Smart to the Core: Grade 5 - BEST - Sample

SMART TO THE CORE

Educational Bootcamp

www.educationalbootcamp.com jandj@educationalbootcamp.com

GRADE 5

Tel. 305-423-1999

EDUCATIONAL BOOTCAMP

sample book STUDENT BOOKLET Student’s Name

®

GRADE 5

BEST Smart to the Core Grade 5 Sample Booklet

THIS BOOKLET INCLUDES: •

4 sample lessons from Smart to the Core Student Booklet

MATH BOOTCAMP® - BEST Smart to the Core Sample Booklets- GRADE 5 (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

1 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

MISSION

FL CODE

BENCHMARKS FOR EXCELLENT STUDENT THINKING

PAGES

NUMBER SENSE AND OPERATIONS MISSION 1 Understanding Place Value MISSION 2 Reading and Writing Multi-Digit Numbers with Decimals MISSION 3 Composing and Decomposing MultiDigit Numbers

MA.5.NSO.1.1

Express how the value of a digit in a multi-digit number with decimals to the thousandths changes if the digit moves one or more places to the left or right.

1-8

MA.5.NSO.1.2

Read and write multi-digit numbers with decimals to the thousandths using standard form, word form and expanded form.

9 - 16

MA.5.NSO.1.3

Compose and decompose multi-digit numbers with decimals to the thousandths in multiple ways using the values of the digits in each place. Demonstrate the compositions or decompositions using objects, drawings and expressions or equations.

17 - 24

MISSION 4 Plotting and Ordering Multi-Digit Numbers

MA.5.NSO.1.4

Plot, order and compare multi-digit numbers with decimals up to the thousandths.

25 - 32

MISSION 5 Rounding Multi-Digit Numbers

MA.5.NSO.1.5

Round multi-digit numbers with decimals to the thousandths to the nearest hundredth, tenth or whole number.

33 - 40

MISSION 6 Multiplying Multi-Digit Whole Numbers

MA.5.NSO.2.1

Multiply multi-digit whole numbers including using a standard algorithm with procedural fluency.

41 - 48

MISSION 7 Dividing Multi-Digit Whole Numbers

MA.5.NSO.2.2

Divide multi-digit whole numbers, up to five digits by two digits, including using a standard algorithm with procedural fluency.

Represent remainders as fractions.

49 - 56

57 - 64

MISSION 8 Adding and Subtracting Multi-Digit Numbers

MA.5.NSO.2.3

Add and subtract multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency.

MISSION 9 Multiplying and Dividing Multi-Digit Numbers with Decimals

MA.5.NSO.2.5

Multiply and divide a multi-digit number with decimals to the tenths by one-tenth and one-hundredth with procedural reliability.

MA.5.NSO.2.4

MISSION 10 Dividing Two Whole Numbers as a Fraction MISSION 11 Adding and Subtracting Fractions with Unlike Denominators

Explore the multiplication and division of multi-digit numbers with decimals to the hundredths using estimation, rounding and place value.

FRACTIONS

65 - 72

MA.5.FR.1.1

Given a mathematical or real-world problem, represent the division of two whole numbers as a fraction.

73 - 80

MA.5.FR.2.1

Add and subtract fractions with unlike denominators, including mixed numbers and fractions greater than 1, with procedural reliability.

81 - 88

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MISSION

FL CODE

BENCHMARKS FOR EXCELLENT STUDENT THINKING

PAGES

MISSION 12 Multiplying Fractions

by Fractions

MA.5.FR.2.2

Extend previous understanding of multiplication to multiply a fraction by a fraction, including mixed numbers and fractions greater than 1, with procedural reliability.

89 - 96

MISSION 13 Predicting the Relative Size of the Product

MA.5.FR.2.3

When multiplying a given number by a fraction less than 1 or a fraction greater than 1, predict and explain the relative size of the product to the given number without calculating.

97 - 104

MISSION 14 Dividing Unit Fractions

by Whole Numbers

MA.5.FR.2.4

Extend previous understanding of division to explore the division of a unit fraction by a whole number and a whole number by a unit fraction.

105- 112

ALGEBRAIC REASONING MISSION 15 Solve Multi-Step Real-World Problems

MA.5.AR.1.1

Solve multi-step real-world problems involving any combination of the four operations with whole numbers, including problems in which remainders must be interpreted within the context.

113 - 120

MISSION 16 Solve Real-World Problems Involving Fractions

MA.5.AR.1.2

Solve real-world problems involving the addition, subtraction or multiplication of fractions, including mixed numbers and fractions greater than 1.

121 – 128

MISSION 17 Solve Real-World Problems Involving Division

MA.5.AR.1.3

Solve real-world problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.

129 - 136

MA.5.AR.2.1

Translate written real-world and mathematical descriptions into numerical expressions and numerical expressions into written mathematical descriptions.

137 - 144

MA.5.AR.2.2

Evaluate multi-step numerical expressions using order of operations.

145 - 152

MA.5.AR.2.3

Determine and explain whether an equation involving any of the four operations is true or false.

MISSION 18 Translate Real-World Problems Into Numerical Expressions MISSION 19 Using the Order of Operations MISSION 20 True or False Equations and Determining the Unknown MISSION 21 Writing Equations to Determine the Unknown MISSION 22 Rules for Describing Patterns as an Expression MISSION 23 Mean, Median, Mode, and Range

MA.5.AR.2.4

MA.5.AR.3.1

MA.5.AR.3.2

153 - 160

Given a mathematical or real-world context, write an equation involving any of the four operations to determine the unknown whole number with the unknown in any position.

161 - 168

Given a numerical pattern, identify and write a rule that can describe the pattern as an expression.

169 - 176

Given a rule for a numerical pattern, use a two-column table to record the inputs and outputs.

177 - 184

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MISSION

FL CODE

FLORIDA BENCHMARK

PAGES

MEASUREMENET MISSION 24 Converting Measurement Units

MA.5.M.1.1

MISSION 25 Solving Real-World Problems Involving Money

MA.5.M.2.1

Solve multi-step real-world problems that involve converting measurement units to equivalent measurements within a single system of measurement.

185 - 192

Solve multi-step real-world problems involving money using decimal notation.

193 - 200

GEOMETRIC MISSION 26 Classifying Triangles and Quadrilaterals

MA.5.GR.1.1

MISSION 27 Classifying ThreeDimensional Figures

MA.5.GR.1.2

MISSION 28 Finding the Perimeter and Area of a Rectangle

MA.5.GR.2.1

MISSION 29 Using Volume as an Attribute of ThreeDimensional Figures

MA.5.GR.3.1

MISSION 30 Finding the Volume of a Right Rectangular Prism MISSION 31 Solving Real-World Problems Involving Volume

MA.5.GR.3.2

MA.5.GR.3.3

MISSION 32 Plotting and Labeling Ordered Pairs MISSION 33 Plotting Points Representative of Real-World Problems

MA.5.GR.4.1

MA.5.GR.4.2

REASONING

Classify triangles or quadrilaterals into different categories based on shared defining attributes. Explain why a triangle or quadrilateral would or would not belong to a category.

201 - 208

Identify and classify three-dimensional figures into categories based on their defining attributes. Figures are limited to right pyramids, right prisms, right circular cylinders, right circular cones and spheres.

209 - 216

Find the perimeter and area of a rectangle with fractional or decimal side lengths using visual models and formulas.

Explore volume as an attribute of three-dimensional figures by packing them with unit cubes without gaps. Find the volume of a right rectangular prism with whole-number side lengths by counting unit cubes.

Find the volume of a right rectangular prism with wholenumber side lengths using a visual model and a formula.

Solve real-world problems involving the volume of right rectangular prisms, including problems with an unknown edge length, with whole-number edge lengths using a visual model or a formula. Write an equation with a variable for the unknown to represent the problem.

Identify the origin and axes in the coordinate system. Plot and label ordered pairs in the first quadrant of the coordinate plane.

Represent mathematical and real-world problems by plotting points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation.

217 - 224

225 - 232

233 - 240

241 - 248

249 - 256

257 - 264

DATA ANALYSIS & PROBABILITY MISSION 34 Creating Tables, Graphs, and Line Plots

MA.5.DP.1.1

Collect and represent numerical data, including fractional and decimal values, using tables, line graphs or line plots.

MISSION 35 Classifying ThreeDimensional Figures

MA.5.DP.1.2

Interpret numerical data, with whole-number values, represented with tables or line plots by determining the mean, mode, median or range.

4 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

265 - 272

273 - 280

PLOTTING AND ORDERING MULTI-DIGIT NUMBERS

MA.5.NSO.1.4 Plot, order and compare multi-digit numbers with decimals up to the thousandths.

Use plotting techniques on a number line to order and compare multi-digit numbers. Start by selecting an appropriate scale for the number line or coordinate plane, placing the whole number part of the decimal in its corresponding position. Then, determine the location of the decimal part by dividing the remaining space between whole numbers into equal intervals based on the place value of the decimal.

Example: Plot the number 625.75 on a number line.

To plot the number 625.75 on a number line, determine the whole numbers that come before and after the number. Place those two numbers on opposite sides of the number line.

First 625

626

Next, find the midpoint between the numbers. Plot the number in the middle of the number line.

Second

625.00

625.50

626.00

Then, find the midpoints between these numbers. Plot the numbers on the number line. In this instance, the number 625.75 can be found between 625.5 and 626.

Third 625.00

625.25

625.50

625.75

626.00

In addition to using place value to compare the values of digits in each place, you can also use the number line. The number line is a visual representation of numbers that can help you compare their values. To use the number line to compare two numbers, plot them on the line, then look at their relative positions. The number to the right is always greater than the number to the left.

Example: To compare 625.75 to 625.67, first plot both points on a line using units that are close to the numbers being compared. Next, locate each point on the line and determine which is farther to the right.

First 625.75

625.65

625.85

Second

625.65

625.75

625.70

625.80

625.85

625.8

625.85

Third 625.65

625.66

625.67

625.68

625.69

625.70

625.71

625.72

625.73

625.74

625.75

In this case, 625.75 is farther to the right than 625.67, so it is greater.

5 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

each pair of numbers below using comparison DIRECTIONS: Compare symbols (>, <, or =).

47.59 288.56

44.59

5.78

5.80

70.4

53.3

53.23

147.4

280.56

70.6 147.40

DIRECTIONS: Select all the numbers as indicated below.

Numbers greater than 0.545

Numbers greater than 0.72

Numbers less than 0.667

Numbers less than 0.08

0.554

0.702

0.667

0.081

0.455

0.720

0.665

0.080

0.556

0.07

0.668

0.078

0.565

0.723

0.686

0.079

0.655

0.732

0.866

0.073

0.555

0.722

0.777

0.087

0.444

0.719

0.607

0.077

DIRECTIONS: Use the number line below to compare (>, <, or =).

POINT A

POINT C

O.76

0.760

POINT F

POINT B

0.12

0.21

POINT C

POINT F

0.25

0.28

POINT D

POINT E

0.58

0.45

6 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

each pair of numbers below using comparison DIRECTIONS: Compare symbols (>, <, or =).

148.213

148.213

78.56

288.755

288.75

258.562

78.65 258.563

189.63

189.603

303.147

300.147

DIRECTIONS: Select all the numbers as indicated below.

Numbers greater than 84.956

Numbers greater than 1,826.83

Numbers less than 6.667

Numbers less than 777.897

84.856

1,826.8

6.688

777.797

84.957

1,826.9

6.067

777.896

84.95

1,826.888

6.7

777.899

84.956

1,826.73

6.657

777.8

84.96

1,826.823

6.707

777.9

84.999

1,826.833

6.667

777.887

84.965

1,826.84

6.66

777.898

DIRECTIONS: Use the number line below to compare (>, <, or =).

POINT A

POINT B

0.76

POINT E

POINT D

POINT B

0.12

POINT B

POINT C

POINT D

0.25

POINT B

POINT B

POINT F

0.46

POINT D

7 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

1 Three decimals are plotted on the number line. They are represented by the letters A, B, and C. Which of the following decimals could not be located between A and B on the number line?

A 24

25

26

B

C

27

28

29

25.53

26.8

25.95

26.943

2 Which of these numbers is the least?

44.302

44.35

44.384

44.3

3 Which of these numbers is the greatest?

58.469

58.694

58.496

58.649

4 Which of these statements is true?

11.285 < 11.258

11.258 = 11.285

11.285 > 11.258

11.258 > 11.285

5 Augustus measured the daily temperature last week and recorded his data on the table.

Which day had the highest recorded temperature?

Monday

DAY

TEMPERATURE

Monday

16.87° F

Tuesday

16.78° F

Wednesday

16.86° F

Thursday

16.68° F

Tuesday

Wednesday

8 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

Thursday

each pair of numbers below using comparison DIRECTIONS: Compare symbols (>, <, or =).

56.900

56.9

278.56

365.77

365.707

7,125.808

278.5 7,125.9

789.553

789.535

4,300.749

4,301.749

DIRECTIONS: Select all the numbers as indicated below.

Numbers greater than 49.53

Numbers greater than 7,852.364

Numbers less than 8.95

49.521

7,852.374

8.895

Numbers less than 125.603 125.063

49.531

7,852.354

8.912

125.61

49.60

7,852.4

8.956

49.50

7,852.32

8.99

125.60 125.56

49.053

7,852.53

8.9

125.78

49.547

7,852.38

8.983

125.654

49.65

7,852.367

8.82

125.06

DIRECTIONS: Use the number line below to compare (>, <, or =).

POINT A

POINT B

0.76

POINT E

POINT D

POINT B

0.12

POINT B

POINT C

POINT D

0.25

POINT B

POINT B

POINT F

0.46

POINT D

9 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

1 Select the symbol that makes the following statement true.

488.645 ? 488.546

>

=

<

None

2 Which of the following sets of decimals is listed in descending order?

95.75, 95.7, 95.175

95.175, 95.75, 95.7

95.7, 95.175, 95.75

95.175, 95.75, 95.7

3 Which of the following sets of decimals is listed in ascending order?

168.2, 168.025, 168.25

168.2, 168.25, 168.025

168.025, 168.2, 168.25

168.25, 168.025, 168.2

4 The table below shows the thickness of Susan’s books. Which one of Susan’s books is the thinnest?

BOOK

THICKNESS

Blue

4.58 inches

Green

4.058 inches

Red

4.08 inches

Yellow

4.508 inches

Blue book

Green book

Red book

Yellow book

5 During a science experiment, Zayn measured the weight of four rocks. The table on the right shows the weight of the four rocks. Which rock was the heaviest?

Basalt

ROCK

WEIGHT

Basalt

300.45 ounces

Granite

300.405 ounces

Marble

300.54 ounces

Slate

300.504 ounces

Granite

Marble

10 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

Slate

1 ITEM

PRICE

Eraser

Eraser

$0.32

Pen

$0.43

Pen

Pencil

$0.34

Pencil

Sharpener

$0.23

Sharpener

RIBBON

LENGTH

Blue

Blue

3.25 feet

Orange

3.205 feet

Pink

3.052 feet

Pink

Violet

3.025 feet

Violet

The table on the right shows the prices of school supplies. Which item has the highest price?

2 The table on the right shows the length of ribbons Carmi found in her drawer. What is the color of the shortest ribbon that Carmi found?

Orange

3 The table on the right shows the hair length of four students.

Who has the longest hair?

STUDENT

LENGTH

Andrea

14.603 inches

Bernice

14.36 inches

Faith

14.63 inches

Faith

Victoria

14.063 inches

Victoria

Andrea Bernice

4 Which of these numbers will round to 962 when rounded to the nearest whole number?

961.89

960.999

961.032

962.589

5 Select the symbol that makes the following statement true.

45.78

>

=

?

45.780

<

11 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

None

6 Select the symbol that makes the following statement true.

5,834.345

>

5,844.345

?

=

<

None

7 Which of the following sets of decimals is listed in descending order?

14.08, 14.18, 14.8

456.2, 456.12, 456.101

78.93, 78.9, 79.9

59.175, 59.75, 59.7

8 Which of the following sets of decimals is listed in ascending order?

809.32, 890.23, 889.1

781.2, 781.12, 781

365.2, 369.2, 356.2

489.12, 489.2, 489.222

9 The table on the right shows the mass of different fruits. Which fruit has the greatest mass?

FRUIT

MASS

Apple

152.568 grams

Banana

118 .9 grams

Orange

136.3 grams

Pineapple

Pineapple

250.2 grams

Apple

Banana Orange

10 The table on the right shows the heights of different buildings. Which building is the second tallest?

BUILDING

HEIGHT

Empire State

443.98 meters

Burj Khalifa

828.32 meters

Burj Khalifa

CN Tower

553.76 meters

CN Tower

Shanghai

632.002 meters

Empire State

Shanghai

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REAL-WORLD PROBLEMS INVOLVING MONEY

MA.5.M.2.1 Solve multi-step real-world problems involving money using decimal notation.

Use decimal notation to solve multi-step real-world problems involving money.

STEP 1: Identify the prices, quantities, discounts, or any other monetary values mentioned in the problem. Record the decimal notation for each value.

STEP 2: Determine the unknown values that need to be solved, along with any comparisons that must be made.

STEP 3: Perform the necessary operations to find the answer.

Example 1 John is at the supermarket and wants to buy orange juice. The first option offers a 32-ounce bottle for $2.99, while the second offer is a 16-ounce bottle for $1.50. Which option is cheaper per ounce? $2.99 ÷ 32 ounces = $0.09 per ounce

and

$1.65 ÷ 16 ounces = $0.10 per ounce

$0.09 per ounce < $0.10 per ounce Therefore, $2.99 for 32 ounces of orange juice is a better buy.

Example 2 Alice, Bob, and Carol decided to contribute money to buy a gift for their friend. Bob contributed $5 more than twice the amount contributed by Alice, and Carol contributed $4 less than the amount contributed by Bob. If the price of the gift was $41, how much did Carol contribute?

B = Bob, A = Alice, and C = Carol B = $5 + 2A

(Bob contributed $5 more than twice the amount contributed by Alice)

C = B - $4

(Carol contributed $4 less than the amount contributed by Bob)

If the price of the gift was $41, how much did Carol contribute?

$41 = A

+

B

+

C

$41 = 1A + $5 + 2A + $5 + 2A - $4 $41 = 5A + $6 $41 - $6 = 5A + $6 - $6

$35 = 5A

B = $5 + 2A

C = B - $4

$35 = 5A 5 5

B = $5 + 2 × $7

C = $19 - $4

B = $5 + $14

C = $15

$7 = A

B = $19

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DIRECTIONS: Compare the price points below. Use the symbols >, <, or =.

NO.

DOLLAR AMOUNT 1

NUMBER OF UNITS 1

$45

COST PER UNIT 1

DOLLAR AMOUNT 2

NUMBER OF UNITS 2

64 ounces

$23

32 ounces

$12.50

12 feet

$10.99

9 feet

$100

32 gallons

$75

18 gallons

$63

24 hours

$30

12 hours

$12.99

12 slices

$10.96

8 slices

DOLLAR AMOUNT 2

NUMBER OF UNITS 2

>, <, or =

COST PER UNIT 3

DIRECTIONS: Compare the price points below. Use the symbols >, <, or =.

NO.

DOLLAR AMOUNT 1

NUMBER OF UNITS 1

COST PER UNIT 1

$12

20 bags

$7.60

16 bags

$25

16 cookies

$50

32 cookies

$45

5 toy cars

$82.75

10 toy cars

$29.95

2 shirts

$37.50

4 shirts

$2.99

20 liters

$5.25

32 liters

DOLLAR AMOUNT 2

NUMBER OF UNITS 2

>, <, or =

COST PER UNIT 3

DIRECTIONS: Compare the price points below. Use the symbols >, <, or =.

NO.

DOLLAR AMOUNT 1

NUMBER OF UNITS 1

COST PER UNIT 1

$24.95

5 books

$49.95

10 books

$1,000

12 hours

$575

6 hours

$64

8 yards

$45

5 yards

$15

10 games

$12.75

12 games

$7.99

24 pencils

$9.99

36 pencils

>, <, or =

COST PER UNIT 3

14 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

DIRECTIONS: Compare the price points below. Use the symbols >, <, or =.

NO.

DOLLAR AMOUNT 1

NUMBER OF UNITS 1

$16

COST PER UNIT 1

DOLLAR AMOUNT 2

NUMBER OF UNITS 2

35 ounces

$26

45 ounces

$9.25

11 feet

$10.76

9 feet

$70

21 gallons

$66

23 gallons

$18

20 hours

$24

17 hours

$9.45

6 slices

$10.65

8 slices

DOLLAR AMOUNT 2

NUMBER OF UNITS 2

>, <, or =

COST PER UNIT 3

DIRECTIONS: Compare the price points below. Use the symbols >, <, or =.

NO.

DOLLAR AMOUNT 1

NUMBER OF UNITS 1

COST PER UNIT 1

$19

22 bags

$22.78

17 bags

$34

18 cookies

$29

16 cookies

$48

12 toy cars

$36

9 toy cars

$27.89

3 shirts

$29.50

4 shirts

$6.29

13 liters

$7.46

16 liters

DOLLAR AMOUNT 2

NUMBER OF UNITS 2

>, <, or =

COST PER UNIT 3

DIRECTIONS: Compare the price points below. Use the symbols >, <, or =.

NO.

DOLLAR AMOUNT 1

NUMBER OF UNITS 1

COST PER UNIT 1

$57.8

7 books

$60.8

8 books

$500

16 hours

$570

17 hours

$55

12 yards

$48

10 yards

$52

11 games

$43.75

9 games

$4.47

15 pencils

$3.91

21 pencils

>, <, or =

COST PER UNIT 3

15 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

1 Sarah is at the store and wants to buy juice. Which option would be cheaper: buying one 32-ounce bottle for $2.56 or buying two 16-ounce bottles for $1.44 each?

16-ounce bottle is $0.09 per ounce

32-ounce bottle is $0.09 per ounce

16-ounce bottle is $0.08 per ounce

32-ounce bottle is $0.08 per ounce

2 Robert, Doug, and Kevin agreed to put their money together buy a new gaming table. Doug gave $4 more than twice the amount that Kevin gave, and Kevin gave $3 less than the amount that Robert gave. If the price of the new gaming table was $27, how much did Kevin give for the new gaming table? $5

$8

$10

$12

3 1 1 Mr. Romero left half of the money in his estate to his wife, 4 to his eldest daughter, 5 to his youngest daughter, and the remaining $100,000 to charity. How much was the total amount of money in Mr. Romero’s estate? $1,000,000

$1,500,000

$2,000,000

$4,000,000

4 Gene has $15 more than Andrew, and together they have a total of $32. How much money does Andrew have? $8.50

$23.50

$24.50

$25.50

5 Together, Frank and Alice initially had $100 when they went to the fair. Frank spent $10 on a bag of chips at the fair. Tt this point, he has twice as much money as Alice, who has not yet spent any of her money. How much money did Frank have initially? $30

$60

$65

$70 16 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

DIRECTIONS: Compare the price points below. Use the symbols >, <, or =.

NO.

DOLLAR AMOUNT 1

NUMBER OF UNITS 1

$25

COST PER UNIT 1

DOLLAR AMOUNT 2

NUMBER OF UNITS 2

49 ounces

$28

40 ounces

$6.89

13 feet

$5.38

10 feet

$34

15 gallons

$36

14 gallons

$17

12 hours

$17

18 hours

$15.45

14 slices

$13.65

15 slices

DOLLAR AMOUNT 2

NUMBER OF UNITS 2

>, <, or =

COST PER UNIT 3

DIRECTIONS: Compare the price points below. Use the symbols >, <, or =.

NO.

DOLLAR AMOUNT 1

NUMBER OF UNITS 1

COST PER UNIT 1

$24

19 bags

$23.3

17 bags

$17

21 cookies

$19

16 cookies

$53

11 toy cars

$106

22 toy cars

$18.5

5 shirts

$13.70

3 shirts

$10.69

23 liters

$8.26

17 liters

DOLLAR AMOUNT 2

NUMBER OF UNITS 2

>, <, or =

COST PER UNIT 3

DIRECTIONS: Compare the price points below. Use the symbols >, <, or =.

NO.

DOLLAR AMOUNT 1

NUMBER OF UNITS 1

COST PER UNIT 1

$27.8

9 books

$28.8

6 books

$400

26 hours

$500

23 hours

$60

9 yards

$64

12 yards

$56

11 games

$54

8 games

$6.72

10 pencils

$7.90

14 pencils

>, <, or =

COST PER UNIT 3

17 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

1 A mechanic normally works 8 hours per day and earns $13.50 per hour. For each hour the mechanic works in excess of 8 hours on a given day, he is paid 1.5 times his normal rate. If the mechanic works 10 hours on a given day, how much does he earn on that particular day? $136.50

$148.50

$155.50

$162.50

2 Evelyn is paid $15 per hour for the first 40 hours she works per week and $20 per hour for each hour she works in excess of the first 40 hours per week. If Evelyn earned $740 last week, how many hours did she work last week?

45 hours

46 hours

47 hours

48 hours

3 If Albert gives Bernard $17 and Bernard gives David $13, the three of them will have the same amount of money. How much more money does Albert have than Bernard at the beginning? $21

$22

$23

$25

4 Vicky has $6 more than Hank has. If Hank gives Leo $2 and Noel gives Hank $5, how much more money does Vicky have than Hank now? $12

$10

$6

$3

5 John worked 40 hours last week, including 6 hours during the weekend. John earns $18 per hour during weekdays (Monday to Friday) and 1.5 times that amount during weekends. How much did John earn last week? $752

$764

$768

$774

18 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

1 Emily has $3 more than Cynthia has, but $5 less than Kim has. If Emily has $17, how much money do Cynthia and Kim have altogether? $32

$34

$36

$40

2 George went to the hardware store and spent 2 of his money to buy a new power drill, 1 to 5 3 1 buy some bolt locks, and to buy some nails. If George spent the remaining $30 to buy a new 4 hammer, how much did George spend at the hardware store? $1,200

$1,500

$1,800

$2,000

3 If Gene has four times the amount of money that he has now, he will have the exact amount of money to buy four video games and two CDs. If each video game costs $12.95 and each CD costs $8.50, how much money does Gene have now? $14.60

$15.80

$16.40

$17.20

4

Mr. Richie left half of the money in his estate to his wife, 1 to his eldest daughter, 1 to his 3 9 youngest daughter, and the remaining $300,000 to charity. How much was the total amount of money in Mr. Richie’s estate? $2,900,000

$5,400,000

$3,000,000

$4,600,000

5 Together, Billy and Laura initially had $150 when they went to the concert. Billy spent $15 on a snack at the concession stand. At this point, he has twice as much money as Laura, who has not yet spent any of her money. How much money did Billy have initially? $90

$105

$100

$120 19 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

6 A carpenter normally works 9 hours per day and earns $11.50 per hour. For each hour the carpenter works in excess of 9 hours on a given day, he is paid 1.7 times his normal rate. If the carpenter works 11 hours on a given day, how much does he earn on that particular day? $142.60

$149.60

$151.60

$164.60

7 Cate is paid $17 per hour for the first 30 hours she works per week and $25 per hour for each hour she works in excess of the first 30 hours per week. If Cate earned $660 last week, how many hours did she work last week?

30 hours

32 hours

35 hours

36 hours

8 If Zack gives Gary $19 and Gary gives Will $11, the three of them will have the same amount of money. How much more money does Zack have than Gary at the beginning? $23

$27

$32

$36

9 Bob has $7 more than Henry has. If Henry gives Logan $4 and Nagel gives Henry $6, how much more money does Bob have than Henry now? $11

$9

$5

$4

10 Jeremy worked 36 hours last week, including 4 hours during the weekend. Jeremy earns $15 per hour during weekdays (Monday to Friday) and 2.5 times that amount during weekends. How much did Jeremy earn last week?

$830

$630

$530

$730

20 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

SOLVING REAL-WORD PROBLEMS INVOLVING VOLUME MA.5.GR.3.3 Solve real-world problems involving the volume of right rectangular prisms, including problems with an unknown edge length, with whole-number edge lengths using a visual model or a formula. Write an equation with a variable for the unknown to represent the problem.

Solve real-world volume problems of right rectangular prisms using a visual model or formula.

STEP 1: Read the problem carefully to identify what is given and what needs to be solved.

STEP 2: List the known values, such as the volume of the rectangular prism and any known edge lengths (length, width, height).

STEP 3: Create a visual representation of the rectangular prism using the given information.

STEP 4: Record the formula for the volume of a right rectangular prism.

STEP 5: Set up the equation with the variable for the unknown.

STEP 6: Solve the equation for the unknown.

STEP 7: Check the solution.

Example A truck with various boxes of merchandise has limited space and needs to calculate the height of the boxes to ensure they fit. What is the maximum height (h) of the boxes that can be loaded into the truck?

V = length (l) × width (w) × height (h) 75 cubic meters = 10 meters × 2.5 meters x h

?

Volume = 75 cubic meters

75 cubic meters = 25 meters2 x h 3

1

75 cubic meters = 25 meters2 x h 25 meters2 = 25 meters2 1

1

3 cubic meters = 1h 3 cubic meters = h 21 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

DIRECTIONS: Use the volume equation to solve the unknown widths. ?

5 in.

21.7 in.

1.5 ft

?

?

Volume = 360 cubic inches

Volume = 7,812 cubic in.

Volume = 4.5 cubic feet

40 in.

DIRECTIONS: Use the volume equation to solve the unknown length.

7.2 in.

14 cm

10 in.

Volume = 1,820 cubic in.

Volume = 2,646 cubic cm

Volume = 280.8 cubic in.

14 in. ?

?

DIRECTIONS: Use the volume equation to solve the unknown height.

Volume = 12.5 cubic inches

?

?

Volume = 86 cubic inches

?

Volume = 150 cubic inches

4.3 in.

22 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

DIRECTIONS: Use the measurements to calculate the unknowns.

Volume = 1.89 cubic ft

3 in.

1.5 ft

Volume = 194.25 cubic in.

7 in. ?

0.7 ft

?

Volume = 12 cubic ft

12 in.

Volume = 864 cubic in.

?

?

2 ft

18 in.

3 ft

Volume = 5,107.2 cubic in.

5 ft

14 in.

Volume = 37.5 cubic ft

?

3 ft

?

23 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

24 in.

1 The base of a gas container, shaped like a rectangular prism, has an area of 6 square feet. If 24 cubic feet of gas can fill half the container, how tall is the gas container?

4 feet

8 feet

10 feet

12 feet

2 A water tank, shaped like a rectangular prism, is 10 feet tall. The base of the water tank is a square. If 120 cubic feet of water can fill one-third of the tank, what is the length of one side of the base of the water tank?

2 feet

3 feet

4 feet

6 feet

3 John made a cube of ice using 64 cubic inches of water. What is the length of one side of the cube of ice that John made?

2 inches

4 inches

8 inches

It cannot be determined.

4 Jane’s water container, shaped like a rectangular prism, is 12 inches long, 6 inches wide, and 4 inches deep. She wants to fill the water container with 200 cubic inches of water. Does she have enough water to fill the water container to capacity?

No

Yes

Maybe

It cannot be determined.

5 Frank has two shoe boxes. Both boxes are shaped like a rectangular prism. Shoebox A has dimensions of 8 inches by 5 inches by 4 inches, and shoebox B has dimensions of 15 inches by 3 inches by 3 inches. Which shoebox has a greater volume?

Shoebox A

Shoebox B

Both shoeboxes have the same volume.

The volumes cannot be compared.

24 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

Use the measurements to calculate the volumes or the

DIRECTIONS: unknowns.

?

Volume = 156 cubic cm

Volume = 384 cubic in.

8 in.

3.5 in.

7 in.

6 in.

5.2 cm

?

Volume = 0.625 cubic in.

6 in.

10 cm

?

2 cm

12 cm

4 cm

2.5 in.

7 cm

3 cm

1 in.

5 cm

8 ft 3 ft

7.5 in.

Volume = 4,000 cubic ft

Volume = 990 cubic in.

?

Volume = 81 cubic ft

12 in.

?

6 ft

25 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

?

12.5 ft

1 A water tank is 12 meters long, 10 meters wide, and 15 meters tall. An inlet pipe fills the water tank at a rate of 90 cubic meters per minute. How many minutes will it take the inlet pipe to fill the empty water tank?

10 minutes

15 minutes

20 minutes

It cannot be determined.

2 A room, shaped like a rectangular prism, is 40 meters long and 25 meters wide. The ceiling of the room is 8 meters high. One air conditioner is enough to cool 2,000 square meters. How many air conditioners are needed to cool the entire room?

2 units of air conditioner

3 units of air conditioner

4 units of air conditioner

It cannot be determined.

3 An oil tank, shaped like a cube, is 8 feet long on one side. How many containers of oil can be poured into the oil tank if each container holds 16 cubic feet of oil?

16 containers

20 containers

32 containers

64 containers

4 A box is 30 feet long, 20 feet wide, and 10 feet tall. The box is filled with cartons each having dimensions of 2 feet by 2 feet by 2 feet. How many such cartons can be put inside the box?

750 cartons

800 cartons

850 cartons

It cannot be determined.

5 A box, shaped like a rectangular prism, has a volume of 25 cubic inches. A box, shaped like a cube, has a volume that is 5 times the volume of the rectangular box. What is the length of one side of the box that is shaped like a cube?

5 inches

15 inches

25 inches

It cannot be determined.

26 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

1 An ice tray, shaped like a cube, is 5 inches on one side. How many ice cubes, with a side length of 1 inch, can fit inside the ice tray?

5 ice cubes

25 ice cubes

75 ice cubes

125 ice cubes

2 A metalsmith melted a bar of iron 12 inches long, 8 inches wide, and 6 inches tall. Using the melted iron, the metalsmith made cubical iron bricks that are 2 inches on one side. How many such cubical iron bricks did the metalsmith make?

56 cubical iron bricks

64 cubical iron bricks

72 cubical iron bricks

84 cubical iron bricks

3 Jake molded and then melted three identical cubes of ice. Each cube measured 2 inches on one side. If all three cubes were melted and stored in a container, what would be the volume of the resulting water?

8 inches

16 inches

24 inches

It cannot be determined.

4 A rectangular swimming pool is 20 meters long, 8 meters wide, and 2 meters deep. If the pool is filled using a hose that delivers water at a rate of 5 cubic meters per minute, how many minutes will it take to fill the pool?

32 minutes

40 minutes

64 minutes

56 minutes

5 A storage room is 12 feet long, 8 feet wide, and 6 feet tall. If one shelf takes up 36 cubic feet of space, how many shelves can be placed in the storage room?

10 shelves

12 shelves

14 shelves

16 shelves

27 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

6 An aquarium is shaped like a rectangular prism with dimensions of 40 inches long, 20 inches wide, and 18 inches tall. If each fish requires a minimum space of 20 cubic inches, how many fish can the aquarium hold at most?

72 fish

90 fish

100 fish

720 fish

7 A rectangular prism box has dimensions of 10 inches by 8 inches by 6 inches. If each small cube used to fill the box has a side length of 2 inches, how many small cubes are needed to completely fill the box?

60 cubes

180 cubes

240 cubes

360 cubes

8 A toy company packs their toy blocks in a rectangular box with dimensions of 8 inches by 6 inches by 4 inches. How many toy blocks can be packed in the box if each block has a volume of 2 cubic inches?

24 blocks

36 blocks

48 blocks

96 blocks

9 A water tank is in the shape of a cuboid with dimensions of 6 meters by 4 meters by 3 meters. If the tank is filled to its maximum capacity, what is the volume of water it can hold?

72 cubic meters

96 cubic meters

144 cubic meters

216 cubic meters

10 Ella and Sam both have gift boxes. Each gift box is shaped like a rectangular prism. Ella's gift box (Box X) has dimensions of 10 inches by 6 inches by 4 inches, while Sam's gift box (Box Y) has dimensions of 8 inches by 5 inches by 6 inches. Which gift box has a larger volume?

Box X

Box Y

Both boxes have the same volume

Not enough information to determine

28 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

CREATING TABLES, GRAPHS, AND LINE PLOTS

MA.5.DP.1.1 Collect and represent numerical data, including fractional and decimal values, using tables, line graphs or line plots.

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).

STEP 1: Determine the range of your data, which is the minimum and maximum values of your measurements. This will help you set up the axis appropriately.

STEP 2: Create a horizontal axis (x-axis) for your line plot. Label it with the fractions you are working with, such as 1/8, 1/4, 3/8, 1/2, and so on.

STEP 3: Divide the x-axis into equal segments based on the fractions you are dealing with. For example, if you are using 1/5, each segment would represent 1/5 of the unit.

STEP 4: Give your line plot a descriptive title that explains what the plot is displaying, such as "Measurements in Fractions of a Unit."

STEP 5: Title the x-axis with a clear label like "Fractions" or "Measurement Units." Add a label to the y-axis if your measurements have corresponding values on another scale.

Example:

Consumed (each)

Number of Slices

Personal Pan Pizza Consumed by Students

0

STUDENTS

1

2

3

4

5

6

7

8

9

10 11 12 13 14

AMOUNT EATEN

1 5

3 5

2 5

1 5

3 5

3 5

1 5

4 5

2 5

2 5

x x x

x x x

x x x x

1 5

2 5

3 5

x x x 4 5

3 5

Personal Pan Pizza Cut in Fifths 29 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

4 5

5 4 5 5

x 1

DIRECTIONS: Use the fractions below to create a tally table and line plot.

2 4

1 4

1 4

2 4

2 4

4 4

1 4

2 4

3 4

4 4

4 4

2 4

4 4

2 4

3 4

4 4

1 4

4 8

1 8

3 8

2 8

5 8

6 8

7 8

6 8

3 8

5 8

2 8

4 8

1 8

3 8

3 8

1 8

1 8

4 4

DIRECTIONS: Plot the set of data in the graph provided.

1

7

3

9

5

10

7

12

9

13

11

14

Time (weeks)

Weight (pounds)

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Week

1

WEIGHT OF A NEWBORN

WEIGHT OF A NEWBORN

0

1

2

3

4

5

6

7

8

9

Weight (pounds)

10

30 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

11

12

13

14

DIRECTIONS: Use the fractions below to create a tally table and line plot.

1 6

1

5 6

1 4

1

1 6

6 6

2 6

3 4

2

1

5 6

1 4

1

5 6

2 6

1 4

1

2 6

2 4

1

1 6

4 6

3 4

1

3 6

1 4

1

2 6

1 6

3 4

1

1 6

2 4

1

4 6

3 6

2 4

1

2 6

1 4

1

2 4

DIRECTIONS: Plot the set of data in the graph provided.

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Distance

(hours)

(miles)

1

2

2

4

3

6

4

8

5

10

6

12

0

7

13

Time (hours)

Time

1

WALKATHON

WALKATHON

1

2

3

4

5

6

7

8

9

10

Distance (miles)

31 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

11

12

13

14

1 Jeff measured the length, in inches, of 12 grasshopper specimens during a science experiment.

The table below shows the data he gathered.

SPECIMEN

1

2

3

4

5

6

7

8

9

10 11 12

LENGTH (in inches) 9 1 8 2 9 2 9 1 9 1 8 2 9 1 9 2 9 1 9 2 8 2 9 1

3

3

3

3

3

3

3

3

3

3

3

3

Which of these tables matches the data displayed above?

LENGTH (in inches) 2 83 1 93 2 93

LENGTH (in inches) 2 83 1 93 2 93

NUMBER OF SPECIMENS

LENGTH (in inches)

4

2 83 1 93 2 93

NUMBER OF SPECIMENS

LENGTH (in inches)

4 4

3

6 3

NUMBER OF SPECIMENS

3 3 6 NUMBER OF SPECIMENS

2 83 1 93 2 93

4

5 3

2 Alfred recorded the number of hours he spent playing video games each day for seven days. He played 1 34 hours on Day 1, 1 14 hours on Day 2, 1 12 hours on Day 3, 1 14 hours on Day 4, 1 34

hours on Day 5, 1 14 hours on Day 6, and 1 12 hours on Day 7. Which of these line graphs matches the data?

32 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

DIRECTIONS: Use the fractions below to create a tally table and line plot.

2 5

5 5

4 5

3 5

2 5

4 5

5 5

2 5

2 5

1 5

2 5

3 5

2 5

1 5

2 5

3 5

4 5

3 5

1 7

5 7

4 7

3 7

2 7

6 7

6 7

5 7

2 7

3 7

2 7

3 7

1 7

2 7

3 7

3 7

6 7

5 7

11

12

13

DIRECTIONS: Plot the set of data in the graph provided.

(each)

(pounds)

1

5

2

8

3

8

4

10

5

11

6

13

7

14

Months (each)

Weight Loss

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

MONTHS

WEIGHT LOSS

1

WEIGHT LOSS

0

1

2

3

4

5

6

7

8

9

10

Weight (pounds)

33 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

14

1 The table below shows the length of some grasshopper specimens. Which of the line plots below matches the data?

LENGTH (in inches) NUMBER OF SPECIMENS

● ● ● 6

7 8 Length (in inches) ● ● ● ●

6

● ● ● ● ● ● ● ● ● ● ● ●

3 1 3 64 72 74

8

1 3 84 84

3

2

4

1

5

● ● ● ●

● ● ● 9

6

● ● ● ● ● ● ● ● ● ● ● ● ● 7 8 Length (in inches)

3

●

6

● ● ● ● ● ● ●

7 8 Length (in inches) ● ● ● ●

9

● ● ● ● ●

9

● ● ● ● ● ● ● ● ● ● ● ● ●

7 8 Length (in inches)

9

2 A vendor recorded how many pounds of potatoes she sold each day for seven days. She sold 5 14 pounds on Day 1, 4 34 pounds on Day 2, 4 12 pounds on Day 3, 5 14 pounds on Day 4, 5 12 pounds on Day 5, 5 34 pounds on Day 6, and 5 14 pounds on Day 7. Which of these line graphs matches the data?

34 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

1 Kim found 12 cans of paint in her garage. The table below shows the amount of paint, in pints, in each of the cans she found.

1

CAN

2

3

4

5

6

7

8

9

10 11 12

51 51 41 51 41 41 43 41 51 41 51 41 4 4 4 4 4 4 4 4 4 4 4 4

PAINT (in pints)

Which of these tables matches the data displayed above?

NUMBER OF CANS

NUMBER OF CANS

PAINT (in pints)

8

44

2

44

2

54

2

1 54

3

PAINT (in pints)

NUMBER OF CANS

PAINT (in pints)

NUMBER OF CANS

PAINT (in pints) 1

44 3

44 1

1 44 3 44 1 54

7 1

4

1

7

3

1 44 3 44 1 54

6 1

5

2 Alfred recorded the amount of rainfall each day for seven days. He recorded 6 12 inches of rainfall on Day 1, 5 14 inches on Day 2, 6 34 inches on Day 3, 6 12 inches on Day 4, 5 34 inches on Day 5, 5 12 inches on Day 6, and 5 34 inches on Day 7. Which of these line graphs matches the data?

35 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

3 The table below shows the distances the students lived from the school. Which of the line plots below matches the data?

● 0

1 2

11 11 1 3 21 21 4 2 4 4 2

NUMBER OF STUDENTS

1

5

● ● ● ● ● ● ● ● ● ● ● ●

● ● ● ● ● ● ● ● ● ● ● ●

3

4

1

● ● ●

1 2 Distance (in miles)

● 0

DISTANCE (in miles)

● 3

0

● ● ●

1 2 Distance (in miles)

2

● ●

1 2 Distance (in miles)

● 3

● ● ● ● ● ● ● ● ● ● ● ●

0

● ● ● ● ● ● ● ● ● ● ●

3

● ● ●

1 2 Distance (in miles)

3

4 1

Ben filled six bottles with oil. He filled the first bottle with 3 4 quarts of oil, the second bottle 1

with 2 34 quarts of oil, the third bottle with 3 2 quarts of oil, the fourth bottle with 3 14 quarts of oil, the fifth bottle with 2 12 quarts of oil, and the sixth bottle with 3 quarts of oil. Which of these line graphs matches the data?

36 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited

sample book

GRADE 5

Tel. 305-423-1999

SMART TO THE CORE

Educational Bootcamp

www.educationalbootcamp.com jandj@educationalbootcamp.com

EDUCATIONAL BOOTCAMP

STUDENT BOOKLET Student’s Name

®

GRADE 5