SMART TO THE CORE
Educational Bootcamp
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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
12 I Math Bootcamp® I BEST Smart to the Core Sample Booklet I Copying is strictly prohibited
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
13 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
$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
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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?
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sample book
GRADE 5
Tel. 305-423-1999
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STUDENT BOOKLET Student’s Name
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GRADE 5