half centimeter. 2 centimeters 3.2 centimeters 3 centimeters 3.5 centimeters

5 The temperature of a hot day in a city is shown on the thermometer below. What is the temperature shown to the nearest degree Celsius? 40 degrees Celsius

25 degrees Celsius 20 degrees Celsius 30 degrees Celsius 159

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6 Bruce wants to use this exact amount of sauce for his dish as shown in the image below. What is the volume of the sauce shown in the graduated cylinder? 230 milliliters 650 milliliters 900 milliliters 160 milliliters

7 Bella wants to measure the length of the toothbrush head. What is the length of her toothbrush head in the picture shown?

1 centimeter

6 centimeters

5 centimeters

5.5 centimeters

8 Melvin measured the temperature of a piece of placed out in the sun. What is the temperature of the metal in degrees Fahrenheit? 95 degrees Fahrenheit 98 degrees Fahrenheit 100 degrees Fahrenheit 104 degrees Fahrenheit

9 What is the weight of the apple to nearest 100 grams if the scale has markings at each 100 grams? 80 grams

50 grams

100 grams

150 grams

10 Frank wants to measure the width of a fence door of a farm. Which of these tools should he use? yardstick

ruler

graduated cylinder

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thermometer 160

SOLVING REAL-WORLD PROBLEMS MA.3.M.1.2 Solve real-world problems involving any of the four operations with whole-number lengths, masses, weights, temperatures or liquid volumes. Solving real-world problems involving any of four operations with whole-number lengths, masses, weights, temperatures, or liquid volumes is the same as solving problems that involve whole numbers. Follow these steps for a better understanding of the question.

Example: Peter had 4 ropes, each 3 feet long. If Peter connected the 4 ropes end to end, what is the length of the resulting rope?

STEP 1

Identify the necessary information. Circle the givens in the problem and underline what needs to be figured out.

Peter had 4 ropes, each 3 feet long. If Peter connected the 4 ropes end-to-end, what is the length of the resulting rope? ADDITON: in all, sum, altogether, combined, plus, increased by, more than, added to, totaled

STEP 2

SUBTRACTION: less, fewer, left, minus, difference, take away, deduct, remaining, decreased by

Identify keywords in the question. Identifying keywords can help you figure out what to do.

MULTIPLICATION: product, times, of, multiplied by, twice, double, triple, each, per DIVISION: quotient, divide, half, split, share, •

Strip diagram: 4 × 3 feet = 12 feet

STEP 3

Use models to visualize the situation given in the questions. You can use base-ten blocks, number • lines, or even draw out a picture.

3 feet

161

3 feet

1 rope

Number line: 1 rope

STEP 4

3 feet

9 10 11 12

Write your final answer. Be sure to Therefore, the length of the resulting rope is 12 feet. include the units.

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DIRECTIONS: Use models to solve each word problem. To make a mixed fruit juice, Beth mixed 3 cups of pineapple juice, 4 cups of apple juice, and 8 cups of water. How many cups of juice did Beth make?

3 + 4 + 8 = 15 cups

ANSWER:

15 cups

Pineapple

Apple

Water

3 cups

4 cups

8 cups

The temperature at noon was 16° Fahrenheit in the winter. If the temperature dropped by 6° Fahrenheit in the evening, what is the new temperature?

16° F - 6° F = 10° F

ANSWER:

Evening temperature

6° F

10° F

16° F A carpenter has a piece of wood that is 24 feet long. If the carpenter cuts the wood into 3 pieces of equal length, what is the length of each piece?

24 ÷ 3 = 8 feet ANSWER: 8 feet

8 feet

24 feet A bag contains 8 marbles. If each marble has a mass of 9 grams, what is the total mass of the marbles in the bag?

8 × 9 grams = 72 grams ANSWER: 9 g

9 g

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72 grams 162

DIRECTIONS: Use models to solve each word problem.

To make a fruit salad for 40 people, Isaac mixed 3 kg of strawberries, 2 kg of apples, 2 kg of bananas, and 1kg of pineapples. What is the total weight of the fruit salad?

3 + 2 + 2 + 1 = 8kg 1kg pineapples

2 kg apples

ANSWER:

2 kg bananas

3 kg strawberries

8 kilograms

The tennis club had 2,900 tennis balls. During the season, 380 tennis balls were lost. How many balls are left at the end of the season?

2,900 - 380 = 2520 balls

ANSWER:

Remaining balls

380 balls

2,520 balls

2,520 balls Samantha wants to share 620g of peanuts among her 4 children equally. How much does each child get?

620 ÷ 4 = 155g ANSWER: 155g

155g

155 grams

620g 9 students brought 3m of wood with them to their woodshop class for a project. How much wood was brought in all?

9 × 3 = 27 meters ANSWER: 3m

163

27 meters

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1 Tim donated two boxes of goods to charity. The first box had a mass of 9 kilograms. The second box had a mass of 5 kilograms. What is the combined mass of the two boxes? 5 kilograms

9 kilograms

14 kilograms

20 kilograms

2 Roberta used 10 inches of red ribbon and 14 inches of pink ribbon to make a flower. How much ribbon did Roberta use? 20 inches

24 inches

30 inches

40 inches

3 One batch of a pancake recipe calls for 3 cups of flour. If Zahra wants to make 4 batches of the pancake recipe for breakfast, how many cups of flour does she need? 6 cups

7 cups

8 cups

12 cups

4 The first delivery truck was carrying 4,318 pounds of packages, while the second truck was carrying 2,386 pounds of packages. How much heavier is the first truck than the second? 3,932 pounds

1,932 pounds

1,876 pounds

2,424 pounds

5 One cargo container was 72 inches tall, and the other cargo container was 96 inches tall. How tall will the cargo containers be if they are stacked on top of the other? 122 inches

168 inches

14 inches

154 inches

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164

DIRECTIONS: Use models to solve each word problem.

Josh has 15 candies, Alexis 9 candies, and Karen 24 candies. How many candies do Josh, Alexis and Karen have altogether?

15 + 9 + 24 = 48 candies 15 candies

9 candies

ANSWER:

24 candies

48 candies

Tom used 10 liters of gasoline today. If the car’s tank had 36 liters before he started driving, how much is left at the end of the day?

36 - 10 = 26 liters Remaining gasoline

ANSWER: 10 liters

26 liters

36 liters A painter needs 56 liters of paint to paint 8 rooms of a house. Each room will require the same amount of paint. How much paint is needed for each room?

56 ÷ 8 = 7 liters ANSWER: 7 liters 7 liters 7 liters 7 liters 7 liters 7 liters 7 liters

7 liters

56 liters Eggs are sold in packs of 6. If we buy 7 packs. How many eggs are in 7 packs?

6 × 7 grams = 42 eggs ANSWER: 6 eggs 6 eggs 6 eggs 6 eggs 6 eggs 6 eggs 6 eggs

165

42 eggs

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1 Arnold needs to put up a fence 36 meters long around his vegetable garden. He already has 20 meters of fencing in his garage. How many more meters of fencing does he need? 10 meters

12 meters

16 meters

20 meters

2 The elephant in the zoo consumes 3 gallons of water each day. How many gallons of water does the elephant consume in 5 days? 8 gallons

15 gallons

20 gallons

25 gallons

3 Daisy had a piece of ribbon 40 centimeters long. She cut the ribbon into 8 pieces of equal length. How long was each piece of ribbon? 5 centimeters

8 centimeters

32 centimeters

48 centimeters

4 This morning, John jogs 7 laps around the circular path in the park. If one lap around the circular path is equivalent to 10 yards, how far did John jog this morning? 17 yards

35 yards

70 yards

100 yards

5 Carl bought 8 quarts of apple juice from the store. He drank 2 quarts of apple juice this morning and 1 quart this afternoon. How many quarts of apple juice were left? 3 quarts

4 quarts

5 quarts

6 quarts

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166

1 Sam the Squirrel weighs 10 ounces. Peter the Rabbit is 24 ounces heavier than Sam the Squirrel. How much does Peter the Rabbit weigh? 10 ounces

14 ounces

24 ounces

34 ounces

2 Jake walked 8 yards from his house to the library and then walked another 6 yards to the museum. How far did Jake walk in all? 6 yards

8 yards

12 yards

14 yards

3 Gene filled a watering can with 24 pints of water. His watering can is empty after pouring 2 pints of water into each of his plants. How many plants did Gene water? 12 plants

13 plants

14 plants

15 plants

4 The kids at the summer camp consumed 24 gallons of water in 6 days. How many gallons of water did the kids consume in one day if they consumed the same amount each day? 2 gallons

5 gallons

4 gallons

12 gallons

5 Hank bought 800 ml of milk at the store. He drank 400 ml of milk this morning and 100 ml this afternoon. How many ml of milk were left?

167

200 ml

300 ml

500 ml

400 ml

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

6 Wayne is packing boxes of vegetables. The first box had a mass of 8 kilograms. The second box had a mass of 7 kilograms. What is the combined mass of the two boxes? 5 kilograms

9 kilograms

13 kilograms

15 kilograms

7 Agatha used 13 inches of green ribbon and 9 inches of violet ribbon for a craft project. How much ribbon did Agatha use? 22 inches

24 inches

30 inches

40 inches

8 One batch of the cupcake recipe calls for 5 cups of flour. If Maria wants to make 3 batches of the cupcake recipe for the bake sale, how many cups of flour does she need? 8 cups

15 cups

20 cups

12 cups

9 On Friday, Hank hauls 3,205 pounds of cement to a worksite in his truck. On Monday, he hauls 1,671 pounds of cement. How much more did he haul on Friday than Monday? 1,354 pounds

1,453 pounds

1,534 pounds

1,543 pounds

10 One cargo container was 66 inches tall, and the other cargo container was 89 inches tall. How tall will the cargo containers be if they are stacked on top of the other? 155 inches

174 inches

142 inches

152 inches

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168

TELLING AND WRITING TIME TO THE NEAREST MINUTE

MA.3.M.2.1 Using analog and digital clocks, tell and write time to the nearest minute using a.m. and p.m. Analog clocks are clocks that use hands to show hours and minutes. The short hand of the clock tells the hours, and the long hand of the clock tells the minutes.

Each number on an analog clock represents an interval of 5 minutes. So, 1 represents 5 minutes, 2 represents 10 minutes, 3 represents 15 minutes, etc.

Using both the short and long hands of an analog clock tells the time.

The short hand is pointing between 10 and 11, so the hours is 10. The long hand is pointing at 5, so the minutes is 25. Therefore, the time is 10:25.

Digital clocks use digital counters to tell time.

In the display of a digital clock, time is usually written in hours and minutes, separated by a colon. The first two digits tell the hours, and the last two digits tell the minutes. Hours

The first two digits show 08, which means the hours is 8. The last two digits show 35, which means the minutes is 35. Therefore, the time is 8:35 a.m. Minutes 169

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DIRECTIONS: Write the times shown on the analog clocks.

6:45

3:10

6:20

11:25

5:55

8:35

DIRECTIONS: Write the times shown on the digital clocks.

4:37 AM

11:28 PM

9:16 AM

3:09 PM

6:52 PM

1:20 AM

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170

DIRECTIONS: Write the times shown on the analog clocks.

171

11 05

3 45

8 35

2 30

6 20

7 25

5 25

12 25

8 55

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Eva goes to bed at night at the time shown on the clock. At what time does she go to bed? 8:25 P.M.

8:25 A.M.

8:30 A.M.

8:35 A.M.

2 What time is shown on the clock? 6:30

7:30

6:23

5:30

3 Ben came back home in the afternoon at the time shown on the clock below. At what time did Ben come back? 6:25 A.M.

4:15 P.M.

9:20 A.M.

3:45 P.M.

4 What is time shown on the clock?

8:15

7:00

12:00

3:40

5 Select all the times that the picture of the clock could be showing. 11:05 A.M.

10:25 A.M.

10:25 P.M.

11:05 P.M.

1:05 A.M.

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172

DIRECTIONS: Write the times shown on the analog clocks.

173

4 00

11 20

9 10

12 25

8 55

10 15

10 55

9 45

4 40

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 What time is shown on the clock? 2:30

1:30

12:30

11:30

2 Janine goes to her music class after school at the time shown on the clock below. At what time does she have her music class? 5:10 A.M.

5:15 P.M.

5:50 P.M.

5:20 A.M.

3 What is time shown on the clock? 8:15

7:10

3:35

3:40

4 Alina goes to school in the morning at the time shown on the clock below. At what time does Alina go to school? 9:15 A.M.

9:15 P.M.

3:45 A.M.

9:10 P.M.

5 Select all the times that the picture of the clock could be showing. 6:05 A.M.

1:30 A.M.

1:30 P.M.

6:05 P.M.

1:05 A.M. COPYING IS STRICTLY PROHIBITED BY LAW

174

1 What time is shown on the clock? 2:05

9:55

12:50

11:30

2 Marlin goes to his gym class at school at the time shown on the clock below. At what time does he have his gym class? 11:10 A.M.

11:15 P.M.

11:50 P.M.

11:20 A.M.

3 What is time shown on the clock? 8:15

7:10

7:40

8:35

4 Joana goes jogging in the afternoon at the time shown on the clock below. At what time does she go jogging? 3:15 A.M.

4:15 P.M.

4:45 A.M.

3:10 P.M.

5 Select all the times that the picture of the clock could be showing. 12:25 A.M.

1:30 A.M.

5:00 P.M.

12:25 P.M.

5:00 A.M. 175

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

6 Lexy goes to the park in the morning at the time shown on the clock. What time does she go to the park? 12:30 P.M.

8:25 A.M.

4:30 A.M.

6:00 A.M.

7 What time is shown on the clock? 9:15

9:45

2:45

2:15

8 John came back home in the afternoon at the time shown on the clock below. At what time did John come back? 1:10 A.M.

7:10 P.M.

7:35 A.M.

1:35 P.M.

9 What is time shown on the clock?

10:10

10:50

2:10

2:50

10 Select all the times that the picture of the clock could be showing. 8:25 A.M.

9:15 A.M.

3:45 P.M.

9:15 P.M.

3:45 A.M. COPYING IS STRICTLY PROHIBITED BY LAW

176

FINDING ELAPSED TIME MA.3.M.2.2 Solve one- and two-step real-world problems involving elapsed time. Use a number line that shows time to determine elapsed time. Jump from one point on the number line to the other point and calculate the time between these two points using addition or subtraction.

Example: Wendy watched TV from 6:20 p.m. to 8:00 p.m. How long did Wendy watch TV? 40 minutes 1 hour

6:00

6:20

6:40

7:00

7:20

7:40

8:00

8:20

8:40

Therefore, Wendy watched TV for 40 minutes + 1 hour = 1 hour and 40 minutes. The modeling on the number line can be done in many ways, too. 1 hour

40 minutes

6:00 6:20 6:40 7:00 7:20 7:40 Notice that in both cases, the answer is the same.

8:00

8:20

8:40

Wendy watched TV for 1 hour and 40 minutes. Elapsed time can also be determine by counting on clocks.

Example: Wendy watched TV from 6:20 p.m. to 8:00 p.m. How long did Wendy watch TV? There are 40 minutes from 6:20 p.m. to 7:00 p.m.

There is 1 hour from 7:00 p.m. to 8:00 p.m. Therefore, Wendy watched TV for 40 minutes + 1 hour = 1 hour and 40 minutes.

177

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DIRECTIONS: Determine the elapsed time.

ELAPSED TIME: 2 hours and 45 minutes

ELAPSED TIME:

50 minutes

ELAPSED TIME:

1 hour and 55 minutes

ELAPSED TIME:

1 hour and 40 minutes

DIRECTIONS: Solve each word problem. Amy worked on her math homework from 7:20 p.m. until 9:10 p.m. How long did Amy work on her math homework? ELAPSED TIME:

1 hour and 50 minutes

Robert stayed at the library from 3:15 p.m. until 6:20 p.m. How long did Robert stay at the library? ELAPSED TIME:

3 hours and 5 minutes

A farmer worked on his field from 8:30 a.m. until 1:25 p.m. How long did the farmer work on his field? ELAPSED TIME:

4 hours and 55 minutes COPYING IS STRICTLY PROHIBITED BY LAW

178

DIRECTIONS: Determine the elapsed time.

START

FINISH

ELAPSED TIME: 7 hours and 20 minutes

START

ELAPSED TIME:

START

ELAPSED TIME: 179

FINISH

1 hour and 5 minutes

FINISH

4 hours and 15 minutes

START

ELAPSED TIME:

FINISH

6 hours and 5 minutes

START

ELAPSED TIME:

FINISH

5 hours

START

ELAPSED TIME:

FINISH

1 hour and 5 minutes

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Fred went to a concert that ended at 10:20 p.m. If the concert lasted for 2 hours and 45 minutes, what time did it start? 7:35 pm

7:45 pm

8:45 pm

8:55 pm

2 Victor spent 3 hours and 30 minutes working on his art project. If he started working on his project at 1:55 p.m., what time did he finish? 5:25 pm

5:05 pm

4:45 pm

4:35 pm

3 Leo left his house at 4:45 p.m. and arrived at his destination at 5:20 p.m. How long did it take Leo arrive? 35 minutes

45 minutes

5 minutes

1 hour and 5 minutes

4 The digital clocks below show the times when Bernard started and finished a hike. How long did Bernard’s hike last? 1 hour and 5 minutes 1 hour and 35 minutes 2 hours and 5 minutes 2 hours and 25 minutes

5 The digital clock below shows the time Glen started mowing the lawn. If he spent 1 hour and 5 minutes mowing the lawn, what time did he finish? 4:35 pm

4:45 pm

5:25 pm

5:35 pm

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180

DIRECTIONS: Determine the elapsed time.

START

FINISH

ELAPSED TIME: 3 hours and 10 minutes

START

FINISH

ELAPSED TIME: 2 hours and 10 minutes

START

ELAPSED TIME: 181

FINISH

1 hour and 15 minutes

START

FINISH

ELAPSED TIME: 2 hours and 35 minutes

START

FINISH

ELAPSED TIME: 7 hours and 30 minutes

START

ELAPSED TIME:

FINISH

25 minutes

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 A car mechanic spent 55 minutes fixing a car’s battery. If the car mechanic started working on the car at 9:50 a.m., what time did the car mechanic finish? 8:05 am

8:55 am

10:45 am

11:05 am

2 Ben started eating breakfast at 7:50 a.m. and finished at 8:15 a.m. How long did it take him to eat his breakfast? 15 minutes

25 minutes

1 hour and 15 minutes

1 hour and 25 minutes

3 Olive took a nap for 2 hours and 45 minutes. The analog clock below shows the time she started her nap. What time did she wake up? 5:30

4:10

4:50

5:50

4 The analog clocks below show the start and end times of Kim’s recital. How long did Kim’s recital last? 35 minutes 55 minutes 1 hour and 35 minutes Start Time

End Time

1 hour and 55 minutes

5 Jane spent 3 hours and 25 minutes cleaning her room. The digital clock below shows the time the she finished cleaning. What time did she start cleaning her room? 7:25 am

7:35 am

7:45 am

7:55 am

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182

1 The analog clock below shows the time Ruby got back from the library. If she was gone for 2 hours and 50 minutes, what time did she leave for the library? 8:15

8:25

8:35

8:45

2 The analog clock below shows the time Jake got to the restaurant. If it took him 55 minutes to get to the restaurant, what time did he leave ? 4:45

2:55

5:45

5:55

3 The analog clocks below show the start and end times of Joel’s training. How long did Joel’s training last? 10 minutes 20 minutes 30 minutes 50 minutes

4 The digital clocks below show the times when Elias started and finished washing his car. How long did Elias take to wash his car? 45 minutes 55 minutes 1 hour and 5 minutes 1 hour and 15 minutes

5 Diana started eating dinner at 6:53 p.m. and finished at 7:12 p.m. How long did it take for her to eat her dinner?

183

19 minutes

12 minutes

1 hour and 12 minutes

1 hour and 19 minutes

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6 Michael went to watch a movie at the theater that ended at 10:40 p.m. If the movie lasted 2 hours and 30 minutes, what time did it start? 7:35 pm

7:45 pm

8:45 pm

8:10 pm

7 Logan spent 2 hours and 50 minutes working on a craft project. If he started working on his project at 2:40 p.m., what time did he finish? 5:25 pm

5:05 pm

5:30 pm

4:35 pm

8 Kevin left his house at 3:55 p.m., but did not arrive at his office until 4:35 p.m. How long did it take Kevin to get to his office? 35 minutes

40 minutes

5 minutes

1 hour and 10 minutes

9 A painter spent 49 minutes painting a room. If the painter started painting the room at 8:25 a.m., what time did the painter finish? 8:49 am

9:14 am

9:25 am

8:25 am

10 The digital clock below shows the time Frank started raking leaves in his lawn the lawn. If he spent 1 hour and 22 minutes raking leaves, what time did he finish? 5:52 pm

4:08 pm

4:25 pm

5:08 pm

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184

IDENTIFYING POINTS, LINES, AND LINE SEGMENTS MA.3.GR.1.1 Describe and draw points, lines, line segments, rays, intersecting lines, perpendicular lines and parallel lines. Identify these in two-dimensional figures. Recognize, describe, and draw representations of basic geometric terms (point, line, line segment, ray).

GEOMETRIC TERM

DESCRIPTION

EXAMPLE

Point

A point gives the exact location in space. It is usually drawn as a dot, but a point really has no size. Points are usually named by a capital letter.

Line

A line is a figure that is straight, has no thickness, and extends in both directions without ends.

Line segment

A line segment is the part of a line that connects two points. It is the shortest distance between the two points.

Ray

A ray is the part of a line that has one endpoint and extends forever in another direction.

Describe when pairs of lines are intersecting, perpendicular, or parallel.

185

GEOMETRIC TERM

DESCRIPTION

Intersecting line

Intersecting lines are lines that cross each other.

Perpendicular lines

Intersecting lines are lines that cross each other at a right angle.

Parallel lines

Intersecting lines are lines that do not cross each other.

EXAMPLE

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whether the figure is a point, a line, a line DIRECTIONS: Identify segment, or a ray.

Point

Ray

Line segment

Line

whether the pairs of lines are intersecting, DIRECTIONS: Identify perpendicular, or parallel.

FIGURE

INTERSECTING

PERPENDICULAR

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PARALLEL

186

whether the pairs of lines are intersecting, DIRECTIONS: Identify perpendicular, or parallel.

LINES

INTERSECTING

PERPENDICULAR

PARALLEL

AB and CD EF and IJ EF and GH CD and GH

AB and EF

AB and GH

187

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1 Which of the following shows a line?

2 Which of the following is a line segment?

3 Which of the following shows parallel lines?

4 Which of the following shows perpendicular lines?

5 Using the image below, select all of the true statements.

There is only 1 pair of parallel lines. There are 3 pairs of perpendicular lines. There are 2 right angles. There are 2 intersecting lines. There are 2 pairs of parallel lines. COPYING IS STRICTLY PROHIBITED BY LAW

188

whether the pairs of lines are intersecting, DIRECTIONS: Identify perpendicular, or parallel.

A G

J L

LINES

INTERSECTING

PERPENDICULAR

PARALLEL

CD and EF GH and IJ MN and GH AB and IJ

KL and MN

AB and GH

189

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1 Using the picture below, select all of the true statements.

There are only 3 points. There are 2 pairs of parallel lines. There are 4 pairs of intersecting lines. There are 2 pairs of intersecting lines. There are 2 right angles.

2 Which of the following shows a point?

3 Which of the following is a ray?

4 Which of the following shapes has only one pair of parallel sides? Square

Trapezium

Rectangle

Triangle

5 Which of the following shape has no parallel sides?

Rectangle

Rhombus

Kite

Triangle

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190

1 Which of the following is a line?

2 Which of the following is a not a line segment?

3 Which of the following shows parallel lines?

4 Which of the following shows perpendicular lines?

5 Using the image below, select all of the true statements.

There is only 1 pair of parallel lines. There is only 1 pair of perpendicular lines. There are 2 right angles. There is 1 intersecting line. There is 1 right angle. 191

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6 Using the picture below, select all of the true statements.

There are only 3 vertices. There are 2 pairs of parallel lines. There are 4 pairs of intersecting lines. There are 3 pairs of intersecting lines. There are two right angles.

7 Which of the following has at least 3 right angles?

8 Which of the following triangles has one pair of perpendicular lines? None

Right

Obtuse

Equilateral

9 Which of the following shapes has all equal sides but is not parallel? Square

Trapezium

Rectangle

Equilateral Triangle

10 Which of the following quadrilaterals has no parallel sides? Rectangle

Rhombus

Kite

Square

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192

IDENTIFYING AND DRAWING QUADRILATERALS

MA.3.GR.1.2 Identify and draw quadrilaterals based on their defining attributes. Quadrilaterals include parallelograms, rhombi, rectangles, squares and trapezoids. Recognize the basic characteristics of different types of quadrilaterals.

QUADRILATERAL Square

Rectangle

Parallelogram

Rhombus

Trapezoid

MAIN CHARACTERISTICS •

All sides are equal

•

All angles are square angles

•

Opposite sides are equal and parallel

•

All angles are square angles

•

Opposite sides are equal and parallel

•

Opposite angles are equal

•

All sides are equal

•

Opposite angles are equal

•

One pair of opposite sides are parallel

DRAWING

Keep in mind the quadrilateral fact family to establish relationships between shapes.

Trapezoid

Rhombus Square

Quadrilateral

Parallelogram

193

Rectangle

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DIRECTIONS: Use check marks to show the quadrilaterals that share the same characteristics.

CHARACTERISTIC

SQUARE

RECTANGLE

PARALLELOGRAM

RHOMBUS

TRAPEZOID

All sides are equal. Opposite sides are equal. Opposite sides are parallel. All angles are equal. All angles are right angles. Opposite angles are equal. Exactly one pair of parallel sides. Exactly two pairs of parallel sides. Exactly one pair of perpendicular sides. Exactly two pairs of perpendicular sides. COPYING IS STRICTLY PROHIBITED BY LAW

194

DIRECTIONS: Use check marks to show the quadrilaterals that share the same characteristics.

CHARACTERISTIC

195

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Identify the shape below.

Square

Parallelogram

Rectangle

Rhombus

2 Identify the shape below.

Parallelogram

Rhombus

Trapezoid

Square

3 Select all the attributes of a parallelogram. The opposite sides are parallel. The sides are perpendicular. All the sides are equal. The opposite sides are equal. There are no perpendicular lines.

4 Select the figure that is not a quadrilateral. Triangle

Parallelogram

Square

Rhombus

5 What is the name of a quadrilateral with only one pair of parallel sides? Parallelogram

Rectangle

Trapezoid

Square COPYING IS STRICTLY PROHIBITED BY LAW

196

DIRECTIONS: Use check marks to show the quadrilaterals that share the same characteristics.

CHARACTERISTIC

All sides are equal. Opposite sides are equal. Opposite sides are parallel.

All angles are equal. All angles are right angles. Opposite angles are equal. Exactly one pair of parallel sides. Exactly two pairs of parallel sides. Exactly one pair of perpendicular sides. Exactly two pairs of perpendicular sides. 197

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Select all the properties of a rectangle. There are 4 pairs of perpendicular lines. There are 2 pairs of parallel lines. All the sides are equal. 2 opposite sides are equal. There are 4 right angles.

2 Select the figure that is not a quadrilateral. Diamond

Parallelogram

Circle

Rhombus

3 Identify the shape below.

Square

Parallelogram

Rectangle

Rhombus

4 What is a quadrilateral with no pairs of parallel sides called? Parallelogram

Kite

Trapezoid

Square

5 Identify the shape below.

Parallelogram

Rhombus

Trapezoid

Square COPYING IS STRICTLY PROHIBITED BY LAW

198

1 Identify the shape below.

Square

Parallelogram

Rectangle

Rhombus

2 Identify the shape below.

Parallelogram

Diamond

Trapezoid

Square

3 Select all the attributes of a square. The opposite sides are parallel. The sides are perpendicular. All the sides are equal. The opposite sides are equal. There are no perpendicular lines.

4 Select the figure that is not a quadrilateral. Rectangle

Pentagon

Square

Rhombus

5 What is the name of a quadrilateral with no right angles?

199

Parallelogram

Rectangle

Trapezoid

Square MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

6 Select all the properties of a kite. Two pairs of adjacent sides are equal. There are no pairs of parallel lines. All the sides are equal. Two opposite sides are equal. There are no right angles.

7 Select the figure that is not a quadrilateral. Diamond

Parallelogram

Rhombus

Line

8 Identify the shape below.

Square

Parallelogram

Kite

Rhombus

9 What is the name of a quadrilateral with no right angles but two pairs of parallel sides? Square

Kite

Trapezoid

Diamond

10 Identify the shape below.

Parallelogram

Rhombus

Trapezoid

Square COPYING IS STRICTLY PROHIBITED BY LAW

200

DRAWING LINES OF SYMMETRY

MA.3.GR.1.3 Draw line(s) of symmetry in a two-dimensional figure and identify line-symmetric two-dimensional figures. A line of symmetry divides a figure into two equal halves that have the same shape and same size. You can fold the figure along the line of symmetry and each half will perfectly fit (all sides and vertices match). Example: Draw the line of symmetry of this rectangle.

If you draw a vertical line along the middle of the rectangle and fold it along the line, you can see that each half fits perfectly along the other half.

Similarly, if you draw a horizontal line along the middle of the rectangle and fold it along the line, you can see that each half also fits perfectly along the other half.

But if you draw a line along the diagonal of the rectangle and fold it along the line, you can see that each half does not fit perfectly along the other half (sides and vertices are not matched).

Therefore, the diagonal is not a line of symmetry of a rectangle. 201

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whether each figure has no, exactly 1, or DIRECTIONS: Determine more than 1 line of symmetry.

FIGURE

NO LINES OF SYMMETRY

EXACTLY ONE LINE OF SYMMETRY

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MORE THAN ONE LINE OF SYMMETRY

202

whether each figure has no, exactly 1, or DIRECTIONS: Determine more than 1 line of symmetry.

FIGURE

203

NO LINES OF SYMMETRY

EXACTLY ONE LINE OF SYMMETRY

MORE THAN ONE LINE OF SYMMETRY

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 How many lines of symmetry does a square have?

2 Which of the following figures has only 2 lines of symmetry? Rhombus

Parallelogram

Square

Trapezoid

3 How many lines of symmetry does an equilateral triangle have?

4 Select the figures that have at least 1 line of symmetry.

5 Which of the figures below have no lines of symmetry?

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204

DIRECTIONS: Determine whether each figure has no, exactly 1, or more than 1 line of symmetry.

FIGURE

205

NO LINES OF SYMMETRY

EXACTLY ONE LINE OF SYMMETRY

MORE THAN ONE LINE OF SYMMETRY

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Select the answer choices with the correct number of lines of symmetry labeled. - 3

- 2

- 1

- 2

- 1

2 How many lines of symmetry does a trapezoid have?

3 Which of the following figures has exactly 4 lines of symmetry?

Rhombus

Parallelogram

Square

Trapezoid

4 How many lines of symmetry does an isosceles triangle have?

5 Which of the figures below have exactly two lines of symmetry?

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206

1 How many lines of symmetry does a parallelogram have?

2 Which of the following figures has only 1 line of symmetry? Rhombus

Parallelogram

Square

Kite

3 How many lines of symmetry does a scalene triangle have?

4 Select the figures that have at least 4 lines of symmetry.

5 Which of the figures below have one line of symmetry?

207

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

6 Select the answer choices with the correct number of lines of symmetry labeled. - 2

- 3

- 4

- 2

- 0

7 How many lines of symmetry does a rhombus have?

8 Which of the following figures has an infinite number of lines of symmetry?

Rhombus

Parallelogram

Square

Circle

9 How many lines of symmetry does a right triangle have?

10 Which of the figures below have five lines of symmetry?

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208

EXPLORING AREA AS AN ATTRIBUTE OF TWO-DIMENSIONAL FIGURES

MA.3.GR.2.1 Explore area as an attribute of a two-dimensional figure by covering the figure with unit squares without gaps or overlaps. Find areas of rectangles by counting unit squares. Use partitioning to divide a rectangle into unit squares. The length of the rectangle tells you how many equal columns you should divide the rectangle, while the width tells you how many equal rows you should divide the rectangle. Count the number of squares the rectangle has to determine its area. Example: Find the area of this rectangle.

8 4 The length of the rectangle is 8. So, divide the rectangle into 8 equal columns. Indicates the number of columns

8 4

The width of the rectangle is 4. So, divide the rectangle into 4 equal rows.

Indicates the number of rows

To find the area of the rectangle, count the number of squares that make up the rectangle. Notice how the squares make up the entire rectangle, and there are no gaps or overlaps between the squares. 1

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Therefore, the area of the rectangle is 32 square units. 209

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each rectangle into unit squares to determine DIRECTIONS: Partition the areas.

10 4 Area:

40 square units

Area:

8 square units

5 8 3

Area:

15 square units

Area:

40 square units

DIRECTIONS: Determine the area of each rectangle.

5 in. 8 cm 2 in. Area:

3 cm 10 square inches

Area:

10 ft

4 ft Area:

24 square centimeters

3m 40 square feet

Area:

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18 square meters 210

each rectangle into unit squares to determine DIRECTIONS: Partition the areas.

9 5 Area:

45 square units

Area:

18 square units 7

16 square units

Area:

42 square units

DIRECTIONS: Determine the area of each rectangle.

10 cm 4 cm Area:

11 ft 5 ft

40 square centimeters

Area:

7 in. 4 in. Area: 211

55 square feet

28 square inches

Area:

54 square meters

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Find the area of the given rectangle. 9 square centimeters

20 square centimeters

18 square centimeters

15 square centimeters

2 Find the area of the given rectangle. 36 square meters

25 square meters

30 square meters

11 square meters

3 Find the area of the given rectangle. 9 square inches

6 square inches

12 square inches

15 square inches

4 Find the area of the given rectangle. 24 square feet

15 square feet

30 square feet

20 square feet

5 Find the area of the given rectangle.

20 square centimeters

24 square centimeters

28 square centimeters

30 square centimeters

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212

DIRECTIONS: Partition each rectangle into unit squares to determine the areas.

5 Area:

35 square units

20 square units

Area:

15 square units

Area:

96 square units

DIRECTIONS: Determine the area of each rectangle.

7m 3m Area:

13 cm 4 cm

21 square meters

Area:

9 ft

15 in. 7 ft

8 in. Area: 213

52 square centimeters

120 square inches

Area:

63 square feet

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Find the area of the given rectangle. 8 square meters

16 square meters

12 square meters

18 square meters

2 Find the area of the given rectangle. 12 square centimeters

32 square centimeters

24 square centimeters

16 square centimeters

3 Find the area of the given rectangle. 8 square inches

14 square inches

12 square inches

15 square inches

4 Find the area of the given rectangle. 22 square feet

10 square feet

12 square feet

25 square feet

5 Find the area of the given rectangle. 20 square meters

15 square meters

28 square meters

30 square meters

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214

1 Find the area of the given rectangle. 9 square centimeters

20 square centimeters

18 square centimeters

15 square centimeters

2 Find the area of the given rectangle. 36 square meters

14 square meters

30 square meters

11 square meters

3 Find the area of the given rectangle. 28 square inches

36 square inches

42 square inches

25 square inches

4 Find the area of the given rectangle. 24 square feet

15 square feet

25 square feet

20 square feet

5 Find the area of the given rectangle.

215

5 square meters

3 square meters

4 square meters

5 square meters

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6 Find the area of the given rectangle. 4 square meters

6 square meters

2 square meters

8 square meters

7 Find the area of the given rectangle. 12 square feet

32 square feet

24 square feet

30 square feet

8 Find the area of the given rectangle. 14 square inches

21 square inches

12 square inches

30 square inches

9 Find the area of the given rectangle. 5 square meters

6 square meters

3 square meters

4 square meters

10 Find the area of the given rectangle. 36 square meters

12 square meters

24 square meters

18 square meters

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216

DETERMINING THE AREA OF A RECTANGLE MA.3.GR.2.2 Find the area of a rectangle with whole-number side lengths using a visual model and a multiplication formula. To find the area of a rectangle, partition it into unit squares by dividing the rectangles into equal columns and rows. The dimensions of the rectangle indicate how many columns and how many rows the rectangle must be divided. Then, count the number of unit squares to get the area. Example: Find the area of this rectangle.

Partitioning the rectangle into unit squares,

Indicates the number of rows

Indicates the number of columns

To find the area of the rectangle, count the number of unit squares the rectangle was divided. 1

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Therefore, the area of the rectangle is 32 square units. Use multiplication formula to find the area of a rectangle. Partitioning a rectangle into unit squares is the same as making an array model of multiplication.

8 8 columns of 4’s = 8 × 4 = 32 or 4 rows of 8’s = 4 × 8 = 32.

4 Therefore, the area of a rectangle is the product of its dimensions, or

Area = length × width 217

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the areas of these rectangles. DIRECTIONS: Find (Note: The rectangles are not drawn to scale.)

7 cm

8 in. 6 cm

3 in. Area:

24 square inches

Area:

42 square centimeters

11 m 9 ft 8m

8 ft Area:

72 square feet

Area:

6 cm

7 in. 6 cm

4 in.

Area:

28 square inches

Area:

3 ft

36 square centimeters

5 ft

Area:

88 square meters

15 square feet

Area:

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56 square meters 218

DIRECTIONS: Find the areas of these rectangles. (Note: The rectangles are not drawn to scale.)

5 ft

12 cm 3 ft

5 cm Area:

60 square centimeters

Area:

15 square feet 8m

8 in. 20 m

3 in.

Area:

24 square inches

Area:

9 cm

15 in. 5 cm

5 in.

Area:

75 square inches

Area:

9 ft

219

45 square centimeters 11 ft

Area:

160 square meters

63 square meters

Area:

99 square feet

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Find the area of the rectangle given below. 9 cm 12 cm

144 square centimeters

108 square centimeters

81 square centimeters

120 square centimeters

2 Find the area of the square given below.

11 m

111 square meters

110 square meters

121 square meters

101 square meters

3 Find the area of a rectangle with a length of 12 inches and a width of 6 inches. 18 square inches

60 square inches

76 square inches

72 square inches

4 Find the area of a rectangle with a length of 10 feet and a width of 7 feet. 70 square feet

100 square feet

49 square feet

77 square feet

5 Find the area of a square with a side of 8 inches. 80 square inches

64 square inches

66 square inches

16 square inches COPYING IS STRICTLY PROHIBITED BY LAW

220

the areas of these rectangles. DIRECTIONS: Find (Note: The rectangles are not drawn to scale.)

13 m

12 ft 7m

11 ft Area:

132 square feet

Area:

16 in.

9 cm 6 cm Area:

4 in.

54 square centimeters

Area:

5 cm

40 square meters

Area:

9 in.

20 in.

Area: 221

64 square inches 7 cm

Area:

91 square meters

35 square centimeters 12 ft

12 ft

180 square inches

Area:

144 square feet

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

1 Find the area of a square with a side of 12 feet. 122 square feet

120 square feet

144 square feet

146 square feet

2 Find the area of a rectangle with a length of 13 feet and a width of 8 feet. 79 square feet

117 square feet

104 square feet

65 square feet

3 Find the area of a rectangle with a length of 8 inches and a width of 7 inches. 48 square inches

56 square inches

66 square inches

76 square inches

4 Find the area of the square given below.

15 m

81 square meters

110 square meters

324 square meters

225 square meters

5 Find the area of the rectangle given below. 7 cm

12 cm

84 square centimeters

64 square centimeters

112 square centimeters

140 square centimeters

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222

1 Find the area of the rectangle given below. 4 cm 7 cm

14 square centimeters

24 square centimeters

28 square centimeters

11 square centimeters

2 Find the area of the square given below.

16 square meters

25 square meters

64 square meters

49 square meters

3 Find the area of a rectangle with a length of 16 inches and a width of 3 inches. 35 square inches

50 square inches

48 square inches

54 square inches

4 Find the area of a rectangle with a length of 14 feet and a width of 4 feet. 86 square feet

44 square feet

38 square feet

56 square feet

5 Find the area of a square with a side of 13 inches.

223

169 square inches

112 square inches

196 square inches

121 square inches

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6 Find the area of a square with a side of 5 feet. 34 square feet

25 square feet

28 square feet

16 square feet

7 Find the area of a rectangle with a length of 22 feet and a width of 3 feet. 74 square feet

50 square feet

92 square feet

66 square feet

8 Find the area of a rectangle with a length of 17 inches and a width of 5 inches. 21 square inches

96 square inches

85 square inches

46 square inches

9 Find the area of the square given below.

18 m

81 square meters

110 square meters

324 square meters

225 square meters

10 Find the area of the rectangle given below. 8 cm

19 cm

134 square centimeters

152 square centimeters

121 square centimeters

173 square centimeters

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224

SOLVING PROBLEMS INVOLVING AREA AND PERIMETER

MA.3.GR.2.3 Solve mathematical and real-world problems involving the perimeter and area of rectangles with whole-number side lengths using a visual model and a formula. When solving mathematical and real-world problems involving the perimeter and area of a rectangle, follow these steps for better understanding of the question.

Example: A rectangular garden is 9 feet long and 6 feet wide. Find the perimeter and area of the garden.

STEP 1

Identify the necessary information. Circle the givens in the problem and underline what needs to be figured out.

A rectangular garden is 9 feet long and 6 feet wide. Find the perimeter and area of the garden. 9 feet

STEP 2

If none is provided, draw a figure to represent the situation.

6 feet

Determine whether the problem is asking for the perimeter or the area. Perimeter refers to the boundary around the rectangle. Area refers to the space the rectangle occupies. Perimeter = 2 × (9 + 6) = 2 × 15 = 30 feet Use the formula to find the perimeter of the garden:

Area = 9 × 6 = 54 square feet

9 feet

Perimeter = 2 × (length + width) STEP 3

Partition the rectangle into unit squares, or use the formula to find the area:

6 feet

Area = length × width

STEP 4

225

Write your final answer. Do not forget to write the units.

Therefore, the perimeter of the garden is 30 feet and the area is 54 square feet.

MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

DIRECTIONS: Solve each word problem. A painter wants to put a frame around his painting. If his painting is 10 feet long and 7 feet wide, how many feet of frame does the painting need?

7 feet

10 feet

The amount of frame the painter needs equals the boundary of the painting, which is the perimeter. Perimeter = 2 × (10 + 7) = 2 × 17

ANSWER:

34 feet

The figure below shows the dimensions of a square window. What is the area of the window? 4 meters Since the window is a square, all sides are equal in length, meaning the length and width are equal.

ANSWER:

16 square m

Area = 4 × 4 = 16 square meters

A piece of construction paper is 12 inches long and 7 inches wide. What is the area of the construction paper? 12 inches

7 inches

The area of the construction paper is determined by multiplying the length times its width.

ANSWER:

84 square in.

Area = 12 × 7 = 84 square inches

A rectangular carpet is 6 meters long and 5 meters wide. If the carpet has a trimmings around its edges, what is the length of the trimmings?

5 meters

6 meters

The length of trimmings around the edges of the carpet equals the length of the boundary of the painting, which is the perimeter.

ANSWER:

22 meters

Perimeter = 2 × (6 + 5) = 2 × 11 COPYING IS STRICTLY PROHIBITED BY LAW

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DIRECTIONS: Solve each word problem. A piece of plywood was cut so that it is 8 feet long and 5 feet wide. What is the area of the piece of plywood? 8 feet

5 feet

The area of the plywood is determined by multiplying the length times its width. Area = 8 × 5 = 40 square feet

ANSWER:

40 square ft

Devin’s driveway is 10 meters long and 5 meters wide. What is the area of Devin’s driveway? 10 m

5 m

The area of the driveway is determined by multiplying the length times its width.

ANSWER:

50 square m

Area = 10 × 5 = 50 square meters

A flower garden is 7 feet long and 5 feet wide. The garden is surrounded on all sides by a fence. What is the length of the fence? 7 feet

5 feet

The fence marks the boundary of the garden, which is the perimeter of the garden. Perimeter = 2 × (7 + 5) = 2 × 12

ANSWER:

24 feet

Perimeter = 24 feet

Andrea’s lot is surrounded on all sides by a walkway. If the lot is 12 meters long and 8 meters wide, what is the entire length of the walkway?

5 meters

6 meters

The entire length of the walkway equals the boundary of the lot, which is the perimeter. Perimeter = 2 × (12 + 8) = 2 × 20

ANSWER:

40 meters

Perimeter = 40 meters 227

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1 Will is painting a wall in his bedroom. The height of the wall is 15 feet and the width is 9 feet. What is the area of the wall? 15 ft 9 ft

145 square feet

135 square feet

150 square feet

130 square feet

2 Nina is wrapping a gift box that is 14 inches long and 8 inches high. What is the perimeter of the gift box? 112 inches

40 inches

44 inches

22 inches

3 Mr. Tomas is fencing his garden. His garden is 25 feet long and 5 feet wide. Find the perimeter of the garden. 60 feet

30 feet

125 feet

50 feet

4 A wooden door has a height of 10 feet and a width of 2 feet. What is the area of the wooden door? 10 square feet

24 square feet

12 square feet

20 square feet

5 Mike is fixing tiles around a swimming pool shown below. What is the area of the pool? 12 m 15 m

150 square meters

180 square meters

120 square meters

175 square meters COPYING IS STRICTLY PROHIBITED BY LAW

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DIRECTIONS: Solve each word problem. The figure below shows the dimensions of a square stained glass. How much framing materials are needed to put a frame around the stained glass?

6 feet

The amount of frame needed equals the boundary of the stained glass, which is the perimeter. Since the window is a square, all sides are equal in length.

ANSWER:

24 feet

Perimeter = 4 × 6 = 24 feet

A blackboard is surrounded on all sides by a wooden frame. What is the entire length of the frame if the blackboard is 8 meters long and 4 meters wide?

4 meters

8 meters

The length of frame equals the boundary of the blackboard, which is the perimeter.

Perimeter = 2 × (8 + 4) = 2 × 12

ANSWER:

24 meters

Perimeter = 24 meters

A rectangular a lot is 9 meters long and 5 meters wide. What is the area of the lot?

5 m

9 m

The area of the lot is determined by multiplying the length times its width. Area = 9 × 5 = 45 square meters

ANSWER:

45 square m

9 inches

The figure below shows the dimensions of a square porch tile. What is the area of the porch tile?

229

The tile is a square. All sides are equal in length, meaning the length and width are equal. Area = 9 × 9 = 81 square inches

ANSWER:

81 square in.

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1 Phil is cutting out a rectangular shape from a sheet of paper that has a length of 10 cm and a width of 6 cm. What is the area of the shape? 60 square centimeters

16 square centimeters

32 square centimeters

30 square centimeters

2 Molly is cutting wood to make a door. The height of the required door is 7 feet and the width is 4 feet. What is the area of the door? 35 square feet

14 square feet

28 square feet

56 square feet

3 Tony’s house has a doormat that is 15 inches long and 12 inches wide. What is the perimeter of the doormat? 24 inches

54 inches

30 inches

27 inches

4 Mr. Lang is fencing his farm. His farm is 32 feet long and 25 feet wide. Find the perimeter of the farm. 123 feet

162 feet

114 feet

185 feet

5 A large painting is hanging on a wall. It has a height of 8 feet and a width of 5 feet. What is the area of the painting? 26 square feet

13 square feet

18 square feet

40 square feet

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1 Kelly is building a wall of a house. The height of the wall is 11 feet and the width is 13 feet. What is the area of the wall? 15 ft 9 ft

143 square feet

165 square feet

120 square feet

150 square feet

2 Cory has a piece of cloth that is 9 inches long and 12 inches high. What is the perimeter of the piece? 63 inches

30 inches

57 inches

42 inches

3 Eddie is fencing in his vegetable garden. His garden is 23 feet long and 19 feet wide. Find the perimeter of the garden. 24 feet

39 feet

84 feet

52 feet

4 A wooden door has a height of 12 feet and a width of 3 feet. What is the area of the wooden door? 15 square feet

36 square feet

20 square feet

42 square feet

5 Mike is fixing tiles around a swimming pool as shown below. What is the perimeter of the pool? 10 m 6m

231

12 meters

20 meters

8 meters

32 meters MATH BOOTCAMP® SMART TO THE CORE | EDUCATIONAL BOOTCAMP, INC.

6 Derek drew a rectangle that had a height of 14 cm and a width of 11 cm. What is the area of the rectangle he drew? 124 square centimeters

134 square centimeters

184 square centimeters

154 square centimeters

7 Rodolfo is cutting cardboard. He needs to cut a piece that is 4 feet in height and 2 feet in width. What is the area of the cardboard piece he needs? 8 square feet

10 square feet

4 square feet

24 square feet

8 Jerry’s house has a framed picture that is 13 inches long and 15 inches wide. What is the area of the framed picture? 125 square inches

176 square inches

195 square inches

116 square inches

9 Jared is putting up a fence around his backyard. His backyard is 20 feet long and 14 feet wide. Find the perimeter of the yard. 94 feet

68 feet

56 feet

37 feet

10 A large mural is on display on a wall in the park. The height of the mural is 6 feet and the width is 7 feet. What is the area of the mural? 42 square feet

25 square feet

36 square feet

32 square feet

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FINDING PERIMETER AND AREA OF COMPOSITE FIGURES MA.3.GR.2.4 Solve mathematical and real-world problems involving the perimeter and area of composite figures composed of non-overlapping rectangles with whole-number side lengths. To find the perimeter of a composite figure, add the lengths of all sides. Be aware that the lengths of all the sides are not always given but can be derived based on the lengths of the other sides.

Example: Find the perimeter of the figure. Notice that the dimension of the bottom side is not given. We can find this length using the lengths of the top side and middle horizontal side. Since the top side is 8 and the middle horizontal side is 4, then the bottom side is 8 - 4 = 4 units.

To find the area of a composite figure, decompose the figure into two or more rectangles. Then, find the areas of these smaller rectangles and add the areas to find the total area of the figure. Be aware that the lengths of all the sides are not always given but can be derived based on the lengths of the other sides.

Example: Find the perimeter of the figure. Notice that the dimensions of the bottom side is not given. We can find this length using the lengths of the top side and middle horizontal side. Since the top side is 8 and the middle horizontal side is 4, then the bottom side is 8 - 4 = 4 units. We can then decompose this figure into two rectangles. One rectangle has an area of 6 × 4 = 24 square units, and the other rectangle has an area of 4 × 3 = 12 square units. Therefore, the area of the figure is the following: 24 + 12 = 36 square units. 233

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DIRECTIONS: Find the perimeters of these composite figures.

Perimeter:

28 units

Perimeter:

18 units

Perimeter:

42 units

Perimeter:

18 units

DIRECTIONS: Find the areas of these composite figures.

Area:

28 square units

Area:

8 square units

Area:

90 square units

Area:

16 square units

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234

DIRECTIONS: Find the perimeters of these composite figures.

Perimeter:

26 inches

Perimeter:

38 feet

Perimeter:

26 cm

3m 2m

Perimeter:

26 meters

DIRECTIONS: Find the areas of these composite figures.

235

Area:

36 square inches

Area:

22 square feet

Area:

28 square meters

Area:

28 square cm

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1 Sylvia cuts a piece of wrapping paper in the shape and size shown below. What is the area of the shape that that Sylvia cuts? 3 in.

9 in.

3 in. 7 in.

22 square inches

24 square inches

30 square inches

48 square inches

2 The shape and dimensions of Ahmed’s basement floor are shown below. What is the perimeter of Ahmed’s basement floor? 5m

60 meters

57 meters

48 meters

35 meters

8m 2m

3 The shape and dimensions of Ahmed’s basement floor are shown below. What is the area of Ahmed’s basement floor? 5m

60 square meters

57 square meters

48 square meters

34 square meters

8m 2m

4 The shape and dimensions of the club’s logo are shown below. What is the perimeter of club’s logo? 2 cm

2 cm 3 cm

30 centimeters

38 centimeters

42 centimeters

48 centimeters

8 cm

5 The shape and dimensions of the club’s logo are shown below. What is the area of club’s logo? 2 cm

2 cm 3 cm

8 cm

30 centimeters2

38 centimeters2

42 centimeters2

48 centimeters2

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236

DIRECTIONS: Find the perimeters of these composite figures.

Perimeter:

26 inches

Perimeter:

32 meters

Perimeter:

26 feet

Perimeter:

32 cm

DIRECTIONS: Find the areas of these composite figures.

Area:

28 square inches

Area:

64 square feet

Area:

24 square cm

3m 2m

Area: 237

30 square meters

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1 The shape and dimensions of a parking lot are shown below. What is the perimeter of the parking lot? 7m

36 meters

48 meters

67 meters

81 meters

9m 2m 9m

2 The shape and dimensions of a parking lot are shown below. What is the area of the parking lot? 7m

9m 2m

36 square meters

48 square meters

67 square meters

81 square meters

3 The shape and dimensions of the proposed city park are shown below. What is the perimeter of the proposed city park? 5 yd 6 yd 10 yd 2 yd 2 yd

34 yards

40 yards

46 yards

54 yards

4 The shape and dimensions of the proposed city park are shown below. What is the area of the proposed city park? 5 yd 6 yd 10 yd 2 yd 2 yd

34 square yards

40 square yards

46 square yards

54 square yards

5 The area of the figure below is 48 square feet. What is the length of the missing side of the figure? 2 ft 4 ft

4 ft ?

8 feet

9 feet

10 feet

12 feet

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238

1 The area of the figure below is 27 square inches. What is the length of the missing side of the figure? ?

2 in.

6 inches

7 inches

8 inches

9 inches

5 in. 3 in.

2 The area of the figure below is 46 square yards. What is the length of the missing side of the figure? ? 5 yd

9 yd

1 yards

2 yards

3 yards

4 yards

4 yd

3 The area of the figure below is 58 square meters. What is the length of the missing side of the figure? 10 m ? 3m 6m

4 meters

5 meters

6 meters

8 meters

4 The area of the figure below is 62 square centimeters. What is the length of the missing side of the figure? 6 cm 5 cm 4 cm

8 centimeters

9 centimeters

10 centimeters

12 centimeters

The shape and dimensions of a building are shown below. What is the perimeter of the building? 5m

8m 2m 8m

239

30 meters

32 meters

67 meters

81 meters

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6 The area of the figure below is 34 square inches. What is the length of the missing side of the figure? ?

3 in. 2 in.

4 inches

6 inches

5 inches

7 inches

7 in.

7 The perimeter of the figure below is 34 yards. What is the length of the missing side of the figure? 3 yd 2 yd 4 yd 3 yd

5 yards

10 yards

8 yards

12 yards

8 The perimeter of the figure below is 18 meters. What is the length of the missing side of the figure? 3 m 2m

3m ?

1 meter

4 meters

2 meters

5 meters

9 The area of the figure below is 12 square centimeters. What is the length of the missing side of the figure? 6 cm

? 1 cm

3 centimeters

4 centimeters

5 centimeters

6 centimeters

7 cm

10 The area of the figure below is 33 square meters. What is the length of the missing side of the figure? 3m 3m 3m

6 meters

8 meters

9 meters

12 meters

? COPYING IS STRICTLY PROHIBITED BY LAW

240

COLLECTING AND REPRESENTING DATA MA.3.DP.1.2 Interpret data with whole-number values represented with tables, scaled pictographs, circle graphs, scaled bar graphs or line plots by solving one– and two-step problems. MA.3.DP.1.1 Collect and represent numerical and categorical data with whole-number values using tables, scaled pictographs, scaled bar graphs or line plots. Use appropriate titles, labels and units. Follow the following steps to interpret information presented in scaled pictographs, circle graphs, scaled bar graphs, or line plots. To read information from scaled pictographs, pay close attention to the key. The key tells how much each picture represents.

Each section in a circle graph shows the relative size of that section compared to the whole. We can see the following: •Blue won 20 medals •Green won 26 medals

The key shows that each represents 4 medals; this means represents 2 medals. Since the Green Team has six means Green Team won.

and one , this

(4 × 6) + (1 × 2) = 24 + 2 = 26 medals To read information from scaled bar graph, check the size of each bar on the graph. The bars also show the relative size of data compared to each other. The bar for Green is halfway between 24 and 28 medals, which means Green won 26 medals. Based on the sizes of each section, we can also see that Yellow won the most medals because the bar for Yellow is the tallest. Red won the least medals because the bar for Red is the shortest. 241

•Red won 12 medals

Based on the sizes of each section, we can also see that Yellow won the most medals because the section for Yellow is the largest section. Red won the least medals because the section for Red is the smallest section. To read information from a line plot, count the number of dots representing each category.

Based on the line plot, we can see that 1 student is 36 inches tall because there is only one dot above 36. We can also see the 3 students are 40 inches tall because there are three dots above 40. We can also see that there are ten dots in the line plot, which means this line plot represents the heights of ten students.

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DIRECTIONS: Use the associated graphs to answer each question. Based on the scaled pictograph, how many more fish did Adam catch than Gary? ANSWER:

4 fish Based on the bar graph, how many more lemon flavor candies are in the bag than orange flavor candies? ANSWER:

20 Based on the line plot, what is the difference between the greatest and least number of cans of soda consumed in a week?

ANSWER:

17 cans Based on the circle graph, how many more kids like dogs than birds?

ANSWER:

16 COPYING IS STRICTLY PROHIBITED BY LAW

242

DIRECTIONS: Use the associated graphs to answer each question. Based on the scaled pictograph, how many more vases did Minerva paint than Harry? ANSWER:

24 vases Based on the bar graph, how many tickets were sold on Friday? ANSWER:

60 tickets Based on the line plot, what is the difference between the tallest and shortest tree?

ANSWER:

3 meters Based on the circle graph, how many more people liked pepperoni than bacon? ANSWER:

6 243

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1 A grocery store created a graph to show the amount of produce sold last week. How many more heads of broccoli and bananas were sold than avocados?

2 Use the graph from Question 1 to answer. How many more mangos will need to be sold in order to be equal to the number of bananas sold? 17

3 Use the graph from Question 1 to answer. If the store sells twice as many mangos this week as last week, how many mangos will they sell next week? 70

4 A teacher took a survey of the pets her students had and created a graph. How many more students had fish as pets than lizards?

5 Use the graph from Question 4 to answer. If each “ many birds would the students have as pets? 12

“ represented 3 pets in the key, how

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244

DIRECTIONS: Use the associated graphs to answer each question. Based on the scaled pictograph, how many ice creams were sold on Thursday? ANSWER:

65 Based on the bar graph, how many more soda cans did Peter collect than John?

ANSWER:

30 soda cans

Based on the line plot, how many people watch TV for at least 3 hours?

ANSWER:

6 Based on the circle graph, how many more people like Superman than Batman?

ANSWER:

4 245

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1 An ice cream shop tracked the number of their ice cream types last week in a graph. How many scoops of gelato, custard, and sherbet were sold?

2 Use the graph from Question 1 to answer. How many more scoops of custard were sold than sorbet? 4

3 Use the graph from Question 1 to answer. If each “ many scoops of sorbet were sold? 5

“ is equal to 4 scoops in the key, how

4 Emma poured candy into a bowl. She created a graph to show the amount of each color candy inside. How many more purple candies would she need to equal the amount of yellow candies in the bowl? 6

5 Use the graph from Question 4 to answer. How many orange and purple candies are in the bowl in all? 10

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246

1 Recess Games

The teacher’s assistant made a graph to determine which games the students were playing during recess. How many students were playing games during recess in all?

Number of Students

2 Use the graph from Question 1 to answer. How many more kids were playing parachute than netball? 6

3 Use the graph from Question 1 to answer. How many more kids would need to play tag to equal the number of of kids playing hopscotch? 4

4 Mia made a table showing her classmates’ favorite foods. How many of her classmates preferred pizza over nachos?

5 Use the table from Question 4 to answer. How many of her classmates picked hot dogs or burgers as their favorite food? 17 247

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6 A play director created a graph to represent the different age ranges of audience members. How many audience members were between the ages of 26 and 45?

18—25 26—35 36—45 Ages of Audience

46+

7 Use the graph from Question 6 to answer. How many more audience members were between the ages 36 and 45 than audience members who were 46 years or older? 2

8 Use the graph from Question 6 to answer. How many audience members attended the play in total? 19

9 Jessie asked her friends how many pairs of shorts they owned. She made a graph to represent the data. How many pairs of shorts do most of her friends own? 1

Number of Pairs of Shorts Owned

10 Use the graph from Question 7 to answer. How many pairs of shorts do her friends own in all?

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248

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GRADE 3 EDUCATIONAL BOOTCAMP

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