SMART TO THE CORE GRADE 3
Building Depth of Knowledge (DOK)
BOOKLET INCLUDES: Train the Brain Practice Drills - drills on the basic skills associated with each individual benchmark (DOK 1) Target Practice Activities - practice problems requiring the application of skills and real-world problem solving (DOK 2)
Think Tank Questions - non-routine task-based problem sets (DOK 3 and 4) Four-Star Challenge - assessments that measure students’ depth of knowledge including their ability to reason abstractly, create models, write arguments, and critique strategies Math Bootcamp - (Grade 3) Publisher: Educational Bootcamp Content Development: Educational Bootcamp Senior Editor: Yasmin Malik Cover Design: Sadiq Malik Copyright © 2014 by J & J Educational Bootcamp Educational Bootcamp Sunrise, Florida 33351 All rights reserved. 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. Printed in the United States of America
SMART TO THE CORE TABLE
OF
CONTENTS
Grade 3 CCSS Code
SMART TO THE CORE MISSIONS
FOUR−STAR CHALLENGE - SCORING RUBRIC
PAGE NUMBER 4
WARM UP - Five Day: Multiplication Warm-up
5—14
3.OA.1 (3.OA.1.1)
MISSION 1: Interpreting Products of Whole Numbers
15—24
3.OA.2 (3.OA.1.2)
MISSION 2: Interpreting Whole Number Quotients
25—34
3.OA.3 (3.OA.1.3)
MISSION 3: Multiplying and Dividing Within 100
35—44
3.O.A.4 (3.OA.1.4)
MISSION 4: Determining the Unknown Value in Equations
45—54
3.OA.5 (3.OA.2.5)
MISSION 5: Applying Properties of Operations
55—64
3.OA.6 (3.OA.2.6)
MISSION 6: Using Division as an Unknown Factor Problem
65—74
3.OA.7 (3.OA.3.7)
MISSION 7: Multiplying and Dividing Within 100
75—84
3.OA.8 (3.OA.4.8)
MISSION 8: Solving Two-Step Word Problems
85—94
3.OA.9 (3.OA.4.9)
MISSION 9: Identifying Patterns
95—104
3.NBT.1 (3.NBT.1.1)
MISSION 10: Rounding Whole Numbers
105—114
3.NBT.2 (3.NBT.1.2)
MISSION 11: Adding and Subtracting Whole Numbers
115—124
3.NBT.3 (3.NBT.1.3)
MISSION 12: Multiplying Whole Numbers by Multiples of 10
125—134
3.NF.1 (3.NF.1.1)
MISSION 13: Understanding Fractions
135—144
3.NF.2 (3.NF.1.2)
MISSION 14: Representing Fractions on a Number Line
145—154
3.NF.3 (3.NF.1.3)
MISSION 15: Understanding Equivalent Fractions
155—164
3.MD.1 (3.MD.1.1)
MISSION 16: Telling Time and Measuring Elapsed Time
165—174
3.MD.2 (3.MD.1.2)
MISSION 17: Measuring Liquid Volume and Mass
175—184
3.MD.3 (3.MD.2.3)
MISSION 18: Representing Data with Graphs
185—194
3.MD.4 (3.MD.2.4)
MISSION 19: Generating Measurements and Making Line Plots
195—204
3.MD.5 (3.MD.3.5)
MISSION 20: Understanding Concepts of Area Measurement
205—214
3.MD.6 (3.MD.3.6)
MISSION 21: Measuring Area by Counting Unit Squares
215—224
3.MD.7 (3.MD.3.7)
MISSION 22: Calculating Area
225—234
3.MD.8 (3.MD.4.8)
MISSION 23: Determining the Perimeter of a Polygon
235—244
3.G.1 (3.G.1.1)
MISSION 24: Classifying Shapes
245—254
3.G.2 (3.G.1.2)
MISSION 25: Partitioning Shapes into Equal Areas
255—264
PRACTICE DRILLS - Two-Minute Multiplication Drills ALL
Student Grids
265—266 267
It is highly recommended that the MATH POWER DRILL be used for direct instruction prior to having the students practice in the SMART TO THE CORE STUDENT BOOKLETS. As with the MATH POWER DRILL, each corresponding lesson increases in depth of knowledge (difficulty level) as you proceed through the Practice and Drills. Lessons in the MATH POWER DRILL and SMART TO THE CORE STUDENT BOOKLETS labeled 1 indicate a review of the basic skills with simple application problems. Lessons in the MATH POWER DRILL and SMART TO THE CORE STUDENT BOOKLETS labeled
2
indicate a slightly more difficult practice of basic skills with grade leveled
application practice problems. Lessons in the MATH POWER DRILL and SMART TO THE CORE STUDENT BOOKLETS labeled 3 indicate extended and/or strategic-like problems. We recommend that each targeted benchmark weakness be addressed over 4 one-hour sessions as follows:
Session 1 (one hour) Power Drill by Benchmark 1 (CD-Rom) Train the Brain Practice 1 (DOK 1) Target Practice 1 (DOK 2)
Session 2 (one hour) Power Drill by Benchmark 2 (CD-Rom) Train the Brain Practice 2 (DOK 1 and DOK 2) Target Practice 2 (DOK 2)
Session 3 (one hour) Power Drill by Benchmark 3 (CD-Rom) Train the Brain Practice 3 (DOK 3) Think Tank Question (DOK 3)
Session 4 (one hour) Four Star Challenge Assessment
INSTRUCTIONS FOR SCORING THE FOUR-STAR CHALLENGE (1) Multiple Choice Section: Assign one point to all multiple choice items answered correctly. (2) Short Answer Section: Assign a maximum of two points. 2 POINTS - Complete correct response, including correct work shown and/or correct labels/units if called for in the item. 1 POINT - Partial correct response. 0 POINTS - No response, or the response is incorrect.
(3) Think Tank Section: Assign a maximum of four points. 4 POINTS - Shows complete understanding of the problem’s mathematical concepts and principles; uses appropriate mathematical terminology; and executes computations correctly and completely. 3 POINTS - Shows nearly complete understanding of the problem’s mathematical concepts and principles; uses mostly correct mathematical terminology; and computations are generally correct, but may contain minor errors. 2 POINTS - Shows some understanding of the problem’s mathematical concepts and principles; uses some correct mathematical terminology, and may contain major computational errors.
1 POINT - Shows limited to no understanding of the problem’s mathematical concepts and principles; may misuse or fail to use mathematical terminology, but attempts an answer. 0 POINTS - No answer attempted.
Intensive Basic Skills Math Strategies
Application of Strategies
Target for Enrichment
1
2
3
4
The student earns ONE star for correctly answering 49% or less.
The student earns TWO stars for correctly answering
The student earns THREE stars for correctly answering
The student earns FOUR stars for correctly answering 90 - 100%.
1
1
1
2
3
Tier 3 In need of Intensive
4
2
3
50 - 69%. Tier 2 In need of Strategic
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4
2
3
4
70 - 89%. Tier 1 * Proficient, but in need of
1
2
3
4
Tier 1 Proficient Target for Enrichment
MULTIPLICATION WARM-UP – 3.OA.1 (3.OA.1.1) Use the hundreds chart to complete the activity below.
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99 100
DIRECTIONS:
1. Draw a tight CIRCLE around the multiples of 2. 2. Draw a tight RECTANGLE around the multiples of 3.
3. Draw an X through the numbers that are multiples of 4. 4. SHADE IN the numbered squares that are multiples of 5. 5. SHADE IN the numbered squares that are multiples of 9. 5 I Copying is strictly prohibited
MULTIPLICATION WARM-UP – 3.OA.1 (3.OA.1.1) Use models to represent the multiplication problems.
6.
2- MINUTE MULTIPLICATION CHALLENGE
7.
8.
6 × 4=
5 × 3=
7 × 8=
6 × 9=
7 × 5=
3 × 9=
9 × 5=
4 × 4=
8 × 6=
2 × 8=
7 × 6=
4 × 3=
8 × 5=
7 × 3=
4 × 8=
9 × 7=
8 × 8=
6 × 4=
4 × 9=
9 × 6=
TOTAL CORRECT: 9.
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MULTIPLICATION WARM-UP – 3.OA.1 (3.OA.1.1)
Study the multiplication table.
X
1
2
3
4
5
6
7
8
9 10 11 12
1
1
2
3
4
5
6
7
8
9
10
11
12
2
2
4
6
8
10
12
14
16
18
20
22
24
3
3
6
9
12
15
18
21
24
27
30
33
36
4
4
8
12
16
20
24
28
32
36
40
44
48
5
5
10
15
20
25
30
35
40
45
50
55
60
6
6
12
18
24
30
36
42
48
54
60
66
72
7
7
14
21
28
35
42
48
56
63
70
77
84
8
8
16
24
32
40
48
56
64
72
80
88
96
9
9
18
27
36
45
54
63
72
81
90
99 108
10 10 20 30 40 50 60 70 80 90 100 110 120 11 11 22 33 44 55 66 77 88 99 110 121 132 12 12 24 36 48 60 72 84 96 108 120 132 144
7 I Copying is strictly prohibited
MULTIPLICATION WARM-UP – 3.OA.1 (3.OA.1.1) Draw arrays to represent the multiplication facts. 2- MINUTE MULTIPLICATION CHALLENGE
1.
2.
3.
7 × 4=
6 × 3=
8 × 8=
7 × 9=
8 × 5=
4 × 9=
8 × 3=
9 × 4=
4 × 6=
3 × 7=
8 × 6=
5 × 3=
5 × 5=
3 × 3=
5 × 8=
1 × 7=
9 × 8=
7 × 4=
6 × 9=
3 × 6=
TOTAL CORRECT: 4.
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MULTIPLICATION WARM-UP – 3.OA.1 (3.OA.1.1)
Use number lines to illustrate the multiplication sentences.
1.
2.
3.
4.
9 I Copying is strictly prohibited
MULTIPLICATION WARM-UP – 3.OA.1 (3.OA.1.1) Complete the fact families.
2- MINUTE MULTIPLICATION CHALLENGE
5.
÷
6.
=
÷ ×
=
7.
÷
8.
=
÷ ×
5 × 5=
3 × 2=
9 × 9=
6 × 8=
8 × 4=
2 × 9=
6 × 3=
8 × 5=
7 × 8=
5 × 7=
8 × 9=
4 × 3=
9 × 4=
3 × 8=
7 × 6=
7 × 3=
10×8=
6 × 9=
7×12=
9 × 6=
TOTAL CORRECT:
=
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MULTIPLICATION WARM-UP – 3.OA.1 (3.OA.1.1) Shade in the grids to represent the multiplication sentences.
1.
2.
3.
4.
11 I Copying is strictly prohibited
MULTIPLICATION WARM-UP – 3.OA.1 (3.OA.1.1) Shade in the grids to represent the multiplication sentences.
5.
2- MINUTE MULTIPLICATION CHALLENGE
6.
4 × 5=
2×12=
8 × 9=
5 × 8=
7 × 4=
3 × 9=
5×11=
7 × 5=
6 × 8=
4 × 7=
7 × 9=
12×3=
6×12=
2 × 8=
8 × 4=
11×9=
2 × 8=
8 × 6=
6 × 9=
6 × 9=
TOTAL CORRECT:
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MULTIPLICATION WARM-UP – 3.OA.1 (3.OA.1.1) Use the key words to help identify multiplication problems. KEY WORDS/PHRASES FOR WORD PROBLEMS INVOLVING MULTIPLICATION
1.
Kyle plays 2 tennis matches every day that he attends practice. He goes to practice 5 times per week. How many times per week does he go to tennis practice?
T
1
2
(Total)
(First Number)
(Second Number)
2.
Paul walks 3 hours daily 6 times per week. How many hours does Paul walk each week?
T
1
2
(Total)
(First Number)
(Second Number)
X
3.
X
Janice sorted her magazines into 5 categories. When Janice finished sorting, each category had 9 magazines. How many magazines did Janice sort?
4.
The cafeteria has 8 rows of tables. There are 6 tables in each row. How many tables are there in all?
T
1
2
T
1
2
(Total)
(First Number)
(Second Number)
(Total)
(First Number)
(Second Number)
X
X
13 I Copying is strictly prohibited
DIVISION WARM-UP – 3.OA.1 (3.OA.1.1) Use keywords to help identify problems.
5.
Patti wants to plant a flower garden in her backyard. She has enough space to grow 8 rows of flowers. She has decided to plant 9 flowers in each row. Which equation will help Patti figure out how many flowers she planted in all?
T
1
2
(Total)
(First Number)
(Second Number)
÷
6.
X
Anna works as an article writer and gets paid $4 per article. If she received $36 last week, which expression could help you find out how many articles she wrote last week?
T
1
2
(Total)
(First Number)
(Second Number)
÷
X
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2- MINUTE MULTIPLICATION CHALLENGE
7 × 5=
5×11=
7 × 9=
5 × 8=
8 × 6=
7 × 2=
8 × 9=
6 × 2=
5 × 6=
4 × 8=
6 × 9=
5 × 3=
6 × 6=
4 × 7=
2 × 4=
3 × 9=
2 × 8=
7 × 8=
8 × 3=
1 × 9=
TOTAL CORRECT:
Mission 1: Interpreting products of whole numbers Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
Bootcamp STRATEGY 1: Interpret 5 × 7 as the total number of objects in 5 groups with 7 objects in each group. Example: 7 objects
×
5
5 groups
= 35
7
Bootcamp STRATEGY 2: Use the number line to represent 5 × 7 as the total number of objects in 5 groups with 7 objects in each group. 1
0
1
2
2
3
4
5
6
7
3
8
9
4
5
6
7
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
5
×
7
= 35
15 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 3.OA.1 (3.OA.1.1) DIRECTIONS: Convert each repeated addition fact into a multiplication fact and solve. 1
4 + 4 + 4 + 4 + 4 + 4 = ___________
2
2 + 2 + 2 + 2 + 2 + 2 + 2 = __________
3
3 + 3 + 3 + 3 + 3 = ______________
4
7 + 7 + 7 = ______________
DIRECTIONS: Convert each multiplication fact into a repeated addition fact and solve.
5
4 x 3 = ______________________
6
3 x 7 = _______________________
7
5 x 6 = ______________________
8
6 x 4 = _______________________
DIRECTIONS: Use the diagrams to determine the answers to the division facts below.
9
10
6 × 6 = ___________
5 × 7 = ___________
12
11
8 × 6 = ___________
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4 × 4 = ___________
Target PRACTICE 1 1
There are 4 tables in the cafeteria. There are 5 people are sitting at each table.
2
Sylvia works in a flower store. She has 8 vases and wants to put 6 flowers in each vase. How many flowers does she need? Grid your answer.
How many people are sitting in the cafeteria? Grid your answer.
3
5
Select the multiplication equations represented by the images below.
4
Select the multiplication equations represented by the images below.
The equation 3 × 3 = 9.
The equation 2 × 6 = 12.
The equation 3 × 4 = 12.
The equation 3 × 3 = 9.
The equation 4 × 3 = 12.
The equation 4 × 4 = 16.
The equation 4 × 4 = 16.
The equation 3 × 4 = 12.
The equation 6 × 2 = 12.
The equation 4 × 3 = 12.
Tina bought 4 packages of ground beef that weighed 3 pounds each. She can use 4 × 3 to find the total weight of all the beef she bought. What equation is equal to 4 × 3?
6
Each day, Ken mows 3 backyards. Which number sentence below shows how many backyards Ken can mow in 7 days?
A a
4+3
A a
7 + 3 = 10
B a
3+3+3
B a
3+3=6
C
3+3+3+3
C
7 × 3 = 21
D a
4+4+4+4
D a
7 × 2 = 14
17 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.OA.1 (3.OA.1.1) DIRECTIONS: Convert each repeated addition fact into a multiplication fact and solve.
1
5 + 5 + 5 + 5 + 5 = _____________
2
3 + 3 + 3 + 3 + 3 + 3 +3 = ___________
3
6 + 6 + 6 + 6 = ________________
4
7 + 7 + 7 + 7 + 7= _________________
DIRECTIONS: Convert each multiplication fact into a repeated addition fact and solve.
5
5 x 4 = ______________________
6
6 x 7 = _________________________
7
3 x 8 = ______________________
8
4 x 4 = _________________________
DIRECTIONS: Use the diagrams to determine the answers to the division facts below.
9
10
6 × 4 = ___________
4 × 8 = ___________ 12
11
5 × 6 = ___________ 18 I Smart to the Core I Educational Bootcamp
5 × 8 = ___________
Target PRACTICE 2 1
Hanson stored 6 video files in each of 5 folders on his computer.
2
How many video files does Hanson have stored in all? Grid your answer.
3
Select the multiplication expressions equivalent to the addition equation below.
4
5 + 5 + 5 + 5 = 20
5
Select the multiplication expressions equivalent to the addition equation below.
6 + 6 + 6 + 6 + 6 = 30
5×5
6×6
4×5
5×5
4×4
6×5
5×4
4×6
5×3
5×6
3×5
6×4
Jack spent 6 hours on each of the 5 paintings he made. He can use 6 × 5 to find the total number of hours he spent painting. What statement is equal to 6 × 5?
6
Luis solves 8 math problems each hour. Which number sentence below shows how many math problems Luis solves in 5 hours?
A a
6+5
A a
8 + 5 = 13
B a
5+5+5+5+5
B a
8 + 8 = 16
Ca
6+6+6+6+6+6
C
8 × 5 = 40
D
5+5+5+5+5+5
D a
8 × 2 = 16
19 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.OA.1 (3.OA.1.1) DIRECTIONS: Answer the following questions. 1 There are 4 booths at a restaurant, and each booth can seat up to 4 people. How many people can be seated in all the booths at a time?
2 Adam bought 4 packs of tennis balls to practice for an upcoming tournament. Each pack contains 3 balls. How many tennis balls does Adam have in all?
3 Sam, Joan, and Mata each have 4 boxes of chocolates, as shown in the figure below. What is the total number of boxes of chocolate Sam, Joan, and Mata have? Explain how you got your answer.
4 A tree has 5 branches, and each branch has 8 leaves on it. How many leaves are on the tree? Write a multiplication sentence to find the answer. _________ × ________ = __________ leaves.
5 Alan was asked to write an equivalent expression for 3 + 3 + 3 + 3 + 3 + 3 using a multiplication statement with only 2 numbers. Write the multiplication statement, and solve the equation.
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THINK TANK QUESTION DIRECTIONS: Study the bar model below. Use the bar model to complete the tasks.
R Dina’s ribbons:
3
Sarah’s ribbons:
3
3
3
3
3
3
3
Part I: Write a story problem using the bar model above.
Part II: Using the bar model, determine how many ribbons Dina has. Show your complete solution.
Part III: Assume Sarah had 4 ribbons. How would the bar model change? Draw the bar model that would show the change.
21 I Copying is strictly prohibited
Four-STAR CHALLENGE - 3.OA.1 (3.oa.1.1) 1
3
5
A poetry book has 9 pages. Jeff bought 7 copies of the poetry book to give to his friends. How many pages are there in all the copies? Grid your answer.
Select the multiplication equations represented by the number line below.
2
4
There are 8 buses taking students to school. Each bus has 9 students. How many students are there in all? Grid your answer.
Select the multiplication equations represented by the number line below.
The equation 6 × 3 = 18.
The equation 7 × 3 = 21.
The equation 3 × 6 = 18.
The equation 4 × 7 = 28.
The equation 9 × 2 = 18.
The equation 4 × 3 = 12.
The equation 2 × 9 = 18.
The equation 3 × 7 = 21.
The equation 18 × 1 = 18.
The equation 7 × 4 = 28.
The equation 1 × 18 = 18.
The equation 3 × 4 = 12.
Mike sold 5 cars each day for 7 days. He can use 7 × 5 to find the total number of cars he sold in 1 week. Which of the following statements is equal to 7 × 5?
6
At summer camp, 5 students can sleep in each cabin. Which number sentence below shows how many students can sleep in 9 cabins?
A
5+5+5+5+5+5+5
A a
9 + 5 = 14
B a
7+7+7+7+7+7+7
B a
9 + 9 = 18
Ca
7+5
C
9 × 5 = 45
D a
5+5+5+5+5
D a
9 × 9 = 81
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7
Write a multiplication sentence that can represent the word problems.
A. John saw 6 hens on the farm. His B. Bill eats 7 cupcakes a month. Mary can brother, Andrew, saw 4 times as many eat 3 times as many cupcakes as Bill hens as he did. Draw pictures that will can in a month. Draw pictures that will help Andrew find the number of hens show the number of cupcakes Mary he saw. How many hens did he see? can eat in 1 month. How many cupcakes can she eat in 1 month?
8
Solve the following word problems. Show your complete solution.
A. There are 7 trays on the table. Each B. Carlos put 5 apples inside each basket. tray contains 4 eggs. How many eggs He has 9 baskets. How many apples are are there in all? there in all?
23 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Study the bar model below. Use the bar model to complete the tasks.
M Tim’s marbles:
4
Joey’s marbles:
4
4
4
4
4
4
4
4
4
Part I: Write a story problem using the bar model above.
Part II: Using the bar model, determine how many marbles Tim has. Show your complete solution.
Part III: Assume Joey had 7 marbles. How would the bar model change? Draw the bar model that would show the change.
24 I Smart to the Core I Educational Bootcamp
Mission 2: interpreting whole number quotients Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
Bootcamp STRATEGY 1: Interpret 35 ÷ 7 as the number of objects in each share when 35 objects are partitioned equally into 7 shares. Example: 7 objects
35
5 groups
÷ 5 =
7
Bootcamp STRATEGY 2: Use the number line to represent 35 ÷ 5 as the number of objects in each share when 35 objects are partitioned equally into 5 shares. 1
0
1
2
2
3
4
5
6
7
3
8
9
4
5
6
7
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
Interpret the model as a division expression:
35 ÷ 5 = n
25 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 3.OA.2 (3.OA.1.2) DIRECTIONS: Use a number line to illustrate the division facts below. 32 ÷ 8 = ____________
1 0
8
16
24
32
40
48
56
64
15 ÷ 3 = ____________
2 0
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
51
54
57
60
63
21 ÷ 7 = ____________
3 0
7
14
21
28
35
42
49
56
63
36 ÷ 9 = ____________
4 0
9
18
27
36
45
DIRECTIONS: Use a model to divide the division facts below. 5
32 ÷ 8 = ____________
6
15 ÷ 3 = ____________
7
21 ÷ 7 = ____________
8
36 ÷ 9 = ____________
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54
63
66
69
Target PRACTICE 1 1
Ken has 24 books. He arranges an equal number of books on 4 shelves of a bookcase.
2
How many books are on each shelf?
3
5
A math book has 72 math problems. Ana wants to solve an equal number of math problems every day for 8 days. How many math problems will she solve each day?
A a
8
B
9
A a
4
Ca
8
Ca
12
B
6
D a
24
D a
21
Josephina has 48 ounces of cleaning solution that she wants to divide into 8 bottles. How many ounces of cleaning solution will be in each bottle? Grid your answer.
Select all the division equations that best describe the figure below.
4
6
A store has 21 pens in all. If the store has an equal number of pens in 7 pen stands, how many pens are in each pen stand? Grid your answer.
Select all the division equations that best describe the figure below.
The equation 20 10 = 2.
The equation 24 3 = 8.
The equation 20 4 = 5.
The equation 24 4 = 6.
The equation 20 2 = 10.
The equation 24 8 = 3.
The equation 20 5 = 4.
The equation 24 6 = 4.
The equation 20 20 = 1.
The equation 24 × 12 = 2. 27 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.OA.2 (3.OA.1.2) DIRECTIONS: Use a number line to illustrate the division facts below. 48 ÷ 6 = ______________
1 0
6
12
18
24
30
36
42
48
54
60
66
24
30
36
42
48
54
60
66
36 ÷ 6 = ____________
2 0
6
12
18
35 ÷ 7 = ______________
3 0
7
14
21
28
35
42
49
56
63
28
35
42
49
56
63
56 ÷ 7 = ______________
4 0
7
14
21
DIRECTIONS: Use a model to divide the division facts below. 5
48 ÷ 6 = ____________
6
36 ÷ 6 = ____________
7
35 ÷ 7 = ____________
8
56 ÷ 7 = ____________
28 I Smart to the Core I Educational Bootcamp
Target PRACTICE 2 1
Ana bought 35 stones. She created 5 bracelets using an equal amount of stones.
2
How many stones are on each bracelet?
3
5
Tomás practiced the guitar for 24 hours last week. If he practiced the same amount of time every day for 6 days, how long did Tomás practice each day?
A
4
B a
6
A
7
Ca
9
Ca
7
B a
8
D a
10
D a
12
Mr. Kim wants to divide his class into 5 equal groups for a debate competition. How many groups of 5 can be made from 25 students? Grid your answer.
Select all the figures that show the division equation 18 3 = 6.
4
6
There are 36 quarters in stacks of 9 on the table. How many stacks are on the table? Grid your answer.
Select all the figures that show the division equation 32 4 = 8.
29 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.OA.2 (3.OA.1.2) DIRECTIONS: Solve the problems below. 1
2
3
4
5
6
There are 5 tables reserved at a restaurant. There are 30 plates divided equally amongst the 5 tables. How many plates are on each table?
Lennon bought 40 chocolates for Valentine’s Day to distribute equally to 10 of his friends. How many chocolates did each of his friends get? How did you get your answer?
Peter sowed a total of 35 seeds in his garden. If each plot had 7 seeds, how many plots did the garden have?
A theater has 5 rooms that can accommodate a maximum of 50 people in total. There are an equal number of available seats in each room. How many available seats are in each room? How did you get your answer?
Laura had a total of 81 plates. Each of her 9 sets had the same number of plates. How many plates were in each set? Fiona is preparing for her final exams by studying 10 hours a day. Her schedule is to study for 2 consecutive hours and then take a break. Determine how many breaks she will take in 1 day. How did you get your answer?
10 hours
30 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: Study the list of numbers below. Use the numbers to complete the tasks below.
1
2
3
4
6
7
8
9 10
5
Part I: Pick 3 numbers from the list above and form a division sentence. Write the division sentence below.
Part II: Using the division sentence you created in Part I, draw a bar model that can represent the division sentence.
Part III: Using the division sentence you created in Part I, draw a grid that can represent the division sentence.
31 I Copying is strictly prohibited
four-STAR CHALLENGE - 3.OA.2 (3.oa.1.2) 13 1
Tina took 27 photos with her digital camera. She stored an equal number of the photos in each of the 3 folders she had on her computer.
14 2
How many photos are in each folder?
3
5
Ken sent a total of 48 messages to his friends. He sent an equal number of messages to each of his 6 friends. How many messages did Ken send to each friend?
A a
5
B a
6
A a
3
C
9
Ca
7
B a
6
D a
12
D
8
Jessy is sorting books on the table. She puts 63 books into groups of 9. How many groups of books are there? Grid your answer.
Sylvia is packing light bulbs in boxes. She wants to equally divide 45 light bulbs into 5 boxes. Select all the division equations that can be used to determine how many light bulbs she will put in each box.
16 4
6
Mark folded 42 sweaters in stacks of 7, with an equal number of sweaters in each stack. How many sweaters were in each stack? Grid your answer.
Tommy has 28 baseball cards. He wants to put the baseball cards into an album for display. If each page will have 4 baseball cards, select all the equations he can use to determine how many pages he needs.
The equation 45 5 = 9.
The equation 28 4 = n.
The equation 9 5 = 45.
The equation 28 n = 4.
The equation 8 5 = 45.
The equation 28 n = 14.
The equation 5 9 = 45.
The equation 28 14 = n.
The equation 5 8 = 45.
The equation 28 28 = n.
The equation 45 9 = 5.
The equation 28 n = 28.
32 I Smart to the Core I Educational Bootcamp
7
Write a division sentence that can help you solve the word problems below.
A. Melissa wants to plant 24 rose bushes B. Sylvia needs to pack 18 donuts in 6 in her garden. She wants to plant the snack boxes. If each snack box needs same number of roses in 8 rows. Draw to have an equal number of donuts, pictures to help you find how many Draw pictures to find how many rose bushes will there be in each row. donuts will she pack in each snack box.
8
Solve the word problems below. Show your complete solution.
A. Andrea bought 36 apples to make pies. B. Lillian wants to arrange 42 tulips in Each apple pie requires 6 apples. How some vases. She wants to put 6 tulips many apple pies can Andrea bake? in each vase. How many vases does she need?
33 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Study the list of numbers below. Use the numbers to complete the tasks.
3
6
4
8 12
9
Part I: Pick 3 numbers from the list above and form a division sentence. Write the division sentence.
Part II: Using the division sentence you created in Part I, draw a bar model that can represent the division sentence.
Part III: Using the division sentence you created in Part I, draw a grid that can represent the division sentence.
34 I Smart to the Core I Educational Bootcamp
MISSION 3: Multiplying and Dividing within 1-00 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Bootcamp STRATEGY 1: Draw arrays to represent word problems involving multiplication and division. Example: A baker cut 4 cakes into 8 equal slices. How many slices of cake did the baker cut? 8
8
8
8
4 × 8 = 32 slices of cake
Bootcamp STRATEGY 2: Use key words to help create equations to represent word problems involving multiplication and division. Example: Jamie baked 42 cookies to sell at a bake sale. She splits the cookies into packages of 7 cookies. How many packages of cookies does she have to sell? KEY WORD MEANING
is
cut
times
each row
shared
each ____
split
Equals (=) Divide (÷) Multiply (×) Multiply (×)
Divide (÷)
Multiply (×)
Divide (÷)
42 cookies split into packages of 7.
42
÷
7
=
6
35 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 3.OA.3 (3.OA.1.3) DIRECTIONS: Underline the key words, and circle the numbers in the word problems. Use the information to create and solve the multiplication equations. 1
Karla is baking cakes to give to her family as gifts. The cake recipe requires 2 eggs for every pound of flour. If Karla uses 10 pounds of flour, how many eggs will she need?
2
Norris has 24 feet of painter’s tape and wants to cover some baseboards that require 6 feet of tape each. How many baseboards can he cover using the painter’s tape?
3
Phillip's display case has 10 shelves with 8 toy cars on each shelf. How many toy cars are in the display case?
4
Chloe has 54 movie tickets to give to 9 people. She wants to give each person the same number of tickets. How many tickets should she give each person?
5
The dancers must practice a performance 7 times in an hour. If the dancers need to practice the performance 35 times before the show, how many hours do they need to practice?
36 I Smart to the Core I Educational Bootcamp
Target PRACTICE 1 1
3
5
Third grade students are gathering on a parade ground. The students stand in 5 rows. There are 6 students in each row. What multiplication sentence describes this array?
2
On Tuesday, Lee drove 9 miles. To reach his destination on Wednesday, he needs to drive double the number of miles he drove on Tuesday. How many miles does Lee need to drive on Wednesday?
A a
5 × 2 = 10
A a
9
B a
6 × 6 = 36
B a
11
Ca
5 × 5 = 25
C
18
D
5 × 6 = 30
D a
81
For the party, Jessica buys 7 packs of spoons. Each pack contains 9 spoons. If s is the total number of spoons she buys, select all the equations she can use to solve for s.
4
Jerry needs to put 81 books on each of 9 shelves. He wants each shelf to have the same number of books. If b is the number of books he needs to put on each shelf, select all the equations he can use to solve for b.
The equation 7+ 9 = s.
The equation b × 9 = 81.
The equation 7 − 9 = s.
The equation 81 + 9 = b.
The equation 9 × 7 = s.
The equation 9 − 81 = b.
The equation 9 7= s.
The equation 81 9 = b.
The equation 9 + 7 = s.
The equation 9 × 81 = b.
The equation 7 × 9 = s.
The equation 81 × b = 9.
A dressmaker has 72 inches of ribbon. If she wants to cut the ribbon in 9-inch pieces, how many pieces of ribbon will she have? Grid your answer.
6
Mimi uses 2 cups of flour to make 1 loaf of bread. If a bag of flour contains 10 cups, how many loaves of bread can she make? Grid your answer.
37 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.OA.3 (3.OA.1.3) DIRECTIONS: Underline the key words, and circle the numbers in the word problems. Use the information to create and solve the multiplication equations. 1
Mrs. Gonzalez gave each of her 4 daughters 7 books to read over the summer break. How many books did they receive in all?
2 There are 48 students attending a field trip to the nature park. Each minibus can hold 8 students. How many minibuses will be needed to transport the 48 students?
3
Vito bought 30 baseball cards to split between his 3 friends and himself. How many baseball cards will each of them get?
4 A gift basket has 4 boxes of candy and 3 boxes of cookies inside. Monica buys 5 baskets for a gift giveaway. How many boxes of cookies were in all of the baskets?
5 A corner store stocks 8 crates of bread. Each crate has 9 loaves of bread. How many loaves of bread does the corner store stock?
38 I Smart to the Core I Educational Bootcamp
Target PRACTICE 2 1
3
5
Neola arranged pictures on the table in 9 rows with 8 pictures in each row. Which multiplication sentence below describes this array?
2
Nancy read 7 pages of a storybook on the first day. To complete the book the next day, she needs to read double the number of pages she read on the first day. How many pages does Nancy need to read the next day?
A a
8 × 8 = 64
A a
7
B a
9 × 9 = 81
B a
9
C
9 × 8 = 72
C
14
D a
8 × 2 = 16
D a
49
Jeremy bought 8 boxes of donuts. If each box contains 8 donuts, select all the statements that describe how many donuts Jeremy bought in all?
4
Tony needs to place 80 chairs at 8 tables. Each table needs to have the same number of chairs. Select all the statements that describe how many chairs Tony will put at each table.
There are more than 60 donuts in all.
At each table: less than 4 chairs
There are less than 70 donuts in all.
At each table: more than 8 chairs
There are 72 donuts in all.
There are 20 chairs at each table.
There are 64 donuts in all.
There are 10 chairs at each table.
There are 81 donuts in all.
At each table: more than 16 chairs
There are more than 100 donuts in all.
There are 24 chairs at each table.
Roland has 35 bricks. How many rows of 7 bricks can he make? Grid your answer.
6
Danni uses 3 bows to make a gift box. If bows come in packages of 12, how many gift boxes can she make using 1 package of bows? Grid your answer.
39 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.OA.3 (3.OA.1.3) DIRECTIONS: Solve the problems below. 1
A chocolate manufacturing company packs a certain number of chocolates in a box, as shown below. Describe the number of rows and columns in this box, and write a multiplication statement that describes the total number of chocolates in the box.
2 A dance troupe is training for an upcoming parade. There are 7 rows of dancers, and each row has 10 dancers in it. Determine how many dancers there are in the troupe. How did you get your answer?
3 Bella was given homework on Monday to write 10 sentences. The following Monday, she was assigned to write twice the number of sentences she wrote on the previous Monday. How many sentences did she write in the 2 weeks combined?
4 Madison is making 2 bookshelves for her living room. If each bookshelf can hold 9 books, how many books can both of the shelves hold?
5 An array of squares is shown below. Write a division statement that explains the number of squares in 1 row.
6 Mai is making diamond-shaped figures using strips of construction paper. If she makes 5 figures, how many strips of construction paper will she use?
40 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: Study the picture below. Use the picture to complete the tasks below.
Part I: Write a multiplication expression that can represent the picture above.
Part II: Create a story problem related to the multiplication expression you created in Part I and then solve and show the solution to the story problem you created.
41 I Copying is strictly prohibited
Four-STAR CHALLENGE - 3.OA.3 (3.oa.1.3) 13 1
13 3
17 5
Gavin has a box of jars. The jars are arranged in 5 rows. There are 8 jars in each row. Which multiplication sentence below describes this array?
14 2
Li wants to buy a toy car. He saved $8 in the first month. To buy a toy car in the second month, he needs to save double the amount he saved in the first month. How much does Li need to save in the second month?
A
5 × 8 = 40
A a
$8
B a
5 × 5 = 25
B a
$10
Ca
8 × 8 = 64
C
$16
D a
8 × 2 = 16
D a
$64
A farmer harvested 8 baskets of corn yesterday. Each basket has 9 corn stalks. If c is the total amount of corn the farmer harvested, select all the equations he can use to find the amount of corn he harvested.
14 4
Linda needs to pack 48 eggs into 8 trays. Each tray should have the same number of eggs. If e represents the number of eggs in 1 tray, select all the equations she can use to find how many eggs should be in each tray.
The equation 8 + 9 = c.
The equation 48 + 8 = e.
The equation c − 9 = 8.
The equation e − 48 = 8.
The equation 9 + c = 8.
The equation 48 e = 8.
The equation 8 × 9 = c.
The equation 8 × 48 = e.
The equation 9 × 8 = c.
The equation 48 × 8 = e.
The equation 8 c = 9.
The equation 48 8 = e.
Marcia sells cookies in packages of 8. She baked 48 cookies. How many packages of cookies can she sell? Grid your answer.
42 I Smart to the Core I Educational Bootcamp
Erick uses 6 candles to make 1 18 6 hexagon. If candles come in boxes of 18, how many hexagons can he make using 1 box of candles? Grid your answer.
7
Solve the word problems below. Show your complete solution.
A. Melvin wants to arrange 5 rows of B. Tommy needs to put 35 eggs on 7 trays. chairs for the party this afternoon. He He wants to put the same number of wants to put 6 chairs in every row. How eggs on each tray. How many eggs does many chairs will he need? he need to put on 1 tray?
8 A.
Create story problems for the number sentences below and solve.
8×7
B.
28 4
43 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Study the picture below. Use the picture to complete the tasks.
Part I: Write a division expression that can represent the picture above.
Part II: Create a story problem related to the division expression you created in Part I and then solve and show the solution to the story problem you created.
44 I Smart to the Core I Educational Bootcamp
MISSION 4: Determining the unknown value in equations Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = [ ] ÷ 3, 6 × 6 = ?.
Bootcamp STRATEGY 1: Use arrays to determine the unknown number that makes the equation true. Example 1:
Example 2:
8 × ? = 48
5=?÷3
8 × 6 = 48
Example 3: 6×6=?
5 = 15 ÷ 3
6 × 6 = 36
Bootcamp STRATEGY 2: Use a T-1-2 chart to help determine the unknown whole number in a multiplication or division equation relating 3 whole numbers. Step 1: Use the T-1-2 chart and the key words to help determine the operation to be used. Step 2: Place the digit that represents the measured (concrete) amount under the number“1.” Step 3: Place the digit that represents the variable (changing) amount under the number“2.” Step 4: If the total is known, place that digit under the total “T.” Step 5: Use the completed chart to solve the equation as written. Example: Selena has 9 dimes. Cassie has 6 times as many dimes as Selena. How many dimes does Cassie have? If Selena has 9 dimes, we know the exact measure amount; therefore, the number 9 will be placed under the number "1" on the T-1-2 chart. Cassie has 6 times as many as Selena. We know that the variable amount is 6; therefore, the number 6 will be placed under the number "2" on the T-1-2 chart. Now the equation can be solved: 9 × 6 = 54 (Total)
54
(Measured Amount)
÷
9
(Variable Amount)
×
6 45 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 3.OA.4 (3.OA.1.4) DIRECTIONS: Use arrays or T-1-2 charts to find the missing number that will make each equation true.
1
15 = 3 × ____
2
18 = 6 × ____
3
_____ = 9 × 5
4
____ ÷ 8 = 6
5
49 ÷ ____ = 7
6
4 = 16 ÷ ____
7
28 = 4 × ____
8
7 = 7 × ____
9
_____ = 7 × 6
10
____ ÷ 9 = 8
11
50 ÷ ____ = 5
12
3 = 12 ÷ ____
13
2 = 8 ÷ ____
14
2 = 1 × ____
15
_____ = 9 × 4
46 I Smart to the Core I Educational Bootcamp
Target PRACTICE 1 1
Tim plans to fence in 6 different areas of a garden. If he uses 24 pieces of wood in all for those areas, how many pieces of wood does he need for each fence?
6×
3
5
2
= 24
Alana spent 54 hours on 9 assignments. She spent the same amount of time on each assignment. Which of the following equations can be used to find the amount of time she spent on each assignment?
A
4
A a
54 ×
B a
6
B a
3×
Ca
7
Ca
54 ×
=6
D a
9
D
9×
= 54
Mr. Perkins spent $54 for a crate of 6 lobster tails. How much did each lobster tail cost? Grid your answer.
Select all the statements below that are correct.
7 × ___ = 42
4
6
=9 =9
Michael arranged 36 tables in 4 equal rows. How many tables are in each row? Grid your answer.
Select all the statements below that are correct.
9 × ___ = 36
The number 4 should go in the blank.
The number 3 should go in the blank.
The number 6 should go in the blank.
The number 7 should go in the blank.
The number 8 should go in the blank.
The number 4 should go in the blank.
The related equation is 4 × 7 = 42.
The related equation is 3 × 9 = 36.
The related equation is 6 × 7 = 42.
The related equation is 7 × 9 = 36.
The related equation is 8 × 7 = 42.
The related equation is 4 × 9 = 36. 47 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.OA.4 (3.OA.1.4) DIRECTIONS: Use arrays or T-1-2 charts to find the missing number that makes each equation true. 1
42 = 7 × ____
2
24 = 6 × ____
3
_____ = 8 × 5
4
____ ÷ 7 = 6
5
56 ÷ ____ = 7
6
4 = 28 ÷ ____
7
30 = 3 × ____
8
9 = 9 × ____
9
10
____ ÷ 8 = 8
11
40 ÷ ____ = 5
12
13
_____ = 8 × 7
14
8 = 1 × ____
15
48 I Smart to the Core I Educational Bootcamp
_____ = 6 × 4
4 = 12 ÷ ____
_____ = 3 × 4
Target PRACTICE 2 1
Mr. James plans to have 30 students for a summer training. If he puts the students into equal groups, how many students will be in each group?
5×
3
2
= 30
A a
5
A a
24 ×
B
6
B a
3×
=6
Ca
7
C
6×
= 24
D a
35
D a
24 ×
=7
Select all the statements that are true of the equation below.
4
63 ___ = 7
Lia has 32 beads to make bracelets. She uses 4 beads per bracelet. How many bracelets can Lia make with the beads? Grid your answer.
=6
Select all the statements that are true of the equation below.
32 ___ = 8
Related multiplication equation: 9 × 7 = 63. Related multiplication equation: 8 × 7 = 56. The number 8 completes the equation above. The number 9 completes the equation above. Related division equation: 63 ÷ 7 = 8. Related division equation: 63 ÷ 8 = 7. 5
Anna uses 24 potatoes to make 6 different kinds of potato chips. If each recipe calls for the same number of potatoes, what equation can be used to find the number of potatoes needed for each recipe?
Related multiplication equation: 4 × 8 = 32. Related multiplication equation: 8 × 4 = 32. The number 4 completes the equation above. The number 6 completes the equation above. Related division equation: 32 ÷ 8 = 4. Related division equation: 32 ÷ 7 = 6. 6
A restaurant needs 48 glasses. If each case contains 8 glasses, how many cases are needed? Grid your answer.
49 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.OA.4 (3.OA.1.4) DIRECTIONS: Solve the problems below. 1 A store is having a sale on hats. Every hat in the store has a price tag of $5. If John buys “p” number of hats, and the total amount of money he spends is $45, what is the value of p? p × $5 = $45 p = _______
2
Bonnie bought a pack of 64 pencils. She wanted to evenly divide the pencils among her 8 friends. How many pencils would each friend receive? Explain how you got your answer.
3 Adam bought 8 tickets to a football game. If he spent $72, how much did each ticket cost?
4
A school is on a field trip to a museum. For every 2 students, there is 1 teacher who is chaperoning them. If 20 students are on the field trip, how many teachers are chaperoning them?
5
= 36 Mandy is being asked this multiplication question on a test: 4 × She has to determine the number that should be placed in the box to make the equation correct. Explain the steps needed to find the answer, and solve.
6 William is taking an online test and is allotted 6 minutes to solve each question. If the test contains 20 questions, how much time in minutes is William given to complete the test?
7
Kevin can type 50 words per minute. If he types for 5 minutes, how many words will he type?
50 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: Study the numbers below. Use the numbers to complete the tasks.
56
7
42
8
36
6
Part I: Find a pair of numbers that have a product of 42.
Part II: Which of the following multiplication equations are correct?
6 × 7 = 56
6 × 8 = 56
7 × 6 = 56
7 × 8 = 56
8 × 6 = 56
8 × 7 = 56
Part III: Find a pair of numbers that have a quotient of 7.
Part IV: Which of the following division equations are correct?
56 ÷ 8 = 6
56 ÷ 8 = 7
8 ÷ 56 = 6
56 ÷ 7 = 6
56 ÷ 7 = 8
7 ÷ 56 = 6
51 I Copying is strictly prohibited
Four-STAR CHALLENGE - 3.OA.4 (3.oa.1.4) 13 1
Martina wants to sew an equal number of quilts in 7 different colors. If she makes 63 quilts, how many quilts will she make in each color?
7×
13 3
17 5
14 2
Sam spent $36 on 4 flowerpots. The cost of each flowerpot was the same. What equation can be used to find the cost of 1 flowerpot?
= 63
A a
4
A a
36 ×
=4
B a
6
B
4×
= 36
Ca
7
Ca
36 ×
=9
D
9
D a
4×
Adrianna wanted to arrange 35 roses into equal groups. Select all the statements that could be true of the number of groups.
14 4
=9
Bob wanted to divide his 42 baseball cards into equal groups. Select all the statements that could be true of the number of groups.
6 groups of 5 roses.
7 groups of 5 baseball cards.
5 groups of 7 roses.
6 groups of 8 baseball cards.
6 groups of 7 roses.
8 groups of 5 baseball cards.
5 groups of 6 roses.
7 groups of 6 baseball cards.
7 groups of 5 roses.
6 groups of 5 baseball cards.
7 groups of 6 roses.
6 groups of 7 baseball cards.
There are 18 students going to watch a football game. There is 1 van for every 6 students going to the stadium. How many vans are needed to go to the stadium? Grid your answer.
52 I Smart to the Core I Educational Bootcamp
Raul brought 80 chairs for a marriage 18 6 ceremony. If he wants to arrange 8 chairs at each table, how many tables does Raul need? Grid your answer.
7
Find the missing number that will make the multiplication sentence correct. Show your complete solution.
A.
8 × ____ = 64
8
A.
B.
7 × ____ = 63
Find the missing number that will make the division sentence correct. Show your complete solution.
49 ____ = 7
B.
____ 4 = 6
53 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Study the 6 numbers below. Use the numbers to complete the tasks.
45
5
20
4
54
9
Part I: Find a pair of numbers that have a product of 45.
Part II: Which of the following multiplication equations are correct?
9 × 4 = 20
5 × 9 = 20
4 × 9 = 20
4 × 5 = 20
9 × 5 = 20
5 × 4 = 20
Part III: Find a pair of numbers that have a quotient of 9.
Part IV: Which of the following division equations are correct?
20 ÷ 5 = 4
20 ÷ 4 = 5
4 ÷ 45 = 9
54 ÷ 9 = 4
4 ÷ 20 = 5
9 ÷ 54 = 4
54 I Smart to the Core I Educational Bootcamp
MISSION 5: Applying Properties of operations Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
Bootcamp STRATEGY 1: Use the top and the bottom of a number line to show the commutative property of multiplication. Example: 4 × 6 = 6 × 4 +4
0 1 2
+4
3 4 5
+4
+4
+4
+4
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
+6
+6
+6
+6
Bootcamp STRATEGY 2: Use arrays to show the associative property of multiplication to multiply 3 factors. Example: 3 × 5 × 2 = 30 (3 × 5) × 2 = 30 5
×
3 × (5 × 2) = 30 5
×
X
3
= 15
×
2
5
×
2
X
X
OR
3
2
×
5
5
= 15 = 10
= 10
= 10
Bootcamp STRATEGY 3: Use arrays to show the distributive property of multiplication. Example: 8 × 7 = (8 × 5) + (8 × 2) ×
7
8
×
5
×
8
8
= 56
2
40
+
16
= 56
55 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 3.OA.5 (3.OA.2.5) DIRECTIONS: Use the top and the bottom of a number line to show the commutative property of multiplication for the equations below. 1
4 × 8 = 32
0 1 2
3 4 5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
2
7 × 6 = 42
0 1 2
3 4 5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
3
5 × 4 = 20
0 1 2
3 4 5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
4
6 × 3 = 18
0 1 2
3 4 5
5
3 × 8 = 24
0 1 2
3 4 5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
56 I Smart to the Core I Educational Bootcamp
Target PRACTICE 1 1
Select all the statements that are true of the equation below.
2
What is the missing value in the equation below?
6×8=
(2 × 6) × 7 = 7 × (2 × 6)
Associative property of multiplication Commutative property of multiplication The answer to the equality is 84. The answer to the equality is 112.
A a
12
B
8
Ca
6
D
3
×6
Distributive property of multiplication 3
What is the missing value in the equation below?
(9 × 4) × 7 = 9 × (
5
4
× 7)
There are 6 rows of 3 soldiers on the march. Which of the following number sentences will determine the number of soldiers on the march using the distributive property? A a
3 × 6 = 15 + 3
7
B
3 × 6 = 3 × (3 + 2)
Ca
9
Ca
3×6=3×6
D
11
D
3 × 6 = (3 × 3) + (3 × 3)
A
4
B
Tim saw 3 vans. Each van carried 3 crates with 6 boxes in each crate. What number sentence can be used to find the number of boxes there are in all using the associative property of multiplication?
6
Which expressions can be used to find 10 × 8? Select all that apply. (6 × 10) × (2 × 10) 8 × 10
A a
3×6=6×3
(2 × 4) × 10 = 2 × (4 × 10)
B
(3 × 6) × 3 = 3 × (6 × 3)
20 × 2
Ca
3 × 6 = (9 × 1) + (9 × 1)
(4 × 10) + (4 × 10)
D a
6 × (3 + 3) = (6 × 3) + (6 × 3)
57 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.OA.5 (3.OA.2.5) DIRECTIONS: Use the top and the bottom of a number line to show the commutative property of multiplication for the equations below. 1
9 × 3 = 27
0 1 2
3 4 5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
2
8 × 5 = 40
0 1 2
3 4 5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
3
5 × 7 = 35
0 1 2
3 4 5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
4
5 × 6 = 30
0 1 2
3 4 5
5
4 × 7 = 28
0 1 2
3 4 5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
58 I Smart to the Core I Educational Bootcamp
Target PRACTICE 2 1
Select all the equations below that show the distributive property of multiplication.
2
What is the missing value in the equation below?
(7 × 10) = (3 ×
6 × 7 = (6 × 5) + (6 × 2)
A a
3
5 × (10 + 2) = (5 × 2) + (5 × 10)
B a
4
6×7=7×6
C
10
D a
17
(2 × 1) × 7 = 7 × (2 × 1)
) + (4 ×
)
(4 × 2) × 1 = 4 × 2 8 × (5 × 3) = (8 × 5) × 3
3
What is the missing value in the equation below?
4
3×4=4×
5
A a
12
B a
7
Ca
4
D
3
There are 4 shelves in Li’s house that each have 4 rows of DVDs. Each row has 8 DVDs. What number sentence can be used to find how many DVDs he has using the associative property of multiplication? A a 8×4=4×8
6
Eric spends 4 hours reading each of his 7 textbooks. Which number sentence below will determine how much time he spent reading using the distributive property? A a
7 × 4 = 20 + 8
B a
7 × 4 = 7 × (2 × 2)
Ca
7×4=4×7
D
7 × 4 = (7 × 2) + (7 × 2)
Select all of the equations that can be used to find 8 × 5. 8 × (2 + 3) 4×5=5×4
5 + (4 + 4)
B
(8 × 4) × 4 = 8 × (4 × 4)
5+3×3+5
Ca
8 × 4 = (8 × 2) + (8 × 2)
5×8
D a
8 × (4 + 4) = (8 × 4) + (8 × 4) 59 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.OA.5 (3.OA.2.5) DIRECTIONS: Solve the problems below. 1
Amy and Betsy are trying to fit a certain number of boxes in a square room. They each want to arrange the boxes in the different formations shown below. Write the multiplication statements for each image shown to find the total number of boxes each depicts. Explain whether or not each arrangement satisfies the commutative property.
2
Helena is counting the number of trading cards in her collection. She wrote the statement 4 × 5 to get the count. She decided to divide her trading cards into 2 parts. Write an equivalent statement modeling how she grouped her trading cards. Explain which property you applied.
3
Use 2 different properties to solve 9 × 10.
4
Mary wants to calculate the total number of pom-poms she has, as shown below. Use the distributive property to find this number.
60 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: Study the sets of equations below. Use the equations to complete the tasks.
Part I: Select the equation that shows the commutative property of multiplication.
Part II: Select the equation that shows the associative property of multiplication.
Part III: Select the equation that shows the distributive property of multiplication.
Part IV: Select the equation that shows the identity property of multiplication. Hint: Identity property of multiplication states that a number multiplied by 1 is the original number.
61 I Copying is strictly prohibited
Four-STAR CHALLENGE - 3.OA.5 (3.oa.2.5) 1
Select all the options that are true of the expression below. 3 × (6 + 4) = (3 ×
2 What is the missing value in the equation below?
) + (3 × 4)
× 10 = (2 × 10) + (2 × 10)
Digit 6 completes equation
A a
2
Digit 7 completes equation
B
4
Digit 9 completes equation
Ca
10
D a
12
Equation shows distributive property Equation shows associative property
3 What is the missing value in the equation below? (
5
4
× 9) × 2 = 3 × (9 × 2)
There are 9 tents with 5 cots in each tent. What number sentence can be used to find how many cots there are using the distributive property? A a
5 × 9 = 40 + 5
3
B a
5 × 9 = 5 × (3 × 3)
Ca
9
Ca
5×9=5×9
D a
18
D
5 × 9 = (5 × 6) + (5 × 3)
A a
2
B
Fran made 9 trays of creampuffs. Each tray had 5 rows with 5 puffs in each row. What number sentence can be used to find how many puffs she made using the associative property of multiplication? A a 9×5=5×9 B a
9 × (5 + 5) = (9 × 5) + (9 × 5)
Ca
9 × 5 = 9 × (5 × 1)
D
(5 × 5) × 9 = 5 × (5 × 9)
62 I Smart to the Core I Educational Bootcamp
6
Select all of the equations that can be used to find 2 × (6 + 4). (6 × 2) × (4 × 2) (2 × 6) × 4 2 × 10 (2 × 6) + (2 × 4) 2 × 20
7
Answer the questions below.
A. Use variables a, b, and/or c to create B. Use variables a, b, and/or c to create the formula for identity property of the formula for commutative property multiplication. Explain this property of of multiplication. Explain this property multiplication using your own words of multiplication using your own words and give an example. and give an example.
8
Answer the questions below.
A. Use variables a, b, and/or c to create B. Use variables a, b, and/or c to create the formula for associative property of the formula for distributive property of multiplication. Explain this property of multiplication. Explain this property of multiplication using your own words multiplication using your own words and give an example. and give an example.
63 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Study the sets of equations below. Use the equations to complete the tasks.
×
×
× × ×
×
×
× ×
× ×
×
× ×
×
×
×
×
×
×
×
Part I: Select the equation that shows the commutative property of multiplication.
Part II: Select the equation that shows the associative property of multiplication.
Part III: Select the equation that shows the distributive property of multiplication.
Part IV: Select the equation that shows the identity property of multiplication.
64 I Smart to the Core I Educational Bootcamp
MISSION 6: Using Division as An unknown factor Problem Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
Bootcamp STRATEGY 1: Use arrays to relate multiplication and division as inverse operations. Example: 32 ÷ 8 32
4
÷
×
8
8
= 32
=4
8 rows of 4 = 32 8 × 4 = 32 32 ÷ 8 = 4
Bootcamp STRATEGY 2: Use bar models to relate multiplication and division as inverse operations. Example: 32 ÷ 8
8 × ? = 32 +4
+4
+4
+4
+4
+4
+4
+4
32
65 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 3.OA.6 (3.OA.2.6) DIRECTIONS: Use arrays or bar models to find the missing number that makes each equation true.
1
18 = 3 × ____
therefore,
18 ÷ 3 = ____
2
____ ÷ 7 = 6
therefore,
7 × 6 = ____
3
24 = 6 × ____
therefore,
24 ÷ 6 = ____
4
____ ÷ 8 = 9
therefore,
8 × 9 = ____
5
36 = 9 × ____
therefore,
36 ÷ 9 = ____
6
40 = 8 × ____
therefore,
40 ÷ 8 = ____
66 I Smart to the Core I Educational Bootcamp
Target PRACTICE 1 1
Carlos received a score of 72 for correctly answering 8 questions on a math test. Each question was worth the same number of points. How many points was each question worth? 8×
= 72
72 ÷
2
Anthony planted 54 flowers in 6 rows. He planted an equal number of flowers in each row. How many flowers did he plant in each row? 6×
= 54
54 ÷
=6
=8
A a
5
A a
4
B a
7
B a
6
Ca
8
C
9
D
9
D a
12
3
Jennifer made pitchers of lemonade. She used 5 ounces of mix for each pitcher of lemonade. If she used 35 ounces of mix, how many pitchers of lemonade did she make? Grid your answer.
4
Julie watched 27 movies during summer vacation. If she watched the same number of movies each month for the 3 months of her vacation, how many movies did she watch each month? Grid your answer.
5
Select all the statements that are correct. 70 ___ = 10
6
Select all the statements that are correct. 56 ___ = 8
Related multiplication expression: 70 × 10 = n.
3 should go in the blank.
6 should go in the blank.
Related multiplication expression: n × 8 = 56
7 should go in the blank.
7 should go in the blank.
Related division expression: 70 ÷ 10 = n.
Related division expression: 56 ÷ 8 = n
10 should go in the blank.
4 should go in the blank.
Related multiplication expression: 10 × n = 70.
Related multiplication expression: 8 × n = 56
67 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.OA.6 (3.OA.2.6) DIRECTIONS: Use arrays or bar models to find the missing number that makes each equation true.
1
49 = 7 × ____
therefore,
49 ÷ 7 = ____
2
____ ÷ 8 = 6
therefore,
8 × 6 = ____
3
30 = 10 × ____
therefore,
30 ÷ 10 = ____
4
____ ÷ 5 = 8
therefore,
5 × 8 = ____
5
64 = 8 × ____
therefore,
64 ÷ 8 = ____
6
56 = 7 × ____
therefore,
56 ÷ 7 = ____
68 I Smart to the Core I Educational Bootcamp
Target PRACTICE 2 1
Mari made 30 caps using 5 different colors. She made the same number of caps in each color. How many caps of each color did Mari make? Grid your answer. 5×
3
5
= 30
30 ÷
4
= 24
24 ÷
16 ____ = 2
21 ____ = 3
28 ____ = 7
56 ____ = 7
24 ____ = 3
35 ____ = 5
30 ____ = 6
63 ____ = 9
45 ____ = 5
24 ____ = 4
32 ____ = 8
3+
6
=4
Which of the following equations can be completed by the number 8? Select all that apply.
36 ____ = 6
There are 27 kids in a cafeteria. There are 3 kids sitting at each table. What equation can be used to find the number of tables in the cafeteria?
B
Factory workers make 24 machine parts in 4 hours. The workers make the same number of machine parts each hour. How many machine parts do they make each hour? Grid your answer. 4×
=5
Which of the following equations can be completed by the number 7? Select all that apply.
A a
2
A photo album has 49 pictures. There are 7 pictures on each page. What equation can be used to find the number of pages in the photo album?
= 27
A a
7 × 49 =
× 3 = 27
B a
49 + 7 =
Ca
3 × 27 =
C
D a
27 + 3 =
D a
× 7 = 49 7+
= 49
69 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.OA.6 (3.OA.2.6) DIRECTIONS: Solve the problems below. 1
Fiona had a party at her house and put 24 cups of soda on the table as shown in the model below. Using the concept of arrays, explain how many glasses there are in 1 row and in 1 column. 4 rows × _______ = 24 cups 6 columns × _______ = 24 cups
2
Laura brought 20 cupcakes to school on her birthday and gave 2 cupcakes to each of her friends. Explain how many friends she has.
3
The figure shown below represents the seating arrangement of a school bus. Explain how many seats there are in the bus. Use the concept of arrays. 4 seats × _________ rows = _________ seats in total
= 2 seats
4
Mia reads 5 pages of a storybook every night before she goes to sleep. If the storybook contains 25 pages, how many days will it take her to complete the storybook?
5
The figure shown below represents the number of desks in a classroom. There are 3 students to each desk. Explain how many seats are available in the classroom. Use the concept of arrays to solve.
= 1 desk
6
Kandy bought 32 rings and packed them in 4 boxes. If she puts an equal number of rings in each box, explain how many rings are in each box. 4×
= 32
32 ÷ 4 = 70 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: Study the division cones below. Use the division cones to complete the tasks. 32 4 30 6 48 8
A
B
C
Complete each division cone by finding the quotient of the 2 numbers. Write your answer in the empty triangle in each division cone. Give a related multiplication equation for each division equation solved.
71 I Copying is strictly prohibited
Four-STAR CHALLENGE - 3.OA.6 (3.oa.2.6) 1
Select the equations that are related to the multiplication equation below.
16 2 Select the equations that are related to the multiplication equation below.
6 × 5 = 30
3
17 5
3 × 8 = 24
The equation 36 6 = 6
The equation 21 7 = 3
The equation 25 5 = 5
The equation 24 3 = 8
The equation 30 5 = 6
The equation 15 5 = 3
The equation 24 6 = 4
The equation 64 8 = 8
The equation 30 6 = 5
The equation 24 8 = 3
The equation 24 4 = 6
The equation 18 6 = 3
A factory processes 56 liters of olive oil. The oil is packaged in bottles. If each bottle contains 7 liters of oil, how many bottles does the factory process? Grid your answer.
Mrs. Bennett sewed 25 quilts. She sewed 5 quilts of each color. What equation can be used to find the number of colors Mrs. Bennett used?
Laurie bought a watch that costs $81. She plans to make payments of $9 each week until the watch is paid in full. How many payments will Laurie make? Grid your answer.
There are 15 birds in a pet store. 18 6 There are 3 birds in each birdcage. What equation can be used to find the number of birdcages in the pet store?
A a
5+
B a
25 + 5 =
B a
15 + 3 =
Ca
5 × 25 =
Ca
3 × 15 =
D a
3+
D
= 25
16 4
× 5 = 25
72 I Smart to the Core I Educational Bootcamp
× 3 = 15
A
= 15
7
Find the quotient to the division expression. Show your complete solutions.
A.
49 7 = ____
8
B.
56 8 = ____
Solve the word problems. Show your complete solutions.
A. Randy wants to share 45 apples equally B. John has 72 baseball cards. He wants to among his 5 friends. How many apples arrange the cards into 8 equal stacks. will he give to each of his friends? How many cards will he put in each stack?
73 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Study the division cones below. Use the division cones to complete the tasks. 36 6 28 7 56 8 63 9 50 10
A
B
C
D
E
Complete each division cone by finding the quotient of the 2 numbers. Write your answer in the empty triangle in each division cone. Give a related multiplication equation for each division equation solved.
74 I Smart to the Core I Educational Bootcamp
MISSION 7: MULTIPLYING AND DIVIDING WITHIN 100 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations.
Bootcamp STRATEGY 1: Use an array to write related multiplication and division facts. Example: 8 × 5 = 40 5
×
Related Facts: 8
8 × 5 = 40
40 ÷ 5 = 8
5 × 8 = 40
40 ÷ 8 = 5
= 40
Bootcamp STRATEGY 2: Use a number line to write related multiplication and division facts. Example: 8 × 5 = 40 ×5
×5
0 1 2
3 4 5
×8
×5
×5
×5
×5
×5
×5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
×8
×8
×8
×8
Related Facts:
8 × 5 = 40
40 ÷ 5 = 8
5 × 8 = 40
40 ÷ 8 = 5
75 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 3.OA.7 (3.OA.3.7) DIRECTIONS: Use an array or a number line to solve each equation below.
1
4 × 3 = ____
2
7 × 8 = ____
3
10 × 4 = ____
4
7 × 4 = ____
5
6 × 5 = ____
6
10 × 8 = ____
7
8 × 6 = ____
8
4 × 9 = ____
9
10 × 5 = ____
10
72 ÷ 8 = ____
11
36 ÷ 9 = ____
12
48 ÷ 6 = ____
13
18 ÷ 6 = ____
14
16
81 ÷ 9 = ____
17
76 I Smart to the Core I Educational Bootcamp
32 ÷ 8 = ____
35 ÷ 7 = ____
15
18
42 ÷ 7 = ____
40 ÷ 8 = ____
Target PRACTICE 1 1
3
There are 7 cars in a rally. Each driver paid a $5 fee to race in the rally. How much money did the drivers pay in all?
2
A a
$10
A a
14
B a
$12
B a
38
Ca
$25
Ca
41
D
$35
D
48
Select all the statements that are correct.
4
10 × 9 = ____
Related division expression: 6 ÷ 54.
The product is 108. Related multiplication expression: 9 × 10.
The quotient is 14. The quotient is 6. Related multiplication expression: 9 × 6.
The product is 99. The product is 72.
The quotient is 8.
Related division expression: 10 ÷ 9. Steve hikes 18 miles over the weekend. Every 3 miles along the hiking path, there is a trail post. How many trail posts will Steve see? Grid your answer.
Select all the statements that are correct.
54 6 = ____
The product is 90.
5
May competed in a fashion contest. Models were judged in 6 categories. May got 8 points in each category. How many points in all did May get?
The quotient is 9. 6
Jolie wants to arrange 20 bouquets of flowers on tables at a reception. Each table can have 4 bouquets. How many tables are there? Grid your answer.
77 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.OA.7 (3.OA.3.7) DIRECTIONS: Use an array or a number line to solve each equation below.
1
5 × 3 = ____
2
9 × 8 = ____
3
8 × 4 = ____
4
7 × 5 = ____
5
8 × 5 = ____
6
4 × 9 = ____
7
7 × 6 = ____
8
3 × 9 = ____
9
4 × 5 = ____
10
70 ÷ 10 = ____
11
45 ÷ 9 = ____
12
36 ÷ 6 = ____
13
30 ÷ 6 = ____
14
56 ÷ 8 = ____
15
49 ÷ 7 = ____
16
35 ÷ 7 = ____
17
78 I Smart to the Core I Educational Bootcamp
28 ÷ 7 = ____
18
36 ÷ 4 = ____
Target PRACTICE 2 1
3
5
Gabe is a goalkeeper of a soccer team. He played 7 games last month. If he caught 4 penalty kicks in each game, how many penalty kicks did he catch in all?
2
There are 4 apartment units on each floor of Lathan’s apartment building. If there are 8 floors, how many apartment units are there in the building?
A a
11
A
32
B
28
B a
22
Ca
35
Ca
12
D a
42
D a
48
Select the multiplication equations that are true.
4
Select the multiplication equations that are true.
The equation 6 × 6 = 30.
The equation 5 × 7 = 40.
The equation 3 × 5 = 15.
The equation 6 × 8 = 48.
The equation 4 × 7 = 21.
The equation 4 × 3 = 12.
The equation 8 × 5 = 40.
The equation 9 × 4 = 36.
The equation 9 × 6 = 54.
The equation 8 × 5 = 40.
The equation 7 × 8 = 48.
The equation 3 × 9 = 27.
Noah ordered 18 wheels for his skateboard. He received the wheels in packages of 3. How many packages of wheels did he receive? Grid your answer.
6
A farmer is buying 24 acres of land on which he can build new farms. If he uses 4 acres for each farm, how many farms can he build in all? Grid your answer.
79 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.OA.7 (3.OA.3.7) DIRECTIONS: Answer the questions below. 1 Steven bought 5 tickets to a puppet show. Each ticket cost him $3. Explain how you would use the number line below to find the total amount he spent on all the tickets. Show jumps of appropriate length on the number line when finding your answer.
0
20
2 Chris has 3 cupcakes. Each cupcake has 4 sprinkles on it. Explain how many sprinkles were used for all 3 cupcakes.
3 In a tennis tournament, the player used 4 packs of balls. Each pack contained 6 balls. Explain how many tennis balls the player used in the tournament.
4 Find the number of rows and columns in the array below. Using those numbers, write 2 unique multiplication sentences that describe the total number of circles in the array.
5 Megan bought 18 party favors for her party and distributed them equally among 3 tables. Draw circles around the number of party favors that will be on each table on the model below. How many party favors will be on each table?
80 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: Study the sets of multiplication expressions below. Use the sets of multiplication expressions to complete the tasks.
Part I: Find the products of the multiplication expressions using mental math and write the answer next to each expression.
Part II: Write 1 related division expression for each multiplication expression on the list.
Part III: Explain how division is related to multiplication.
81 I Copying is strictly prohibited
Four-STAR CHALLENGE - 3.OA.7 (3.oa.3.7) 13 1
13 3
17 5
It took Laurie 6 weeks to complete her assignment. There are 7 days in 1 week. How many days are in 6 weeks?
14 2
Kapadia saw 8 lifeguard towers at the beach. Each tower had 3 lifeguards. How many lifeguards were there in all?
A a
13
A a
11
B a
24
B
24
Ca
36
Ca
34
D
42
D a
42
Which division equations below are true? Select all that apply.
14 4
Which division equations below are true? Select all that apply.
The equation 42 7 = 6
The equation 21 7 = 3
The equation 48 6 = 6
The equation 36 9 = 4
The equation 25 5 = 5
The equation 35 5 = 5
The equation 18 2 = 8
The equation 25 4 = 6
The equation 30 5 = 6
The equation 34 5 = 7
The equation 16 8 = 2
The equation 60 8 = 8
Dimitri drove 21 miles to visit his grandparents. Every 3 miles, he stopped at a traffic light. How many times did Dimitri stop at traffic lights? Grid your answer.
82 I Smart to the Core I Educational Bootcamp
Raye went on vacation for 16 days. 18 6 She stayed 4 days at each city. How many cities did she visit? Grid your answer.
7
Using mental math, find the products of the multiplication expressions as fast as you can.
A.
8×4=?
C.
7×8=?
8
A.
C.
B.
D.
6×7=?
9×8=?
Using mental math, find the quotients of the division expressions as fast as you can.
28 7 = ?
40 8 = ?
B.
D.
24 6 = ?
27 9 = ?
83 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Study the set of division expressions below. Use the set of division expressions to complete the tasks.
50 ÷ 5 = 36 ÷ 6 = 56 ÷ 7 = 48 ÷ 8 = 81 ÷ 9 = Part I: Find the quotients of the division expressions using mental math and write the answer next to each expression. Part II: Write 1 related multiplication expression for each division expression on the list.
Part III: Explain how multiplication is related to division.
84 I Smart to the Core I Educational Bootcamp
MISSION 8: Solving Two-Step Word Problems Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Bootcamp STRATEGY 1: Use a bar model to solve two-step addition and subtraction word problems. Example: Maria has a bracelet that has 57 stones. Patrice has 2 bracelets. There is 1 bracelet that has 12 stones and the other has 31 stones. How many more stones does Maria’s bracelet have than Patrice’s 2 bracelets combined? Maria Patrice
57 stones 12 stones
31 stones
?
Step 1: Add Patrice’s stones together. 12 + 31 = 43 Step 2: Subtract to find the difference between the total number of Patrice’s stones and Maria’s stones. 57 − 43 = 14; therefore, Maria has 14 more stones on her bracelet than Patrice has on her 2 bracelets.
Bootcamp STRATEGY 2: Represent two-step word problems using equations with a letter standing for the unknown quantity. Example: A farmer planted a vegetable garden over 2 days. On the first day, he planted 7 rows of peas and 6 rows of beans. On the second day, he planted 9 rows of corn. How many rows of vegetables did he plant in all? Let V = number of vegetables planted
Step 1: Add the number of rows of vegetables the farmer planted on the first day: V=7+6 V = 13
Step 2: Add the answer you got in Step 1 to the number of rows the farmer planted on the second day: V = 13 + 9 V = 22
Example: There are 2 girl scouts troops that participated in a cookie sale last Saturday. Troop 1 sold 5 cases and Troop 2 only sold 5 boxes. Each case contains 4 boxes of cookies. How many cookies did the 2 girl scout troops sell in all? Let C = number of boxes of cookies sold by both troops
Step 1: Multiply to find the number of boxes of cookies Troop 1 sold: C=5×4 C = 20 Step 2: Add the product you got in Step 1 to the number of cookies Troop 2 sold: C = 20 + 5 85 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 3.OA.8 (3.OA.4.8) DIRECTIONS: Underline the key words and circle the numbers in the following word problems.
1
There were 522 bottles of water and 123 bottles of soda in a cooler before a company picnic. There were 352 beverages taken from the cooler in all. How many beverages were left after the picnic?
2
Van has 76 votes for class president, Deidra has 57 votes for class president, and 10 people voted for Ian as class president. How many votes were placed in all?
3
Katie had 49 ounces of homemade cleanser, but spilled 7 ounces of it. She wants to pour the remaining cleanser into 6 containers equally. How many ounces of cleanser will be in each container?
4
Frankie needs 72 party favors for a New Year's Eve party. He has 23 party favors left over from last year and 12 party favors that were given to him by his neighbor. How many more party favors does he need?
5
There were 2 girl scouts troops that participated in a cookie sale last Saturday. Troop 1 sold 5 cases, and Troop 2 sold 6 cases. Each case contains 5 boxes of cookies. How many boxes of cookies did the 2 girl scout troops sell in all?
86 I Smart to the Core I Educational Bootcamp
Target PRACTICE 1 1
3
On Monday, Carla read 254 pages of her new book. On Tuesday, she read 18 fewer pages than on Monday. How many pages did Carla read in all on Monday and Tuesday? Grid your answer.
Mr. Rodriguez owns 2 aquariums. Each aquarium has 9 goldfish and 4 angelfish. If f is the total number of fish in the aquariums, select all the statements that are true.
2
4
f = 2 × (9 × 4)
5
Amy had 5 cartons of eggs with 4 eggs in each carton. She used 3 eggs. How many eggs did Amy have left? Grid your answer.
Arthur bought 3 boxes of donuts. Each box contains 10 donuts. He equally divides the donuts between his 5 nephews. If d is the number of donuts each nephew will get, select all the statements that are true. d = 15
f = 2 × (4 + 9)
d = (3 + 10) 5
f = 2 + (9 + 4)
d = (10 + 3) 5
f = (9 + 4) × 2
d = (3 × 10) 5
f = 26
d = 5 (3 × 10)
f = 38
d=6
Lita bought 5 packages of tennis balls. Each package has the same number of tennis balls. Her coach gave her 4 more tennis balls. Now she has 39 tennis balls. How many tennis balls were in each package?
6
Sierra bought 4 cupcakes for $7 each. She gave the cashier $30. How much change should Sierra get?
A a
5
A
$2
B
7
B a
$4
Ca
35
Ca
$7
D a
39
D a
$28 87 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.OA.8 (3.OA.4.8) DIRECTIONS: Underline the key words and circle the numbers in the following word problems. 1
The Brooks family has been saving canned goods for an emergency. They had 61 canned goods, but they donated 25 of them for a food drive. They purchased 15 more canned goods. How many canned goods does the family have?
2
A restaurant has 35 ounces of maple syrup brought out for the early morning customers and 28 ounces brought out for the early afternoon customers. At the end of the day, they only had 15 ounces of maple syrup left. How many ounces of maple syrup did the customers use?
3
The third grade students are having a holiday party. There are 18 students in the class. Each student brings $2, and the teacher gives $30. How much money has been collected for the holiday party in all?
4
An office clerk has 6 packs of pens to split evenly among staff members. Each pack has 3 pens. If there are 2 staff members in the office, how many pens will each staff member get?
5
Francis wants to buy a music collection that costs $89. He has $65 saved and plans on saving the rest with the money from his weekly newspaper delivery job. He can save $4 each week to buy the collection. How many weeks will it take Francis to earn the rest of the money needed to buy the music collection?
88 I Smart to the Core I Educational Bootcamp
Target PRACTICE 2 1
3
5
In 1 week, 412 people went to a movie theater. The next week, 24 fewer people came than the week before. How many people came in all during those 2 weeks? Grid your answer.
Mai bought 15 apples at the market. She gives her daughter 6 apples, and equally divides the rest between her 3 nieces. If a is the number of apples each niece will get, which equations below can be used to find a.
2
4
Normally, Ms. Silva separates her students into 5 equal groups with 3 students in each group for field trips. If 4 students are absent today, how many students are present on the field trip? Grid your answer.
There are 14 crayons left in Ms. Granger’s classroom. She bought 6 more boxes of crayons. Each box has 10 crayons. If c is the total number of crayons the school will have, which equations below can be used to find c?
a=9
c = (6 × 10) + 14
a = (15 6) 3
c = (10 × 6) + 14
a=3
c = 14 + (6 × 10)
a = 3 (15 - 6)
c = 14 + (10 × 6)
a = (15 - 6) 3
c = 44
Annabelle went to lunch with 4 of her friends. The total bill was $50, and they divided it evenly. Annabelle left $5 for tip. How much did she spend on lunch?
6
Deon sold 7 books for $5 each. The customer gave him $40. How much change should Deon give back to the customer?
A a
$10
A a
$2
B
$15
B
$5
Ca
$20
Ca
$7
D a
$25
D a
$15 89 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.OA.8 (3.OA.4.8) DIRECTIONS: Answer the questions below. 1
Mya was scheduled to work 40 hours over 5 days last week. On Friday, she decided to pick up 3 extra hours to help her coworker. How many hours did she work on Friday?
2
Karen has a bookshelf in her room. So far she has placed 6 books on each section of the bookshelf. She still has 10 more books to put on the shelf. How many books does she have in all?
Bookshelf
3
A school has 4 buses. Each bus uses a different amount of gas each day. The north bus uses 5 liters of gas per day, the east bus uses 8 liters, the west bus uses 3 liters, and the south bus uses 6 liters. How many more liters does the East and West bus use together than the North bus? Determine how much each bus uses at the end of 5 days Bus
4
Day 1 Day 2 Day 3 Day 4 Day 5 Total
North
5
5
5
5
5
East
8
8
8
8
8
West
3
3
3
3
3
South
6
6
6
6
6
Mr. Swanson has 15 oranges and 5 apples. He wants to make 4 gift baskets that have the same amount of fruits in each. How many fruits are in each basket?
5 Mario is saving money to buy tickets to a basketball game. So far, he only has $28. Luckily, his father gave him $12 to help him save. If each ticket costs $4, how many tickets can he buy now?
90 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: Determine the value of the letter for each of the expressions below. Note: Perform the operations in the bubble labeled “first” before performing the operations labeled “second”.
(14 − a)
÷3=2
First
Second
(36 ÷ b)
+ 20 = 26
First
Second
(20 ÷ c)
+ 44 = 48
First
Second
(15 − d)
÷3=3
First
Second
(18 ÷ e)
× 10 = 20
First
Second
91 I Copying is strictly prohibited
Four-STAR CHALLENGE - 3.OA.8 (3.oa.4.8) 13 1
3
5
In the first month, a bakery sold 365 loaves of bread. In the second month, it sold 69 fewer loaves than in the first month. How many loaves did the bakery sell in those 2 months? Grid your answer.
Lisa bought a 3-pack of gum. Each pack of gum has 10 pieces. If she gave 5 pieces of gum away, how many pieces of gum does Lisa have left?
14 2
16 4
Lia divided her books into 6 groups with 3 books in each group. She lent 4 books to her friend. How many books did Lia have left? Grid your answer.
Yasmin had $51. Each day for the past 6 days, she spent $3. How much more does she have to spend before she does not have any money left?
A
25
A a
17
B a
30
B a
18
Ca
35
Ca
21
D a
40
D
33
Select all the equations where t = 20.
16 6 Select all the equations where t = 30.
(4 × 8) - 12 = t
(5 × 10) 3 = t
(20 2) - 20 = t
(15 + 25) − 3 = t
(8 + 2) × 2 = t
24 + (30 5) = t
(35 - 20) + 15 = t
3 × (20 2) = t
25 + (30 10) = t
(6 × 10) 3 = t
(5 + 5) + 10 = t
10 + (4 × 5) = t
92 I Smart to the Core I Educational Bootcamp
7
Give the equation that can be used to solve each word problem. Solve the word problem using the equation.
A.
B. Liam’s class is going on a field trip. There are 60 kids in total. They will be broken up into groups of 10. There will be 3 chaperons to each group of 10. How many chaperons will there be? Write the equation and solve.
C.
For a baseball game, 565 tickets were sold during presale. Of those tickets, 59 were returned. On game day, 384 tickets were sold at the door. How many tickets were sold in all? Write the equation and solve.
D. Jenna has $216 saved. Andy has $144 saved. They used the combined savings to buy tickets to a concert that costs a total of $198, and will use the remaining money for the trip to the concert. How much do they have left after purchasing the concert tickets? Write the equation and solve.
For an art show, 9 artists created 5 works of art each. By the end of the show, 16 art pieces were sold. How many art pieces remained? Write the equation and solve.
93 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 8
DIRECTIONS: The value of the letter will be the same for both unknowns. Determine the value of the letter for each of the expressions below. Note: Perform the operations in the bubble labeled “first” before performing the operations labeled “second”.
(7 × m) First
(3 + n) First
(20 − r) First
(64 ÷ p) First
(49 − q) First
94 I Smart to the Core I Educational Bootcamp
+ (6 × m) = 39 Second
× (5 + n) = 35 Second
÷ (10 − r) = 3 Second
− (48 ÷ p) = 2 Second
+ (21 − q) = 52 Second
MISSION 9: IDENTIFYING PATTERNS Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
Bootcamp STRATEGY 1: Create a drawing to model arithmetic patterns. Example: 4, 8, 12, 16, ? 4
8
12
16
20
?
=
20 squares
Bootcamp STRATEGY 2: Use a multiplication table to help identify arithmetic patterns. Example: 4, 8, 12, 16, ?
X
1
2
3
4
5
6
7
8
9
10
11
12
1
1
2
3
4
5
6
7
8
9
10
11
12
2
2
4
6
8
10
12
14
16
18
20
22
24
3
3
6
9
12
15
18
21
24
27
30
33
36
4
4
8
12
16
20
24
28
32
36
40
44
48
5
5
10
15
20
25
30
35
40
45
50
55
60
6
6
12
18
24
30
36
42
48
54
60
66
72
7
7
14
21
28
35
42
49
56
63
70
77
84
8
8
16
24
32
40
48
56
64
72
80
88
96
9
9
18
27
36
45
54
63
72
81
90
99
108
10
10
20
30
40
50
60
70
80
90
100
110
120
11
11
22
33
44
55
66
77
88
99
110
121
132
12
12
24
36
48
60
72
84
96
108
120
132
144
95 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 3.OA.9 (3.OA.4.9) DIRECTIONS: Complete the patterns below.
1
12, 14, 16, 18, 20, 22, 24,
,
3
100, 90, 80, 70, 60, 50,
5
5, 9, 13, 17, 21,
7
68, 77, 86, 95,
9
66, 79, 92, 105, ___ , ___ , ___
,
,
,
11 46, 39, 32, 25, ___ , ___ , ___
96 I Smart to the Core I Educational Bootcamp
2
0, 3, 6, 9, 12, 15, 18, 21,
,
4
27, 24, 21, 18, 15, 12, 9, 6,
6
68, 71, 74, 77,
8
4, 12, 20, 28,
10
88, 77, 66, 55, ___ , ___ , ___
12
17, 21, 25, 29, ___ , ___ , ___
,
,
,
Target PRACTICE 1 1
Select the true statements based on the table.
4
Select the true statements based on the table.
INPUT (x)
OUTPUT (y)
INPUT (x)
OUTPUT (y)
5
2
3
6
10
7
6
12
15
12
9
18
20
17
10
20
Rule: Subtract 2
If x: 30, y: 27
Rule: Add 3
If x: 7, y: 10
Rule: Divide by 3
If x: 57 , y: 60
Rule: Add 5
If x: 4, y: 9
Rule: Subtract 3
If x: 24 , y: 20
Rule: Multiply by 2
If x: 5, y: 10
Use the multiplication table for 2–3.
Use the table for 5–6.
Clara is making necklaces. The table shows how many stones she will need.
5
2
3
Which row of the table has only even numbers? A a
Row 3
Ca
Row 5
B
Row 4
D a
Row 7
6
Necklace
2
3
4
Stones
10 15 20
5
6
Which 2 numbers below complete the table? A a
21 and 26
C
25 and 30
B a
23 and 28
D a
27 and 32
Which of the following describes the pattern in this table?
Which statement below describes the pattern in Column 5? A a
All the products are even.
A a
Add 8
B a
All the products are odd.
B a
Subtract 5
Ca
Each product is twice the product above it.
Ca
Multiply by 8
D
Each product is 5 more than the product above it.
D
Multiply by 5
97 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.OA.9 (3.OA.4.9) DIRECTIONS: Complete the patterns below.
2
39, 42, 45, 48, 51, 54, 57,
4
113, 106, 99, 92, 85, 78, 71,
6
65, 68, 71, 74,
8
2, 4, 6, 8,
2, 4, 6, 8, 10, 12, 14, 16, _____, _____, _____
10
91, 87, 83, 79, _____, _____, _____
5, 10, 15, 20, 25, 30, 35, _____, _____, _____
12
1, 2, 4, 8, _____, _____, _____
1
24, 32, 40, 48, 56, 64, 72,
3
119, 103, 87, 71, 55, 39,
5
5, 8, 11, 14, 17,
7
11, 23, 35, 47,
9
11
,
,
,
,
98 I Smart to the Core I Educational Bootcamp
,
,
,
,
Target PRACTICE 2 1
The table below follows the rule “add 5”. Select the missing numbers.
4
The table below follows the rule “multiply by 3”. Select the missing numbers.
INPUT
OUTPUT
2
7
INPUT
OUTPUT
4
9
1
3
6
11
3
9
8
?
5
15
?
?
7
?
?
?
The number 12
The number 10
The number 13
The number 20
The number 9
The number 21
The number 14
The number 16
The number 12
The number 27
The number 24
The number 32
Use the multiplication table for 2–3.
Use the table for 5–6.
Ms. Hall is buying candy for her students. The table shows how much candy she will buy.
5
2
3
Which column of the table has only even numbers? A a
Column 7
C
Column 4
B a
Column 5
D a
Column 3
Which statement below describes the pattern in Column 7? A Each product is 7 more than the product above it. B a
All the products are odd.
Ca
Each product is twice the product above it.
D a
All the products are even.
6
Students
5
Candy
15
6
7
21
8
9
27
Which 2 numbers below complete the table? A a
17 and 23
Ca
19 and 25
B
18 and 24
D a
20 and 26
Which of the following describes the pattern in this table? A a
Subtract 3
B a
Add 10
Ca
Multiply by 10
D
Multiply by 3
99 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.OA.9 (3.OA.4.9) DIRECTIONS: Answer the questions below. Use the multiplication table for Questions 1–2.
1 Explain which row and column products alternate between only 0 or 5 in the ones place. Write the products of the whole row.
2 Identify all the rows in the table above that have products which follow the pattern of alternating between an odd number and an even number 10 times.
3
Kate is playing a game of chance at the local fair. To win the game, all you have to do is press a button, and the machine will randomly stop at a number; if the number is even, you get a prize, but if the number is odd, you lose. The first time Kate played, she got the number 70. Did Kate get a prize? Explain your answer.
4
Nina is buying chocolates for her friends. She wants to give the same number of chocolates to each friend. The table below shows how many chocolates she would need, depending on the number of friends she has. Determine what the missing values are and explain how you got your answer. Friends
3
4
5
6
7
Chocolates
18
24
30
?
?
100 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: Study the 4 input/output tables below. Use the tables to complete the tasks. Table 1
Table 2
Table 3
Table 4
Input
Output
Input
Output
Input
Output
Input
Output
1
9
10
8
1
2
20
10
2
10
8
6
2
4
10
5
4
12
6
4
3
6
8
4
5
13
5
3
5
10
4
2
Part I: Study the numbers in Table 1. Find the rule being followed in Table 1. Explain how you were able to determine the rule.
Part II: Study the numbers in Table 2. Find the rule being followed in Table 2. Explain how you were able to determine the rule.
Part III: Study the numbers in Table 3. Find the rule being followed in Table 3. Explain how you were able to determine the rule.
Part IV: Study the numbers in Table 4. Find the rule being followed in Table 4. Explain how you were able to determine the rule.
101 I Copying is strictly prohibited
Four-STAR CHALLENGE - 3.OA.9 (3.oa.4.9) 1 Select all the tables that use the rule “add 2”. INPUT
OUTPUT
INPUT
4 Select all the tables that use the rule “multiply by 4”. INPUT
OUTPUT
OUTPUT
INPUT
OUTPUT 4
10
12
20
22
2
8
1
11
13
40
24
4
16
3
12
12
14
50
26
6
24
5
20
13
15
60
28
8
32
7
28
INPUT
OUTPUT
INPUT
OUTPUT
INPUT
OUTPUT
INPUT
OUTPUT
5
7
1
2
1
4
5
20
6
8
3
6
2
8
6
24 28 32
7
9
6
12
3
12
7
8
10
8
16
4
16
8
Use the table for 5–6.
Use the multiplication table for 2–3.
Mr. Bond is putting players into groups. The table shows how many players there would be depending on the number of groups. Groups
3
Players
5
2
Which row of the table has only odd numbers? A Ca Row 7 a Row 3 B a
3
D None of them Row 5 Which statement below describes the pattern in Column 9?
6
4
24 30
6
7
42
Which 2 numbers below complete the table? A a
16 and 34
C
18 and 36
B a
17 and 35
D a
19 and 37
Which of the following describes the pattern in this table?
A a
Each product is twice the product above it.
A a
Multiply by 9
B a
All the products are odd.
B
Multiply by 6
C
Each product is 9 more than the product above it.
Ca
Subtract 6
D a
All the products are even.
D a
Add 9
102 I Smart to the Core I Educational Bootcamp
5
7
Complete the addition and subtraction input/output tables below following the given rules in the table.
A.
B. Rule: Add 5 Input
8
Rule: Subtract 2
Output
Input
Output
1
1
2
2
4
3
5
8
10
10
15
13
Complete the multiplication and division input/output tables below following the given rules in the table.
A.
B. Rule: Multiply by 4 Input
Output
Rule: Divide by 3 Input
Output
1
1
2
2
4
3
5
5
10
10
103 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
Part I: Complete each input/output table following the rules indicated in each table. Use the space below to do your computation and fill in your answers in the tables.
Rule: Add 6 Input
Output
Rule: Subtract 5 Input
Output
Rule: Multiply by 7 Input
Output
Rule: Divide by 5 Input
1
10
1
20
2
8
2
15
4
6
3
10
5
5
5
5
Part II: Write a short explanation of what an input/output table is.
104 I Smart to the Core I Educational Bootcamp
Output
MISSION 10: rounding whole numbers Use place value understanding to round whole numbers to the nearest 10 or 100.
Bootcamp STRATEGY 1: Use place values to round multi-digit whole numbers.
9,273 STEP 1: Underline the targeted digit to be rounded. STEP 2: Look at the number to the right of the underlined digit. If that number is 0 – 4, then the underlined digit stays the same. If the number is 5 – 9, then the underlined digit increases by 1. STEP 3: Change all of the digits to the right of the targeted digit to zeros. The rounded number becomes:
9,300
Bootcamp STRATEGY 2: Use a number line to round multi-digit whole numbers.
9,273 STEP 1: Underline the targeted digit to be rounded. STEP 2: Draw a number line with interval lines at the far right and the left sides of the line. STEP 3: Keep the targeted digit the same and change all of the digits to the right of the targeted digit to zeros. The new number will be 9,200. Place this number on the far left side of the number line. 9,200
STEP 4: Increase the targeted digit by 1 number and change all of the digits to the right of the targeted digit to zeros. 9,200
9,300
STEP 5: Add interval lines in to allow for the number that needs to be rounded to be placed on the number line. Place a dot on the line that represents the number to be rounded. 9,200
9,273
9,300
The number is closest to 9 , 3 0 0. Therefore, this is the rounded number. 105 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 3.NBT.1 (3.NBT.1.1) DIRECTIONS: Use a number line to help round the numbers below to the nearest 10.
1
567
2
713
3
675
4
137
DIRECTIONS: Use a number line to help round the numbers below to the nearest 100.
5
938
6
659
7
398
8
596
DIRECTIONS: Round to the nearest 10.
DIRECTIONS: Round to the nearest 100.
9
159
15
159
10
293
16
293
11
718
17
718
12
649
18
649
13
989
19
989
14
658
20
658
106 I Smart to the Core I Educational Bootcamp
Target PRACTICE 1 1
3
5
A printing press printed 817 pages of a book yesterday. What is 817 rounded to the nearest 10?
2
It takes the dwarf planet Pluto 247 years to revolve once around the sun. What is 247 rounded to the nearest 100?
A a
800
A
200
B a
810
B a
240
C
820
Ca
250
D a
900
D a
300
Mike correctly rounded the number 466. Select all the statements that are true.
4
Tony correctly rounded the number 781. Select all the statements that are true.
Rounded to the nearest 100’s: 400
Rounded to the nearest 10’s: 780
Rounded to the nearest 100’s: 300
Rounded to the nearest 10’s: 790
Rounded to the nearest 100’s: 500
Rounded to the nearest 10’s: 770
Rounded to the nearest 10’s: 460
Rounded to the nearest 100’s: 670
Rounded to the nearest 10’s: 470
Rounded to the nearest 100’s: 680
Rounded to the nearest 10’s: 450
Rounded to the nearest 100’s: 600
What is 684 rounded to the nearest 10? Grid your answer.
6
What is 991 rounded to the nearest 100? Grid your answer.
107 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.NBT.1 (3.NBT.1.1) DIRECTIONS: Use a number line to help round the numbers below to the nearest 10.
1
465
2
823
3
974
4
331
DIRECTIONS: Use a number line to help round the numbers below to the nearest 100.
5
741
6
592
7
301
8
172
DIRECTIONS: Round to the nearest 10.
DIRECTIONS: Round to the nearest 100.
9
492
15
492
10
513
16
513
11
218
17
218
12
649
18
649
13
789
19
789
14
158
20
158
108 I Smart to the Core I Educational Bootcamp
Target PRACTICE 2 1
3
5
A bus driver travels 334 miles every day. What is 334 rounded to the nearest 10?
2
The total weight of the Statue of Liberty is 225 tons. What is 225 rounded to the nearest 100?
A a
300
A
200
B
330
B a
220
Ca
340
Ca
230
D a
400
D a
300
Select all the numbers that when rounded to the nearest tens is 810.
4
Select all the numbers that when rounded to the nearest hundreds is 200.
The number 800
The number 280
The number 809
The number 240
The number 814
The number 260
The number 792
The number 180
The number 794
The number 170
The number 798
The number 190
What is the greatest number that can be rounded to 500 when rounding to 100? Grid your answer.
6
What is the least number that can be rounded to 500 when rounding to 100? Grid your answer.
109 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.NBT.1 (3.NBT.1.1) DIRECTIONS: Answer the questions below. 1
Stacy bought a pack of 990 sheets of copy paper for the office. Round this number to the nearest 100.
2
What is 639 rounded to the nearest hundred? What is 639 rounded to the nearest 10?
3
Write all of the numbers that round to 250 when rounding to the nearest 10 that are less than 250.
4 Write all of the numbers that round to 250 when rounding to the nearest 10 that are greater than 250.
5 Write all of the numbers that round to 590 when rounding to the nearest 10.
6
What is 978 rounded to the nearest 100? What is 998 rounded to the nearest 10?
110 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: Use the number below to solve the questions.
794 Part I: Alan just beat his old score in his favorite video game. His new score is shown above. How would he write this number rounded to the nearest 10? ________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________
Part II: If he wants to round his score to the nearest 100, what would be his score? Explain how to round the number and write his score. ________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________
Part III: Alan’s brother, Aiden, has a high score of 775. Do they have the same score when rounded to the nearest 10? Explain why or why not. ________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________
Part IV: Does Aiden have the same score as Alan when rounding to the nearest 100? Explain why or why not. ________________________________________________________________________________________________________________
________________________________________________________________________________________________________________
111 I Copying is strictly prohibited
Four-STAR CHALLENGE - 3.NBT.1 (3.nbt.1.1) 1
3
5
A company manufactures 594 toy cars each day. What is 594 rounded to the nearest 10?
2
The Empire State Building in New York City is 443 meters tall. What is 443 rounded to the nearest 100?
A a
600
A a
500
B
590
B a
450
Ca
580
Ca
440
D a
500
D
400
Study the table below. Select the statements that are correct.
4
Study the table below. Select the statements that are correct.
Player
Points
Name
Savings
John
18
Diana
$344
Mathew
24
Sarah
$569
John’s number of points is 20 when rounded to the nearest tens.
Diana’s savings is $300 when rounded to the nearest hundreds.
John’s number of points is 10 when rounded to the nearest tens.
Diana’s savings is $400 when rounded to the nearest hundreds.
Mathew’s number of points is 20 when rounded to the nearest tens.
Diana’s savings is $500 when rounded to the nearest hundreds.
Mathew’s number of points is 30 when rounded to the nearest tens.
Sarah’s savings is $500 when rounded to the nearest hundreds.
Mathew’s number of points is 25 when rounded to the nearest tens.
Sarah’s savings is $600 when rounded to the nearest hundreds.
What is the greatest number that can be rounded to 900 when rounding to the nearest 100? Grid your answer.
112 I Smart to the Core I Educational Bootcamp
6
What is the least number that can be rounded to 900 when rounding to the nearest 100? Grid your answer.
7
Plot the Points A through E that are given below. Determine what each number is when rounded to the nearest tens and hundreds by filling out the table below. Explain how to round to the nearest tens and then hundreds.
0
Points
Numbers
Point A
165
Point B
247
Point C
398
Point D
102
Point E
451
100
Rounded to Nearest Tens
200
Rounded to Nearest Hundreds
300
400
500
___________________________________________________________________________________________________________ ___________________________________________________________________________________________________________ ___________________________________________________________________________________________________________
8
Jose is solving a math question and wants to round the number 287. Part I: Where will the point be on the number line if he rounds 287 to the nearest 100? Place an “x” on the rounded number and explain your reasoning.
250
260
270
280
290
300
310 320
______________________________________________________________________________ ______________________________________________________________________________
Part II: Find 2 other numbers that when rounded to the nearest 100, will get the same number as in Part I. Write the 2 possible answers below.
First possibility: ______________
Second possibility: ______________
113 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Use the numbers given below to solve the questions. Master Number
926 Number Bank:
100
800 930
2,000 193
900 190
949 19
920 950
Part I: Alison has to round the master number to the nearest 100. What number from the number bank will be the correct answer? Write the answer below. __________________________________________________________________________________________________________ __________________________________________________________________________________________________________ __________________________________________________________________________________________________________
Part II: Help Alison round the master number to the nearest 10. What number from the number bank should Alison choose? Write the answer below and explain how you got your answer. _________________________________________________________________________________________________________ _________________________________________________________________________________________________________
Part III: If Alison’s master number is 1,000, what is the least number from the number bank above that could round to 1,000 when rounded to the nearest 100? _________________________________________________________________________________________________________ _________________________________________________________________________________________________________
114 I Smart to the Core I Educational Bootcamp
MISSION 11: ADDING AND SUBTRACTING WHOLE NUMBERS Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Bootcamp STRATEGY: Use place value charts to add/or subtract whole numbers. Example: 273 + 451 = 724 Stack the numbers by place value and add each place value column. Regroup as necessary. HUNDREDS
TENS
ONES
2
7
3
4
5
1
7
2
4
1
+
Explain regrouping as: 10 ones equals 1 ten 10 tens equals 1 hundred
Example: 873 − 481 = 392 Stack the numbers by place value and subtract each place value column. Regroup as necessary. HUNDREDS
ONES
1
7
-
TENS
8
7
3
4
8
1
3
9
2
Explain regrouping as: 10 ones equals 1 ten
115 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 3.NBT.2 (3.NBT.1.2) 1
Use a place value chart to add the following whole numbers:
56 + 37 = HUNDREDS
TENS
ONES
+ Use a place value chart to add the following whole numbers:
2
503 + 254 = HUNDREDS
TENS
ONES
+ 3
Use a place value chart to subtract the following whole numbers:
56 − 13 = HUNDREDS
TENS
ONES
−
Use a place value chart to subtract the following whole numbers:
4
733 − 654 = HUNDREDS
TENS
−
116 I Smart to the Core I Educational Bootcamp
ONES
Target PRACTICE 1 1
3
Paco has a collection of 234 football cards and 86 baseball cards. How many cards does Paco have in all?
2
A a
210
A a
483 miles
B a
211
B a
491 miles
Ca
220
C
493 miles
D
320
D a
494 miles
Select all the statement(s) that are true.
4
450 + _____ = 736
Select all the statement(s) that are true.
989 − _____ = 128
The number 296 goes in the blank.
Related addition expression:
The number 186 goes in the blank.
Related addition expression:
The number 286 goes in the blank.
Related addition expression:
989 + 128 = x
128 + x = 989 x + 128 = 989
Related subtraction expression:
The number 771 goes in the blank.
450 - 736 = x
Related subtraction expression: x - 186 = 736
The number 861 goes in the blank.
Related subtraction expression:
The number 781 goes in the blank.
736 - x = 450
5
Tom drove 325 miles to the shopping mall on the way to his grandparents’ home. He then drove an additional 168 miles to his grandparents’ home. How many miles did Tom drive?
Russell drove a total of 385 miles in 2 days. He drove 198 miles the first day. How many miles did Russell drive the second day? Grid your answer.
6
Maximus has 170 paintings in his collection. He has 59 of the paintings displayed in a gallery. The rest are in his storage room. How many of Maximus’s paintings are in the storage room? Grid your answer.
117 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.NBT.2 (3.NBT.1.2) 1
Use a place value chart to add the following whole numbers:
46 + 52 = HUNDREDS
TENS
ONES
+
Use a place value chart to add the following whole numbers:
2
502 + 232 = HUNDREDS
TENS
ONES
+ 3
Use a place value chart to subtract the following whole numbers:
65 − 19 = HUNDREDS
TENS
ONES
− Use a place value chart to subtract the following whole numbers:
4
561 − 138 = HUNDREDS
TENS
−
118 I Smart to the Core I Educational Bootcamp
ONES
Target PRACTICE 2 1
3
On Tuesday, 98 men and 396 women came to the book fair. How many men and women were at the book fair on Tuesday?
2
A fishing boat travels 576 miles downstream. Then it travels 374 miles upstream. How far did the boat travel?
A a
384
A a
850 miles
B a
394
B a
900 miles
C
494
Ca
940 miles
D a
484
D
950 miles
Select all the equations that are correct.
4
Select all the equations that are correct.
123 + 456 + 78 = 647
1,000 − 546 = 454
347 + 598 = 835
978 − 125 = 853
437 + 151 + 206 = 794
849 − 762 = 187
849 + 36 = 885
707 − 498 = 209
24 + 87 + 56 = 157
639 − 540 = 199
5 Gene sold a total of 735 books over 2 months. He sold 429 books the first month. How many books did Gene sell the second month? Grid your answer.
6 A train has 920 seats. On Sunday, only 348 people bought tickets for the last ride of the day. How many empty seats were there? Grid your answer.
119 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.NBT.2 (3.NBT.1.2) DIRECTIONS: Answer the questions below. 1
2
There are 820 students in a school. If 511 of them are boys, how many girls are there in the school?
The table below shows the average attendance of students on Monday through Thursday. What is the total number of students who came to school on those days? Day
Students
Monday
261
Tuesday
233
Wednesday
212
Thursday
245
3
Adam started his journey from Point A to Point B at 10:00 A.M. The distance between Point A and Point B is about 355 km. After a few hours, Adam checked how far he has traveled and realized he had gone 180 km. About how much farther will he need to travel?
4
Sam, Harry, and Tom want to combine their money to buy a bicycle that is $600. Sam had $200, Harry had $325, and Tom had $400. If only 2 kids were going to combine their money together to buy the bicycle, which 2 kids would have the exact amount together to pay for it?
120 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: In the questions below, add or subtract the 2 numbers. Show your work in the space provided to find the answer. Part I: Add 241 to 499.
Part II: Add 99 to 89.
Part III: Subtract 218 from 428.
Part IV: Subtract 199 from 300.
121 I Copying is strictly prohibited
Four-STAR CHALLENGE - 3.NBT.2 (3.nbt.1.2) 1
3
5
There are 158 pine trees and 67 elm trees in a botanical garden. How many trees are in the botanical garden?
2
A plane traveled 467 miles to New York City. Then it traveled 215 miles to Boston. How far did the plane travel in all?
A
225
A a
672 miles
B a
215
B
682 miles
Ca
205
Ca
681 miles
D a
115
D a
691 miles
Select all the equations that have a sum or difference of 917.
4
Select all the equations that have a sum or difference of 119.
890 + 27 = 917
56 + 73 = 119
993 - 76 = 917
964 - 845 = 119
736 + 174 = 917
119 - 62 = 119
64 + 853 = 917
1,000 - 761 = 119
917 - 107 = 917
87 + 32 = 119
Carlos earned a total of $285 in 2 weeks working part-time at the movie theater. He earned $167 the first week. How much money did Carlos earn the second week? Grid your answer.
122 I Smart to the Core I Educational Bootcamp
6
The organizers of a kite festival expect 850 people to attend. By noon, there are 587 people. How many more people need to attend to reach the organizers’ expectations? Grid your answer.
7
A shipping factory has 260 employees. On Monday, 120 drivers and 56 loaders came to work. Answer the following questions and show your work.
Part I: How many employees were present on that day?
_________________________________________________________________________________________________ _________________________________________________________________________________________________ Part II: How many employees were absent on that day?
_________________________________________________________________________________________________ _________________________________________________________________________________________________
8
Place the symbol ( + or −) that makes each statement true.
Part I:
459
216 = 243
Part II:
212
399 = 611
Part III:
781
89 = 692
Part IV:
811
109 = 920
123 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Use the table below to answer the questions.
Day
Boys
Girls
Monday
59
41
Tuesday
63
47
Wednesday
70
52
Thursday
45
42
Friday
61
39
Part I: The table shows the attendance of boys and girls in a school for 1 week. Determine which days the greatest and the least number of boys and girls were present that week. Show your work below. ___________________________________________________________________________________________ ___________________________________________________________________________________________ Part II: What is the difference between the attendance of students on Tuesday and Thursday? ___________________________________________________________________________________________ ___________________________________________________________________________________________ ___________________________________________________________________________________________ Part III: How many boys were present and how many girls were present the whole week? Show your work below. Boys:
124 I Smart to the Core I Educational Bootcamp
Girls:
MISSION 12:: Multiplying whole numbers BY MULTIPLES OF 10 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
Bootcamp STRATEGY 1: Use place value strategies to multiply one-digit whole numbers by multiples of 10. Example: 7 × 80 = 560 Step 1: Break the equation into the simple multiplication fact 7 × 8 = 56 Step 2: Add zero to the product to account for the multiple of 10.
Bootcamp STRATEGY 2: Use models to multiply one-digit whole numbers by multiples of 10. Example: 7 × 80 = 560 Step 1: Draw 7 groups of 80 in which each line represents 10.
Step 2: Regroup in groups of 100. 100
1 2 3 4 5 6
100
100 100
100
Bootcamp STRATEGY 3: Use the distributive property to multiply one-digit whole numbers by multiples of 10. Example: 7 × 40 = 280 Step 1: Break 40 into 10 + 10 + 10 + 10. Step 2: Create a model to demonstrate 4 groups of 7 × 10. Step 3: Find the sum of the 4 products. 10
7
70
10
7
70
10
7
70
10
7
70
125 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 3.NBT.3 (3.NBT.1.3) DIRECTIONS: Use place value strategies, models, or the distributive property to multiply the numbers below. Show your work. 1
4
7 × 40 =
40 × 3 =
126 I Smart to the Core I Educational Bootcamp
2
5
40 × 6 =
4 × 30 =
3
6
60 × 3 =
50 × 5 =
Target PRACTICE 1 1
3
5
There are 5 mailboxes in a building. A postal worker puts 30 letters in each mailbox. How many letters are in all the mailboxes? Grid your answer.
Select all the equations below that have a product of 40.
2
4
A dressmaker made rolls of 40-foot ribbons. How many feet are in 9 rolls? Grid your answer.
Select all the equations below that have a product of 80.
2 × 20 = 40
20 × 40 = 80
1 × 40 = 40
40 × 2 = 80
4 × 10 = 40
10 × 40 = 80
0 × 40 = 40
20 × 20 = 80
20 × 20 = 40
4 × 20 = 80
4 × 20 = 40
8 × 10 = 80
Ash plays football for 50 minutes each day. How many minutes will Ash play in 7 days?
6
A teacher purchased 60 notebooks. Each notebook costs $3. How much did the teacher spend in all?
A a
12 minutes
A a
$18
B a
35 minutes
B a
$90
Ca
225 minutes
C
$180
D
350 minutes
D a
$360
127 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.NBT.3 (3.NBT.1.3) DIRECTIONS: Use place value strategies, models, or the distributive property to multiply the numbers below. Show your work. 1
5 × 60 =
4
80 × 5 =
128 I Smart to the Core I Educational Bootcamp
2
5
20 × 3 =
3
10 × 3 =
6
40 × 8 =
8 × 20 =
Target PRACTICE 2 1
3
There are 8 computer labs at the high school. Each computer lab has 30 computers. How many computers are in all the labs? Grid your answer.
Select all the expressions that have the same product as the expression below.
2
4
Biscuits come in packages of 40. How many biscuits would there be in 6 packages? Grid your answer.
Select all the expressions that have the same product as the expression below.
7 × 40 = ?
5
3 × 90 = ?
28 × 10
90 × 3
14 × 10
3 × 27
40 × 7
30 × 3
10 × 28
27 × 10
Tina has a café. She bakes 80 muffins each day. How many muffins will Tina bake in 9 days?
6
Abby wants to make 70 bows to sell at the fair. To make each bow, 6 feet of ribbon is needed. How many feet does Abby need?
A
720
A a
42 feet
B a
630
B a
76 feet
Ca
540
C
420 feet
D a
450
D a
720 feet
129 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.NBT.3 (3.NBT.1.3) DIRECTIONS: Answer the questions below. 1
A school has 10 third grade classrooms. Each classroom can have a maximum of 50 students. Determine how many students can be held in all the classrooms and explain how you got your answer.
2
Melanie bought 5 bags of oranges. There are 10 oranges in each bag. How many oranges does she have?
3
Kandy spends 10 hours a day in her office and works 4 days a week. How many hours does Kandy spend in her office after 4 weeks? What are the steps you used to find the answer?
4
Write a multiplication sentence that models the figures shown below.
5
Alan gave money to his 4 nephews for Christmas. If he gave $30 to each nephew, how much money did Alan spend?
130 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: Show your work to solve the questions in the space provided. Part I: Multiply 20 by 7.
Part II: Multiply 90 by 7.
Part III: Multiply 20 by 3 and multiply the result by 4.
Part IV: Solve both sides of the equation to determine whether the following statement is correct: 5 × (50 + 40) = (5 × 50) + (5 × 40).
131 I Copying is strictly prohibited
Four-STAR CHALLENGE - 3.NBT. 3 (3.nbt.1.3) 1
3
5
There is a 7-story shopping plaza in a town. Each story has 60 shops. What is the total number of shops in the shopping plaza? Grid your answer.
Lisa ordered 8 crates of soda to sell at her store. If each crate contains 60 cans of soda, select all the statements that are true.
2
4
Bottles of juice are sold in cases of 40. How many bottles are there be in 8 cases? Grid your answer.
The school bought 7 boxes of copy paper. If each box contains 80 packs of paper, select all the statements that are true.
Lisa ordered 420 cans.
More than 560 packs were bought.
Lisa ordered 480 cans.
Less than 480 packs were bought.
Lisa ordered 360 cans.
More than 520 packs were bought.
Lisa ordered more than 420 cans.
The school bought 560 packs.
Lisa ordered less than 480 cans.
The school bought 420 packs.
Lisa ordered more than 360 cans.
The school bought 630 packs.
Todd gives each of his 4 kids $70 for their birthday. How much money does Todd give to his kids in all?
6
In a zoo, there are 8 cages with 50 birds in each cage. How many birds are in the zoo?
A a
$70
A a
40
B a
$74
B a
58
Ca
$200
C
400
D
$280
D a
580
132 I Smart to the Core I Educational Bootcamp
7
Terry wants to multiply 2 numbers together to get a product of 320. One of the multipliers must be in multiples of 10 (20, 30, etc.). Give 2 equations in which a number will be multiplied by a multiple of 10 to get a product of 320 and solve.
First equation: ___________________________________________________________________________________________________ ___________________________________________________________________________________________________ Answer: _______ × ________ = 320 Second equation: _________________________________________________________________________________________________ _________________________________________________________________________________________________ Answer: _______ × ________ = 320
8
Walt bought a set of 4 books from his favorite fiction series. Each book costs $40. Show your work to solve the questions below. Part I: How much did this 1 set of 4 books cost Walt?
_____________________________________________________________________________________________ _____________________________________________________________________________________________ _____________________________________________________________________________________________ Part II: If Walt buys 2 more sets for his friends, how much will he have spent on books in all? _____________________________________________________________________________________________ _____________________________________________________________________________________________ _____________________________________________________________________________________________ _____________________________________________________________________________________________
133 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Fill in the missing number or symbol to complete the equations.
Part I:
30 × _______ = 150
Part II:
70 ×
_______ = 560
Part III:
20 ×
40 = _________
134 I Smart to the Core I Educational Bootcamp
MISSION 13: understanding fractions Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Bootcamp STRATEGY 1: Use a model to form equal parts of a whole. Example:
Example:
Example:
1 4
1 8
1 4 1 4
1 4 1 4
1 8
1 8
1 8
1 8
1 8
1 8
1 8
1 8
Example:
1 6
1 6
1 3
1 3
1 3
1 6
1 6
1 6
1 6
1 6
1 3
Bootcamp STRATEGY 2: Use a circle graph to demonstrate the number of parts formed when a whole is divided into equal parts. Example:
3 4
1 4
1 4
1 4
1 4
Bootcamp STRATEGY 3: Use a rectangle to model the number of parts formed when a whole is divided into equal parts.
Example:
3 4
1 4
1 4
1 4
1 4
135 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 3.NF.1 (3.NF.1.1) DIRECTIONS: Identify the fraction represented in the shaded figures below. 1
3
2
4
5
6
7
8
9
10
11
136 I Smart to the Core I Educational Bootcamp
Target PRACTICE 1 1
Select all the option(s) below that represent the image.
1 8 1 6
A
Foursixths
B a
Sixsixths
Ca
Sixfourths
D a
5
1 2 2 6
6 1 1 out of 3
Maximillian shaded this model to represent the part of the project he completed. What fraction names the shaded part of the model?
4
Twofourths
There are 18 tulips on Alma's front lawn. Of all the tulips, 13 are yellow. How many of the tulips are yellow? Grid your answer.
Select all the option(s) below that represent the image.
1 out of 6
One-sixth
One-third
3
2
6
Two-sixth
1 6 One-half
Jong has 8 cucumbers. He chops 5 cucumbers to make a salad. What fraction of the cucumbers does Jong chop? 8 A a 5 B a
1 5
Ca
1 8
D
5 8
There are 12 students in Ms. May’s third grade class. The number of her third grade class represents 12 of all the third graders in the entire school. How many third grade students are there in the entire school? Grid your answer.
137 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.NF.1 (3.NF.1.1) DIRECTIONS: Identify the fraction represented in the shaded figures below. 1
2
3
5
4
6
9
138 I Smart to the Core I Educational Bootcamp
8
7
10
Target PRACTICE 2 1
Alison divided this shape into equal parts.
2
There are 6 cakes, but only 5 boxes available. How much cake can be put into each box equally?
What is the fraction that this shape represents?
3
5
Aa
Halves
Aa
1 whole and 1 half
B a
Thirds
B
1 whole and 1 fifth
Ca
Fourths
Ca
2 wholes
D
Sixths
D a
2 wholes and 1 half
Which of the following models show 1 the fraction ? Select all that apply. 3
There are 8 students that attended a 1 math lab. Of the students, 4 were boys. How many of the students were boys? Grid your answer.
☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺
4
6
Which of the following models show 1 the fraction ? Select all that 4 apply.
Lucy has 8 comic books. These books are 12 of the books in her collection. How many books does Lucy have in her collection? Grid your answer.
139 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.NF.1 (3.NF.1.1) DIRECTIONS: Answer the questions below. 1
Ed bought 6 chocolates for his 4 kids to share. Explain how many chocolates each kid received.
2
Oliver ate pizza for dinner and left some for his brother. The amount of pizza he left is represented by the shaded part of the figure below. Explain what fraction of the pizza Oliver left for his brother.
3
The figure below shows a bookshelf in which the shaded regions represent the presence of a book, and the regions that are not shaded represent the absence of a book. What fraction of the total number of books is absent from the bookshelf?
4
In the box of chocolates shown below, 1 of the chocolates are made of white 4 chocolate. How many chocolates are made of white chocolate?
140 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: For the questions below, shade in the fraction indicated in the circle provided. Part I: Shade the circle for the fraction
3 . 8
Part II: Shade the circle for the fraction
1 . 8
Part III: Shade the circle for the fraction
1 . 2
Part IV: Shade the circle for the fraction
8 . 8
141 I Copying is strictly prohibited
Four-STAR CHALLENGE - 3.NF.1 (3.NF.1.1) 1
This shape is divided into equal parts.
2
What fraction of the pies does each neighbor get?
What is the fraction that this shape represents?
3
Gabby made 8 pies. She wants to share the pies equally among 9 of her neighbors.
Aa
Sixths
Aa
9 ninths
B
Fifths
B a
8 thirds
Ca
Fourths
Ca
9 eighths
D a
Thirds
D
8 ninths
Elena bought 12 eggs. When she got home, she found out that 3 of the eggs were broken. What fraction of the eggs are broken? Select all the option(s) that apply.
4
Donald has 15 trading cards, and 5 of the cards are special edition. What fraction of the cards are special edition? Select all the option(s) that apply.
3 12 1 6 3 of 12
5
1 4
1 15
One-fourth
1 5
Josh had 24 apples. He sliced 16 of the apples. How many of the apples did he slice? Grid your answer.
6
5 15 2 5 out of 15 10 1 One-fifteenth 8 David makes up 14 of the members of the debate team. How many members are on the team? Grid your answer. David
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7
Select all of the models that are shaded to represent the fraction
4 . 6
8
Select all of the models that are shaded to represent the fraction
2 . 8
143 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
Part I: Divide the shape below into 3 equal parts and shade in 1 part. What fraction is made? Explain.
_____________________________________________________________________________________________ ___________________________________________________________________________________________ Part II: Divide the shape below into 10 equal parts and shade in 3 parts. What fraction is made? Explain.
___________________________________________________________________________________________ ___________________________________________________________________________________________ Part III: Divide the shape below into 4 equal parts and shade in 2 parts. What fraction is made? Explain
___________________________________________________________________________________________ ___________________________________________________________________________________________ 144 I Smart to the Core I Educational Bootcamp
MISSION 14: representing fractions on a number line Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
Bootcamp STRATEGY: Use a number line to represent fractions. Example 1: Represent 3 on a number line. 4 Draw a number line with intervals from 0 to 1 to show fourths. Identify the targeted fraction on the number line.
1 4
0
2 4
3 4
1
Example 2: Represent 4 on a number line. 6 Draw a number line with intervals from 0 to 1 to show tenths. Identify the targeted fraction on the number line.
1 6
0
2 6
3 6
4 6
5 6
1
Example 3: Represent 3 on a number line. 8 Draw a number line with intervals from 0 to 1 to show eighths. Identify the targeted fraction on the number line.
0
1 8
2 8
3 8
4 8
5 8
6 8
7 8
1
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TRAIN THE BRAIN PRACTICE 1 3.NF.2 (3.NF.1.2) DIRECTIONS: Identify the location of the point on the number lines below.
1 0
2
1
3
4
2 0
3
0
146 I Smart to the Core I Educational Bootcamp
2
1
1
3
2
4
3
5
4
Target PRACTICE 1 1
What fraction names Point A on the number line? 0
1 1 8
0
3
1 8 1 8
1 8 2 8
1 8 3 8
1 8 4 8
1 8 5 8
1 8 A
What fraction names Point A on the number line? 0 1 6
1 8 7 8
1
8 8
0
1 6 1 6
1 6 A
1 6 3 6
1 6
1 6
4 6
5 6
6 6
Aa
1 8
C
6 8
Aa
1 6
Ca
3 6
B a
5 8
D a
7 8
B
2 6
D a
6 6
Select all the statements that are correct. 0
5
2
A
B
4
C
1
Select all the statements that are correct. 0
A
B
C
D
E
1
Possible midpoint: 1 2 Possible midpoint: 1 3 Possible midpoint: 1 4
Possible midpoint: 1 6 Possible midpoint: 1 3 Possible midpoint: 2 4
Midpoint is 1 if C represents 2.
Midpoint is 1 if E represents 2.
Midpoint is 2 if C represents 3.
Midpoint is 2 if E represents 3.
A missing fraction on a number line is located exactly halfway between 2 6 and 4 . What is the missing fraction? 6 Grid your answer.
6
A missing fraction on a number line 1 is located exactly halfway between 4 and 3 . What is the missing fraction? 4 Grid your answer.
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TRAIN THE BRAIN PRACTICE 2 3.NF.2 (3.NF.1.2) DIRECTIONS: Identify the location of the point on the number lines blow.
1
0
1
2
3
2 0
2
1
3
4
3 0
1
2
148 I Smart to the Core I Educational Bootcamp
3
4
5
6
7
8
9
10
Target PRACTICE 2 1
What fraction names Point A on the number line? 0
1 1 6
1 6
1 6 A
0
3
2 6
1 6
1 6 3 6
4 6
What fraction names Point A on the number line? 0
1
1 6
1 3
5 6
6 6
A
1 3 1 3
1 3 2 3
3 3
A
1 6
Ca
3 6
Aa
3 3
Ca
1 3
B a
2 6
D a
1 1
B a
2 3
D
0
Jaden can walk around the path 4 times for a total of 1 mile. How many times will he walk around the path to go 3 mile? Grid your answer. 4 0
0
4
1
1 4
5
2
1 4
1 4
Stephen ran 6 times around his neighborhood to complete a total of 1 mile. How many times will he need to run to complete 3 of a mile? Grid 6 your answer. 0
1 4
1 1 6
4 4
Which of the following models show the fraction 1 on a number line? 2 Select all that apply.
0
6
1 6
1 6
1 6
1 6
1 6 6 6
Which of the following models show the fraction 1 on a number line? 3 Select all that apply.
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TRAIN THE BRAIN PRACTICE 3 3.NF.2 (3.NF.1.2) DIRECTIONS: Answer the questions below. 1 At a birthday party, Elizabeth cut the cake into 8 equal pieces (as shown in the figure below) and gave 2 pieces (shown in the shaded region) to the birthday boy. What fraction of the total cake did the birthday boy get? Explain how you got your answer. 1 1 8 8 1 1 8 8 1 1 8 8 1 1 8 8 2 The length of the racing track is 4 miles, and each mile contains 3 hurdles. If Johnny jumped 6 hurdles, what fraction of the total track has he completed?
3 Adam cut a long rope into 6 equal parts as shown below. What is the length of each small piece of rope in terms of a fraction? Describe how you determined your answer.
4 Alvaro uses a number line to measure the length of the base of a triangle as shown below. What is the length of that triangle?
0 6
1 6
2 6
3 6
4 6
5 6
6 6
5 What fraction is represented by the X on the number line shown below? Explain how you determined the answer.
0 8
1 8
2 8
3 8
4 8
5 8
6 8
150 I Smart to the Core I Educational Bootcamp
7 8
X
THINK TANK QUESTION DIRECTIONS: For each problem below, make intervals and determine the point on the number line that represents each fraction indicated. Part I: Find
3 4
on the number line. Mark an X on that point.
Part II: Find
3 4
Part III: Find
4 6
Part IV: Find
1 2
on the number line. Mark an X on that point.
on the number line. Mark an X on that point.
on the number line. Mark an X on that point.
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Four-STAR CHALLENGE - 3.NF.2 (3.NF.1.2) 13 1
What fraction names Point A on the number line? 0
1 1 4
1 4
1 4 A
0
3
2 4
What fraction names Point A on the number line? 0
3 4
1 1 8
1 4 4 4
1 8
0
1 8
1 8 2 8
1 8
1 8 3 8
A
1 8
1 8 5 8
6 8
1 8 7 8
8 8
A
1 4
Ca
3 4
Aa
1 8
C
4 8
B a
2 4
D
4 4
B a
3 8
D a
8 8
Gerry can ride his bicycle around the track 3 times for a total of 1 mile. How many times will he ride around the track to go 23 mile? Grid your answer. 0
16 4
1 1 3
1 3
0
5
14 2
0
1 3
1 1 6
3 3
Carlo found a piece of wood that was 8 yards long and divided it into 6 equal pieces. Select the statements that are true if a number line is created to represent this problem. There should be 6 segments in the number line. There should be 8 segments in the number line. There should be 7 segments in the number line. There should be 7 points on the number line. There should be 6 points on the number line.
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Will jogged 6 times around a garden to complete a total of 1 mile. How many times will he need to jog to complete 56 of a mile? Grid your answer.
0
6
1 6
1 6
1 6
1 6
1 6 6 6
Ava bought a ribbon that was 6 inches long and cut it into 4 equal segments. Select the statements that are true if a number line is created to represent this problem. There should be 6 segments in the number line. There should be 5 segments in the number line. There should be 4 segments in the number line. There should be 6 points on the number line. There should be 5 points on the number line.
Looking at the shaded circle below, determine what the equivalent fraction would be for the fraction given below.
7
____________
8
=
John is trying to measure the length of the base of the triangle shown below using a number line. Label the number line. Explain what the length of the base will be in terms of a fraction.
0
1
_____________________________________________________________________ _____________________________________________________________________
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1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: For each problem below, make intervals and determine the point on the number line that represents each fraction indicated. Part I: Find
2 3
on the number line. Mark an X on that point.
Part II: Find
4 4
Part III: Find
2 8
Part IV: Find
5 6
on the number line. Mark an X on that point.
on the number line. Mark an X on that point.
on the number line. Mark an X on that point.
154 I Smart to the Core I Educational Bootcamp
MISSION 15: UNDERSTANDING EQUIVALENT FRACTIONS Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Bootcamp STRATEGY 1: Use fraction models to find equivalent fractions. Example: Write 2 fractions that are equivalent to 3 . 4 3 Step 1: Create a model to represent . 4
Step 2: Divide the model in half and use the model to determine the equivalent fraction.
6 8 Step 3: Divide the model from Step 2 in half and determine the equivalent fraction. 12 16
Bootcamp STRATEGY 2: Use multiplication to find equivalent fractions. Example: Write 3 fractions that are equivalent to 3 . 4 Step 1: Multiply the numerator and denominator by the same number. Each fraction used represents 1 whole and, therefore, will give an equivalent product. 3 4
×
2 2
=
6 8
3 4
×
3 3
=
9 12
3 4
×
4 4
=
12 16
3 4
×
5 5
=
15 20
Equivalent fractions
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TRAIN THE BRAIN PRACTICE 1 3.NF.3 (3.NF.1.3) DIRECTIONS: Place the following fractions in order from least to greatest. 1
2
1 4
<
<
1 3
<
<
2 4
<
<
4
3
1 4
<
<
DIRECTIONS: Place the following fractions in order from greatest to least. 6
5
2 2
>
>
4 6
>
>
7 8
>
>
8
7
5 8
>
>
156 I Smart to the Core I Educational Bootcamp
Target PRACTICE 1 1
Study the fraction model below. Select all the fractions that are equivalent to the fraction model.
2
Study the number line below. Select all the fractions that are equivalent to the fraction model. 0
1 4 2 6 1 2 3
1 2 1 3 2 4
1 3 2 4 2 2
Flora sliced 2 lemons into equal parts.
4
B
What fraction, greater than 1, names both lemons? 2 6 Aa Ca 6 12 B
5
D a
Ca D a
6 6
Dayna used 26 cup of flour and 23 cup of sugar to make a sponge cake. Which statement below correctly compares the fractions?
6
3 3 3 4 3 6
Which of the following represents fractions in order from greatest to least? A a
12 6
1
3 8 3 4 3 8 3 6
3 3 4 3 3 ,6 8 3 3 ,6 4 3 3 ,8 4 ,6
Alison owns a farm. She uses 46 acre for animals to graze, 26 acre to grow 3 vegetables, and 6 acre to build a house. Which list below orders the fractions from greatest to least?
A a
4 >2 6 3
B a
4 <2 6 3
B a
Ca
2 >4 3 6
C
D
4 =2 6 3
D a
A a
2 , 3, 4 6 6 6 3, 2 , 4 6 6 6 4, 3 , 2 6 6 6 2, 4 , 3 6 6 6 157 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.NF.3 (3.NF.1.3) DIRECTIONS: Identify the fractional parts below as greater than (>), less than (<), or equal to (=). 1
2
3
4
5
3 4
2 4
6
4 6
1 6
7
1 4
2 4
8
2 3
2 6
9
4 4
4 8
10
1 2
1 8
11
1 4
3 4
12
1 3
2 3
13
7 6
7 8
158 I Smart to the Core I Educational Bootcamp
Target PRACTICE 2 1
Allie jogged for 34 hour on Monday. The figure below represents the time Allie jogged on Monday.
2
Dagmar is painting a wall in various colors. She is painting 14 of the wall green. Which shape below has a shaded part equivalent to 14 ? A
Ca
B a
D a
What fraction is equivalent to 34 ?
3
Aa
1 4
B
6 8
Ca
3 6
D a
6 12
Edith drew 2 identical squares and divided them into the same number of equal parts.
4
Which of the following represents fractions in order from least to greatest?
A a B a
What fraction, greater than 1, names the parts that she divided? 8 Aa 16 Ca 4 16 B
5
16 8
D a
1 Fractions 2 2 Fractions 3 Fractions 4 8 Fractions 1 2 Fractions 2 3
3 2 and 3 4 and 8 and 4 6 and 4 8 and 4 6
8
D a
2 16
Study the set of fractions below. Select all the statements that are true. 1 2 4 4
2
C
6
are equivalent. are equivalent.
are equivalent. are equivalent. are equivalent.
6
1 4 1 6 1 8 1 4
1 1 8 1 1 ,8 4 1 1 ,6 4 1 1 ,6 8 ,6
Study the set of fractions below. Select all the statements that are true. 1 1 2 2
3 1 Fractions 2 Fractions 2 6 1 Fractions 3 Fractions 1 3 Fractions 1 2
2
6
2 and 6 and 2 4 2 and 6 and 2 4 and 2 4
4
are equivalent. are equivalent.
are equivalent. are equivalent. are equivalent.
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TRAIN THE BRAIN PRACTICE 3 3.NF.3 (3.NF.1.3) DIRECTIONS: Solve the problems below. 1
The figure shown below represents a pizza. The shaded regions represent the pizza slices that have not been eaten, and the un-shaded regions represent the pizza slices that have been eaten. What fraction of the pizza is left?
1 3 Nancy used 9 of her pencils, and Mia used 3 of her pencils. Who used more pen2 cils? Write a mathematical expression that shows the correct comparison of these 2 fractions.
3 Juan and Gibbs are reading the same book. Juan has read 8 of the book, and 3 5 Gibbs has read 8 of the book. Who has read fewer pages? Shade the fraction circles below to show the portion each has read.
4
Amy runs a fraction of a mile every day before going to school. The figure below represents the distances she ran on 3 consecutive days. Which day did she run the most? What is the fraction of a mile that she ran? 0 8
1 8
2 8
3 8
4 8
5 8
6 8
Day 1 Day 2 Day 3
160 I Smart to the Core I Educational Bootcamp
7 8
8 8
THINK TANK QUESTION DIRECTIONS: Shade in the first fraction model to show the fraction given. Use the second fraction model to find an equivalent fraction and write the fraction to show equivalency.
A.
B.
2
=
3
9
1
2
=
4
C.
1
=
2
D.
4
8
=
8
6
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Four-STAR CHALLENGE - 3.NF.3 (3.NF.1.3) 13 1
Ashley walked 12 mile to the library. Then she walked an equal distance to the post office.
14 2
Mandy solved a problem that had an answer of 12 . Which shape below has a shaded part equivalent to 12 ?
A a
C
B a
D a
What fraction is equivalent to 12 ?
3
Aa
1 6
C
3 6
B a
2 6
D a
3 1
Nick broke 2 sticks into equal parts.
16 4
Which of the following represents fractions in order from greatest to least? A
What fraction, greater than 1, names the broken parts of the sticks? 8 4 A Ca 4 8 B a
5
8 2
D a
2 8
Compare the 2 fractions below. Select all the statements that are true.
B a Ca D a
1 4 1 6 1 8 1 8
1 1 8 1 1 ,4 8 1 1 ,6 4 1 1 ,4 6 ,6
16 6 Compare the 2 fractions below. Select all the statements that are true.
3
5
5
3
6
6
8
8
The fraction 3 is greater than 5 . 6 6 5 The fraction is greater than 3 . 6 6 3 5 The fraction is less than . 6 6 The fractions are equal. 162 I Smart to the Core I Educational Bootcamp
5 3 is greater than . 8 8 The fraction 3 is greater than 5 . 8 8 The fractions are equal. The fraction
The fraction 3 is less than 5 . 8 8
1
7
2 are the same point on the
Using the number lines below, show that and 2 4 number line.
For 1
2
0
1
0
1
For 2
4
8
1
Part I: Shade Figure A to show the fraction . Shade Figure B to show the 4 2 fraction .
8
Figure A
Figure B
Part II: Explain why the 2 fractions are equal. _____________________________________________________________________________________________ _____________________________________________________________________________________________ _____________________________________________________________________________________________
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1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: For the questions, determine what the numerator and denominator are for each fraction, number, or decimal. Part I: Write the numerator and denominator of
2 . 8
Numerator: ____________ Denominator: ____________ Equivalent Fraction:
Part II: Write the numerator and denominator of
5 . 6
Numerator: _____________ Denominator: _____________ Equivalent Fraction:
Part III: Write the numerator and denominator of
Numerator: _____________ Denominator: _____________ Equivalent Fraction:
Part IV: Write the numerator and denominator of 1.
Numerator: _____________ Denominator: _____________ Equivalent Fraction: 164 I Smart to the Core I Educational Bootcamp
1 . 2
MISSION 16: telling time and measuring elapsed time Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
Bootcamp STRATEGY 1: Use the hands on a clock to help determine the time being represented. Step 1: Identify the short hand as the hour hand.
Example:
Step 2: Use the clock to determine the hour being represented. Note: The short hand represents the number it is on or past before landing on the following number of the clock. Step 3: The hour represented on the clock should be written before the colon. Step 4: Identify the long hand as the minute hand. Step 5: Count intervals of 5, starting at the “12” on the clock. Each number
2:10
represents 5 minutes. Therefore, the long hand on the “2” represents 10 minutes. Step 6: The minutes counted using the long hand should be written after the colon.
Bootcamp STRATEGY 2: Use the clock/number line to determine the time elapsed. IDENTIFYING THE STARTING TIME 10 min
Example: It took 35 minutes for Frank to cut the grass. He finished cutting the grass at 2:10. At what time did Frank start cutting the grass?
15 min 20 min
Step 1: Identify 2:10 on the clock.
25 min
Step 2: Count backward in 5-minute intervals for 35 minutes. Step 3: Identify the starting time. Remember to subtract 1 hour when 5 min 5 min 5 min 5 min 5 min 5 min passing the 12.
30 min 5 min
35 min 2:10
2:05
2:00
1:55
1:50
1:45
1:40
1:35
STARTING TIME: 1:35
5 min
IDENTIFYING THE FINISHING TIME Example: It took 35 minutes for Carlton to cut the grass. He started cutting the grass at 2:10. At what time did Carlton finish cutting the grass? Step 1: Identify 2:10 on the clock.
35 min
5 min
30 min
10 min
Step 2: Count forward in 5-minute intervals for 35 minutes.
25 min
Step 3: Identify the finishing time. Note: Remember to add 1 hour when 5 min 5 min 5 min 5 min 5 min 5 min 5 min passing the 12. 2:45
2:40
2:35
2:25
2:20
2:15
2:10
2:30
FINISHING TIME: 2:45
15 min 20 min
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TRAIN THE BRAIN PRACTICE 1 3.MD.1 (3.MD.1.1) DIRECTIONS: Record the time after 15 minutes have passed using the number line below. 1
New Time: 2
New Time:
DIRECTIONS: Record what the time should be on each of the clocks 1 hour and 10 minutes before the time shown. 4
3
6
5
DIRECTIONS: Record the time that has elapsed from Clock 1 to Clock 2. Clock 1
Clock 2
Clock 1
Clock 2
8
7
_______ hour(s) _______ minute(s) 166 I Smart to the Core I Educational Bootcamp
_______ hour(s) _______ minute(s)
Target PRACTICE 1 1
3
5
Select all the statement(s) that express the time below.
2
Select all the statement(s) that express the time below.
The time is 7:03.
The time is 1:45.
The time is quarter past seven.
The time is half past one.
The time is half past seven.
The time is quarter past one.
The time is quarter before seven.
The time is quarter before two.
The time is seven o’clock.
The time is quarter past two.
The time is 7:15.
The time is 1:09.
Miguel looked at his watch before he began reading a storybook. The hour hand was between the 9 and the 10. The minute hand was on the 5. At what time did Miguel begin reading?
4
Stefan wakes up at a quarter after 8:00 in the morning. At what time does Stefan wake up?
A
9:25
A a
7:45 A.M.
B a
9:05
B a
7:45 P.M.
Ca
5:10
C
8:15 A.M.
D a
5:09
D a
8:15 P.M.
Jane started jogging at 7:20 A.M. and finished jogging at 7:43 A.M. How many minutes did Jane jog? Grid your answer.
6
Mr. Cheung left his house to go to his office at 9:43 A.M. He got to his office at 10:11 A.M. How many minutes did it take him to get to his office? Grid your answer.
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TRAIN THE BRAIN PRACTICE 2 3.MD.1 (3.MD.1.1) DIRECTIONS: Record the time after 30 minutes have passed using the number lines below. 1
New Time: 2
New Time: DIRECTIONS: Record what time should be on each of the clocks 30 minutes before the time shown. 4
3
6
5
DIRECTIONS: Record the time that has elapsed from Clock 1 to Clock 2. Clock 1
Clock 2
Clock 1
Clock 2
8
7
_______ hour(s) _______ minute(s) 168 I Smart to the Core I Educational Bootcamp
_______ hour(s) _______ minute(s)
Target PRACTICE 2 1
3
5
Select all the clock(s) that show a time between 9 and 10.
Pamela looked at her watch before she started making a fruit cake. The hour hand was between the 7 and the 8. The minute hand was on the 6. What time did Pamela start making the cake?
2
4
Select all the clock(s) that show a time between 5 and 6.
Yana began practicing badminton at a quarter to 7:00 in the evening. What time did Yana begin practicing?
A a
6:07
A
6:45 A.M.
B a
6:08
B a
7:15 A.M.
Ca
7:06
C
6:45 P.M.
D
7:30
D a
7:15 P.M.
A TV channel telecasts a program at 8:05 A.M. The program ends at 8:49 A.M. How many minutes did the TV channel telecast the program? Grid your answer.
6
A dressmaker started making a new dress design at 11:32 A.M. She completed the design at 12:17 P.M. How many minutes did it take to make? Grid your answer.
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TRAIN THE BRAIN PRACTICE 3 3.MD.1 (3.MD.1.1) DIRECTIONS: Answer the questions below. 1
2
3
Rhodes went to the supermarket to buy some groceries. He left his house at the time shown on Clock 1. He came back at the time shown on Clock 2. How long did it take Rhodes to buy his groceries and come back? Explain how you got your answer.
Clock 1 Clock 2 Peter started his homework at 3 P.M. He finished his homework when the hour hand of the clock was between the 4 and the 5 and the minute hand was pointing at 9. What time did Peter finish his homework?
Ron woke up for school and saw the time that was on Clock 1. He got ready for school and left his house at the time shown on Clock 2. He got to school at the time shown on Clock 3. How long did it take Ron to get dressed and go to school? Explain how you got your answer.
6:30
7:30
8:00
Clock 1
Clock 2
Clock 3
4
Charlie went to see a concert at 11 A.M. and stayed there for 1.5 hours. After the concert, he left for home and got there in 30 minutes. What was the exact time Charlie got home?
5
Everyday, Amy jogs on the track for 35 minutes. It takes her 10 minutes to walk between her house and the track each way. When she gets home, the time is 8:45 A.M. What time does Amy leave her house to go jogging each morning?
170 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: Study the analog and digital clocks below. Use the clocks to complete the tasks.
Part I: Match the analog clocks to the digital clocks that show the same time.
Part II: Explain how to read the time on an analog clock.
Part III: Use a number line to explain how to determine the time after 40 minutes have elapsed.
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Four-STAR CHALLENGE - 3.MD.1 (3.md.1.1) 1
3
5
Which of the following statements could be true about the 2 clocks below? Check all that apply.
2
Which of the following statements could be true about the 2 clocks below? Check all that apply.
The elapsed time is 5 hours.
The start time is 3:30.
The start time is 6:12.
Elapsed time: 5 hours and 30 minutes.
The elapsed time is 4 hours.
Elapsed time: 4 hours and 30 minutes.
The end time is 10:00.
The end time is 8:00.
The elapsed time is 6 hours.
The start time is 3:06.
Irma looked at her watch before starting her exam. The hour hand was a little past the 8 and the minute hand was pointing to the 5. At what time did the examination start?
4
Henry received his pizza delivery 12 minutes after 2:00 in the afternoon. What time did Henry receive the pizza delivery?
A a
9:25
A a
2:12 A.M.
B a
9:05
B a
12:02 A.M.
C
8:25
C
2:12 P.M.
D a
5:09
D a
12:02 P.M.
The first airplane leaves the airport at 6:10 A.M. The second airplane leaves at 7:05 A.M. How many minutes later does the second plane leave after the first plane? Grid your answer.
172 I Smart to the Core I Educational Bootcamp
6
Joey received a call from his friend at 11:51 A.M. and it ended at 12:12 P.M. How many minutes long was the phone call? Grid your answer.
7
Identify the time and explain how you were able to determine the time on the analog clocks.
A.
B.
Time: _____________ Explanation:
Time: _____________ Explanation:
8
A.
Determine the time on the digital clocks. Draw a long hand and a short hand on the analog clock to represent the same time shown on the digital clocks. B.
173 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Study the analog clocks below. Use the analog clocks to complete the tasks.
Clock A
Clock B
Clock C
Clock D
Part I: Identify the time shown on each clock. Clock A: ________________ Clock C: ________________ Clock B: _______________ Clock D: ________________ Part II: Use a number line to model the elapsed time between Clock A and Clock B.
Elapsed Time:
__________ hr
__________min
Part III: Use a number line to model the elapsed time between Clock B and Clock C.
Elapsed Time:
__________ hr
__________min
Part IV: Use a number line to model the elapsed time between Clock C and Clock D.
Elapsed Time:
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__________ hr
__________min
MISSION 17: Measuring Liquid Volume and Mass Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units.
Bootcamp STRATEGY 1: Use a graduated cylinder to measure the volume of a liquid. A graduated cylinder is a clear glass or plastic tube marked with units, such as milliliters to measure the volume. To measure the volume of liquids: Step 1: Place graduated cylinder on flat surface.
Eye level
Measure from bottom of curve
Step 2: Place your eye level at the top of the water line. Step 3: Measure from the bottom of the curved surface (meniscus).
Bootcamp STRATEGY 2: Use a triple beam balance to measure the mass of a solid in grams. A triple beam is a mechanical balance that has a beam supported by a fulcrum. To measure the mass of an object: Step 1: On the other side of the measurement tray, the beam is split into 3 horizontal beams that together each support 1 weight. Slide all 3 weight poises (metal brackets) along the beams to the leftmost position. Step 2: Place the object to be measured on the center of the pan, located on the left side of the triple beam balance. Note: The index pointer will rise to the top, above the 0.
g g g
Step 3: Slide the 100-gram poise to the right, 1 notch at a time, until the index pointer drops below the 0. Move the poise left 1 notch. Step 4: Slide the 10-gram poise to the right, 1 notch at a time, until the index pointer drops below the 0. Move the poise left 1 notch. Step 5: Slide the 1-gram poise to the right, 1 notch at a time, until the index pointer lines up with the 0 mark. Step 6: Add the values from all 3 beams to determine the mass of the object.
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TRAIN THE BRAIN PRACTICE 1 3.MD.2 (3.MD.1.2) DIRECTIONS: Estimate the measurements for each of the following. 1
2
5
6
3
4
7
8
DIRECTIONS: Record the mass for each of the triple beam balances below. 10
9
g
g
g
g g
g
DIRECTIONS: Identify the object with the greater mass.
11
Circle
13
12
Triangle
Equal
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Circle
Triangle
Equal
Circle
Triangle
Equal
Target PRACTICE 1 1
3
Select all the statements below that are a good estimate for the object in each statement.
Select all the statements below that are a good estimate for the object in each statement.
A pen weighs about 6 grams.
An apple is about 15 kilograms.
A dog weighs about 25 kilograms.
An apple is about 5 ounces.
A pen weighs about 6 kilograms.
An apple is about 140 grams.
A pencil weighs about 7 grams.
An apple is about 4 tons.
A dog weighs about 25 grams.
An apple is about 10 pounds.
A pencil weighs about 7 kilograms.
An apple is about 14 milligrams.
Rosalinda will use grams to measure the mass of an object in her room. Which of the following objects would be best measured using grams? A a
B
5
2
Ca
Toothpaste
D a
An oil factory has a tank that holds 24 liters of oil. The clerk uses a 3-liter container to fill the tank. How many times does the clerk have to fill the 3-liter container in order to fill the oil tank? Grid your answer.
4
Teresa’s suitcase has a mass of 17 kilograms. She put a large gift in the suitcase that has a mass of 12 kg. What is the total mass of Teresa’s suitcase?
A
29 kilograms
B a
32 kilograms
Ca
45 kilograms
D a
57 kilograms
6
A small organic juice manufacturing company manufactured a total of 28 liters of juice in 4 hours. The same amount of juice is manufactured each hour. How many liters of juice was manufactured each hour? Grid your answer.
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TRAIN THE BRAIN PRACTICE 2 3.MD.2 (3.MD.1.2) DIRECTIONS: Estimate the measurements for each of the following. 1
2
5
6
3
4
7
8
DIRECTIONS: Record the mass for each of the triple beam balances below. 10
9
g
g
g
g g
g
DIRECTIONS: Identify the object with the greater mass.
11
Circle
13
12
Triangle
Equal
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Circle
Triangle
Equal
Circle
Triangle
Equal
Target PRACTICE 2 1
3
5
Identify the statement(s) below that are true. Check all that apply.
2
Identify the statement(s) below that are true. Check all that apply.
A peach weighs about 150 inches.
A crayon weighs about 8 inches.
An orange weighs about 150 feet.
A crayon weighs about 8 pounds.
An apple weighs about 150 grams.
A crayon weighs about 8 grams.
A peach weighs about 5 ounces.
Two crayons weigh about 16 cm.
An orange weighs about 5 meters.
Two crayons weigh about 16 feet.
An apple weighs about 5 yards.
Two crayons weigh about 16 grams.
Jessy wants to find the mass of her new cat. What unit should she use?
A a
Inches
B a
Liters
C
Kilograms
D a
Grams
Wu has a bucket filled with 30 liters of water that he uses to fill a 5-liter watering can. How many times can Wu fill the 5-liter watering can from the bucket of water he has? Grid your answer.
4
6
Molly pours 17 liters of water into 1 bucket and 19 liters of water into another bucket. Each bucket is filled completely. What is the total liquid volume of the 2 buckets? A a
26 liters
B
36 liters
Ca
38 liters
D a
45 liters
An old engine uses 24 liters of gas in 6 hours. The same amount of gas is used each hour. How many liters of gas is used each hour? Grid your answer.
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TRAIN THE BRAIN PRACTICE 3 3.MD.2 (3.MD.1.2) DIRECTIONS: Solve the problems below. 1 A scientist has to use a beaker for his experiment. He needs to fill the beaker with 2 liters of a chemical. He has 2 beakers in his lab: 1 with 1.5 liters capacity and the other with 2.5 liters capacity. Explain which beaker he should choose and why.
2 A fisherman needs to buy a weight for his fishing pole. The store sells weights that are available in 0.5 kg, 0.6 kg, and 0.7 kg. The fisherman wants to buy the lightest weight the store sells. Explain which weight the fisherman would buy.
3 A truck driver needs to rent some trucks to carry a total load of 4,000 kg. He is being offered three trucks: T1, T2, and T3. Their load-carrying capacities are as follows: T1 takes 1,500 kg, T2 takes 2,500 kg, and T3 takes 500 kg. If he wants to rent the least number of trucks possible, explain which truck or combination of trucks he would need to rent to meet the weight of his entire load.
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THINK TANK QUESTION DIRECTIONS: Use the information from the beakers below to complete the tasks.
Beaker 1
Beaker 2
Beaker 3
Beaker 4
Beaker 5
Part I: Estimate the volume of the liquid inside each beaker. Beaker 1: _______________ Beaker 4: _______________ Beaker 2: _______________ Beaker 5: _______________ Beaker 3: _______________
Part II: If you pour the contents of Beaker 1 and Beaker 2 into an empty container, what will be the total amount of liquid inside the container? Show your complete solution.
Part III: What is the difference in the amount of liquid between Beaker 3 and Beaker 4? Show your complete solution.
Part IV: If you wanted to pour 4 times the amount of liquid inside of Beaker 5 into an empty container, what would be the total amount of liquid inside the container? Show your complete solution.
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Four-STAR CHALLENGE - 3.MD.2 (3.MD.1.2) 1
Select all true statements below.
2
Jenny has 16 liters of soda. She spilled 4 liters. She has 12 liters left. Lily weighs 60 kilograms. Her dog weighs 6 times less than she does. Her dog weighs 54 kg. Jack has 750 grams of chocolate. He put the same amount of g in each of 10 gift bags. Each gift bag has 75 g of chocolate. Al has 150 liters of green detergent and 200 l of blue detergent. He has 350 l of detergent in all.
3
Lita works at a restaurant. She uses liters to measure the volume of a menu item. Which menu item would be best measured using liters? A a
B
5
RICE
Ali has to lift a total of 100 kilograms of cans. The cans are in 4 equal piles. There are 20 kg of cans in each pile Herbert has 67 grams of gravel. He will use 28 g at work. He will have 39 g left. Lucy is making 200 liters of punch at work every day. After 5 days, she made 1,000 l of punch. Vincent lifted 45 kilograms of weights yesterday. Today, he lifted 19 kg more than yesterday. He lifted 54 kg today.
4
Ca
D a
A bathtub holds 27 liters of water. Khan uses a 3-liter container to fill the bathtub. How many times does Khan have to fill the 3-liter container in order to fill the bathtub? Grid your answer.
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Select all true statements below.
6
Ira received 3 gift boxes. The boxes had masses of 9 kilograms, 14 kilograms, and 7 kilograms. What is the total mass of the 3 boxes? A a
29 kilograms
B
30 kilograms
Ca
45 kilograms
D a
57 kilograms
Wei sold a total of 40 liters of apple juice in 8 hours. The same amount of apple juice was sold each hour. How many liters of apple juice were sold each hour? Grid your answer.
7
Identify the amount of liquid inside the beakers.
A.
B.
Amount: _______________
C.
Amount: _______________
D. Amount: _______________
8
Amount: _______________
Solve the word problems. Show your complete solution.
A. Linda has 15 cups of milk and 20 cups B. George bought 18 liters of soda for his of flour to add to the wedding cake party. While he was pouring drinks, he batter. Give the steps needed to find spilled 11 liters. Give the steps needed how many cups of ingredients will be to find how much soda is left to serve, added to the batter, then solve. then solve.
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1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Study the 4 test tubes below. Use the test tubes to complete the tasks.
Test Tube 1
Test Tube 2
Test Tube 3
Test Tube 4
Part I: Estimate the volume of the liquid inside each test tube. Test tube 1: _______________ Test tube 3: _______________ Test tube 2: _______________ Test tube 4: _______________
Part II: If you mix all the contents of Test tube 1 and Test tube 3 in an empty beaker, what is the total amount of liquid inside the beaker? Show your complete solution.
Part III: If you mix all the contents of Test tube 2 and Test tube 4 in an empty beaker, what is the total amount of liquid inside the beaker? Show your complete solution.
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MISSION 18: Representing Data with Graphs Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
Bootcamp STRATEGY 1: Represent data in a picture graph. The picture graph can be setup vertically or horizontally. The symbols used in a pictograph represent quantities of items to be compared. The symbols representing the amounts are inside the graph, next to each item. Each picture may represent more than one item. Creating a picture graph:
STUDENTS DRINKING FRUIT JUICE AT LUNCH
Step 1: Identify the title for the picture graph. Step 2: Identify the labels for the picture graph. Step 3: Select the picture and the number
that is represented by each symbol. Step 4: Place the number of pictures required to represent the data.
Bootcamp STRATEGY 2: Represent data in a bar graph. Bar graphs are used to help visually represent data so that comparisons and trends will be easier to identify.
Step 1: Identify the title for the bar graph. Step 2: Identify the labels for the axes (y-axis and x-axis) on the bar graph. Step 3: Identify the intended value for each bar. Step 4: Determine the intervals (scale) to be used for the bar graph. Step 5: Draw the bars to represent the data.
y-axis Number of Students (each)
Creating a bar graph:
x-axis Favorite Colors
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TRAIN THE BRAIN PRACTICE 1 3.MD.3 (3.MD.2.3)
Number of Students
DIRECTIONS: Use the graph to answer the questions below.
y
x
Sports
1
How many more students prefer football than soccer?
2
According to the graph, how many third grade students voted for their favorite sport?
3
How many students preferred either tennis or basketball?
4
According to the graph, how many students did not say basketball was their favorite sport?
DIRECTIONS: Construct a bar graph using the table below. 5 Favorite Subject
Number of Votes
Math Science History Reading
22 40 18 30
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Target PRACTICE 1 1
The third graders voted for their favorite lunch item. They organized the data in a tally table. Favorite Lunch
Bailey made a picture graph showing how many shirts each shop sold at a flea market.
2
Brands
Votes
Sandwiches
Epic Wear
Mini Pizzas
Trill Wear
Black Bean Tacos
Bravo Clothing
Pasta
Protective Clothing = 2 shirts
How many of the third graders chose sandwiches and pasta? B Ca 18 A D 21 a 12 a 9 3
Ash took a survey to learn how many students played 2 different games. He wrote the results in a table and used the data to make a picture graph with a key of = 3 students.
How many shirts were sold in all? B C 35 A D a 24 a 18 a 42 4
Anika wants to use the data from the table to make a bar graph. Products Sold
Student’s Games
Products
Number of Products
Pen
15
Games
Number of Students
Book
10
Chess
18
Eraser
12
Tennis
27
How many bars will Anika have on the x-axis of her bar graph? Grid your answer.
How many will be drawn for tennis? Grid your answer.
5
Amount Sold
Which of the following statements could be correct about the graph below? Check all that apply.
Highest water level: May Lowest water level: 200 meters Lowest water level: July Highest water level: 800 meters Highest water level: September
6
Which of the following statements could be correct about the graph below? Check all that apply.
Donald made 3 points. Greatest number of points: Michael Michael made 18 points. Dennis made 14 points. Greatest number of points: Harry 187 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.MD.3 (3.MD.2.3) DIRECTIONS: Use the graph to answer the questions below.
Free Throws
1
How many more free throws did Mark make than Lonnie?
2
According to the graph, how many free throws were made in all?
3
How many free throws did Jaime and Marsha make together?
DIRECTIONS: Construct a bar graph using the table below. 4 Players
Number of Free Throws
Mark Lonnie Jamie Marsha
8 4 8 6
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Target PRACTICE 2 1
Amber asked her classmates which cartoon they liked best. The tally table shows the results. Cartoons
2
Votes
Families
Tom and Jerry
Greg’s family
The Simpsons
Mari’s family
The Flintstones
Tessa’s family
How many students chose Looney Tunes and The Flintstones? B a 16
3
C 20
= 4 gallons
How much water was used in all?
D a 24
Pat made a table to show the number of E-mails each employee sent last week and made a picture graph with a key of = 5 E-mails to show the data. Employee E-mails
B a 92
A 122
4
Ca 67
Data Table of Pets
Pets
Number of Pets
Number of E-mails
Cat
8
Lia
15
Dog
4
Jerica
25
Hamster
6
Horse
3
Parrot
10
Which of the following statements could be correct about the graph below? Check all that apply.
The tree was tallest in June. The height of the tree in May is 7 feet. The height of the tree in July is 8 feet. The height of the tree in June is 6 feet. The height of the tree in April is 2 feet.
D a 32
Shari made a bar graph by using the data she collected on the types of pets her classmates have.
Employees
How many will be drawn for Lia? Grid your answer.
5
Gallons Used
Ari’s family
Looney Tunes
A a 9
There are 4 families living in an apartment building. The picture graph shows how much water each family used last week.
How many bars will Shari have on the x-axis of her bar graph? Grid your answer. 6 Which statements could be correct about the graph? Check all that apply.
30 donuts were sold on Wednesday. 2 donuts were sold on Monday. 25 donuts were sold on Thursday. 15 donuts were sold on Tuesday. Each on the legend = 1 donut . 189 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.MD.3 (3.MD.2.3) DIRECTIONS: Solve the problems below. 1 Jason’s mother hired a tutor for him. Together, they created the schedule shown below in the table. Tell how many hours a week Jason is being tutored and explain your answer. Week Schedule Day
Hours
Monday
2
Wednesday
1
Saturday
3
Sunday
2
2 Peter, Alan, Emma, and John attend the same school. Their teacher recorded their attendance for 1 week and recorded it in her grade book. If they were present, she marked a “P ,” and if absent, an “A.” Determine who had the lowest and the highest attendance. Attendance Sheet
Name
Attendance
Peter
P,P,P,P,A
Alan
P,A,A,P,P
Emma
A,A,P,P,A
John
P,P,A,P,A
3
Sylvia was asked to count the sides of each of the figures shown in the box below. How many sides do all the figures have in total?
4
There were 4 players that flipped a coin 3 times to determine whether anyone could get tails (T) or heads (H) every single time. Jack flipped {H, H, T}, Adrian flipped {T,H,T}, Jared flipped {T,T,H}, and Anthony flipped {T,H,H}. Determine which side (H or T) the coin landed on more frequently.
190 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: The table below shows the number of chocolate cakes a bakery sold in the past week. Day Number of Chocolate Cakes Sold Monday
15
Tuesday
20
Wednesday
10
Thursday
20
Friday
25
Part I: Draw a bar graph to represent the data in the table.
Part II: Which day did the bakery sell the most number of chocolate cakes?
Part III: Which day did the bakery sell the least number of chocolate cakes?
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Four-STAR CHALLENGE - 3.MD.3 (3.MD.2.3) 1
Tony asked his colleagues how they traveled to their last vacation spot. The tally table shows the results. Transportation
2
Week
Frequency
Week 2
Airplane
Week 3
Bus
Week 4
Boat
= 6 people
How many people traveled by car and bus?
3
B a 10
C 19
How many people visited the theme park during Week 2 and Week 4? B Ca 56 A D 87 a 42 a 36
D a 20
Mandy did a survey to find out which color her friends liked best. She wrote the results in a table and used the data to make a picture graph with a key of = 7 friends.
4
Colors
Number of Friends
White
42
Black
35
How many will be drawn for white? Grid your answer. Dylan wanted to make a bar graph based on the information in the tally table below. Which of the following statements could be true? Check all that apply.
John’s bar will be longer than Andrew’s. Ava’s bar will be shorter than John’s. Ava’s bar will be longer than Michelle’s. Michelle’s bar will be the shortest. Andrew’s bar will be the longest. 192 I Smart to the Core I Educational Bootcamp
Third graders voted for their favorite class competition. Ana organized the data in a table to make a bar graph. Favorite Class Competitions
Favorite Colors
5
People
Week 1
Car
A a 9
The picture graph shows the number of people who visited a theme park each week.
Competition
Number of Votes
Sports Competition
18
Drawing Competition
13
Math Competition
11
Singing Competition
16
How many bars will Ana have on the x-axis of her graph? Grid your answer.
6
If 1 represents 3 flowers, which of the following statements could be true? Check all that apply.
Maria will have 3 on the graph. Kim will have 2 on the graph. Sylvia will have 9 on the graph. Jenny will have 5 on the graph. Greatest number of : Maria
7
Solve the word problems involving bar graphs.
A. The graph shows the number of apples B. The number of shipments a factory collected on a farm over the last 5 made over the last 5 months is shown months. What month did the farm below. What month did the factory collect the most apples? make the least number of shipments?
Month: _________________________
8
Month: _________________________
Solve the word problems involving pictographs.
A. Study the pictograph below.
B. Study the pictograph below.
Mickey
Number of Flowers Collected Hogan
Wendy
Dina
Sarah
Chloe
Tracy
Damien
Anne
Jane
Number of Cakes Baked
= 4 cakes
= 10 flowers
According to the pictograph, how many According to the pictograph, how many cakes did Wendy bake? flowers did all the kids collect?
193 I Copying is strictly prohibited
1
2
3
THINK TANK QUESTION 9
DIRECTIONS: The table below shows the number of light bulbs that were manufactured by a factory over the last 5 months. Month
Number of Light Bulbs
March
60,000
April
40,000
May
50,000
June
80,000
July
40,000
Part I: Draw a pictograph and a key to represent the data in the table.
Part II: Explain the importance of a key in a pictograph.
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4
MISSION 19: Generating Measurements and Making Line Plots Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
Bootcamp STRATEGY: Use a ruler to measure an object to the nearest inch.
1 of an 2
Step 1: Identify the intervals located on the ruler. The ruler should show the numbers that represent each inch. Step 2: Notice that between each 2 numbers on the ruler below, there are 3 lines that divide the 1 inch into 4 parts. The 4 parts represent a quarter of an inch.
Step 3: If the object being measured reaches the ¼-inch mark after the number 1, then the line is 1 1 inch long. 4
3 Step 4: If a line reaches the ¾-inch mark after the number 2, then the line is 2 inches 4 long.
2 1 Step 5: If a line reaches the mark (also the mark) after the number 7, then the line 4 2 1 is 7 inches long. 2
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TRAIN THE BRAIN PRACTICE 1 3.MD.4 (3.MD.2.4) DIRECTIONS: Measure the following objects. in.
1
2
in.
3
in.
4
in.
5
in.
DIRECTIONS: Create a line plot using the measurements from the objects above. 6
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Target PRACTICE 1 1
3
Stan uses an inch ruler to measure a leaf in a drawing book. What is the length of the leaf to the nearest fourth inch?
2
A a
1 12 inches
C
2 14 inches
A
1 14 inches
Ca
2 12 inches
Ba
2 34 inches
D a
3 inches
Ba
1 inch
D a
3 inches
Study the image below. Which of the following statements are true? Select all that apply.
4
Study the image below. Which of the following statements are true? Select all that apply.
The crayon is 5 inches long.
The carrot is longer than 10 inches.
The crayon is longer than 7 inches.
The carrot is 7 inches long.
The crayon is 7 inches long.
The carrot is shorter than 9 inches.
The crayon is shorter than 5 inches.
The carrot is 9 inches long.
The crayon is 6 inches long.
The carrot is longer than 7 inches.
The crayon is longer than 5 inches.
The carrot is 8 inches long.
3
5
Andrea uses an inch ruler to measure a safety pin. What is the length of the safety pin to the nearest half inch?
The tail of Sonny’s cat is 4 4 inches long. This length is between which 2 inch marks on a ruler?
1
6
Hanson’s pencil is 5 4 inches long. This length is between which 2 inch marks on a ruler?
A a
1 inch and 2 inches
A a
2 inches and 3 inches
B a
2 inches and 3 inches
B a
3 inches and 4 inches
Ca
3 inches and 4 inches
Ca
4 inches and 5 inches
D
4 inches and 5 inches
D
5 inches and 6 inches
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TRAIN THE BRAIN PRACTICE 2 3.MD.4 (3.MD.2.4) DIRECTIONS: Measure the following objects. 1
cm
2
cm
3
cm
4
cm
5
cm
DIRECTIONS: Create a line plot using the measurement of the objects above. 6
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Target PRACTICE 2 1
3
5
Harold uses an inch ruler to measure the length of a paperclip. How long is the paperclip to the nearest fourth inch?
2
Billy uses an inch ruler to measure a pushpin. What is the length of the pushpin to the nearest half inch?
A a
1 inch
Ca
114 inches
A a
1 inch
Ca
2 12 inches
B
1 24 inches
D a
2 inches
B
1 34 inches
D a
2 inches
Use an inch ruler to measure the image below. Select all that are true of the feather.
4
Use an inch ruler to measure the image below. Select all that are true of the baseball bat.
The feather is about 3 inches long.
The baseball bat is longer than 2 inches.
The feather is shorter than 6 inches.
The baseball bat is about 2 inches.
The feather is about 5 inches long.
The baseball bat is shorter than 5
The feather is longer than 5 inches.
The baseball bat is about 3 inches.
The feather is about 4 inches long.
The baseball bat is longer than 6 inches.
The feather is shorter than 3 inches.
The baseball bat is about 4 inches.
There is a sticker of a flag on a 1 notebook. The flag is 5 5 inches long. This length of the flag is between which 2 inch marks on a ruler?
6
A diary is 6 34 inches long. This length is between which 2 inch marks on a ruler?
A
5 inches and 6 inches
A
6 inches and 7 inches
B a
4 inches and 5 inches
B a
2 inches and 3 inches
Ca
3 inches and 4 inches
Ca
1 inch and 6 inches
D a
2 inches and 3 inches
D a
0 inch and 6 inches
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TRAIN THE BRAIN PRACTICE 3 3.MD.4 (3.MD.2.4) DIRECTIONS: Solve the problems below. 1 George stretched a spring as shown in the figure below. He was asked to measure the length of the stretched spring from Point A to B using an inch ruler. Explain how he would measure the object. What is the measure of the spring?
2 Adam planted a tree 20 months ago. He measured the height of the tree every 5 months. Based on the diagram below, what do you think the height of the tree was at 15 months? 5 feet 20 months
15 months
10 months
5 months
1 foot 200 I Smart to the Core I Educational Bootcamp
1 month
THINK TANK QUESTION DIRECTIONS: The tables below shows the length of different screws. Use the tables to complete the tasks below. Screw Screw 1 Screw 2 Screw 3 Screw 4
Length (in.) 3 4 1 2 1 4 1 2
Screw Screw 5 Screw 6 Screw 7 Screw 8
Length (in.) 1 4 1 4 1 2 3 4
Screw Screw 9 Screw 10 Screw 11 Screw 12
Length (in.) 1 2 3 4 3 4 1 2
Part I: Create a tally table using the information from the tables above.
Part II: Create a bar graph using the tally table you created in Part I.
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Four-STAR CHALLENGE - 3.MD.4 (3.MD.2.4) 1
3
17 5
Study the images below. Which of the following statements could be true? Select all that apply.
2
Study the images below. Which of the following statements could be true? Select all that apply.
The nail is 4 inches long.
The branch is longer by 5 inches.
The pencil is longer by 10 inches.
The comb is 5 inches long.
The nail is shorter by 9 inches.
The branch is longer by 4 inches.
The pencil is longer by 8 inches.
The branch is 10 inches long.
The nail is longer by 10 inches.
The branch is longer by 6 inches.
Nicola uses an inch ruler to measure a picture of a knife. What is the length of the knife to the nearest fourth inch?
16 4
Molly uses an inch ruler to measure a picture of a teaspoon. What is the length of the teaspoon to the nearest fourth inch?
A a
2 inches
C
2 14 inches
A a
3 12 inches
Ba
1 12 inches
D a
114 inches
Ba
1 4 inches
Jon bought a banana. The banana was 7 14 inches long. This length is between which 2 inch marks on a ruler?
3
C
2 12 inches
D a
2 inches
1
A cable is 9 inches long. This length 18 6 is between 4which 2 inch marks on a ruler?
A a
1 inch and 7 inches
A a
1 inch and 8 inches
B
7 inches and 8 inches
B a
4 inches and 5 inches
Ca
3 inches and 4 inches
C
9 inches and 10 inches
D a
6 inches and 7 inches
D a
0 inch and 9 inches
202 I Smart to the Core I Educational Bootcamp
7
Create a tally table using the information from each line plot below.
A.
B.
Length of Horns (in feet)
Length of Screws (in inches)
8
Draw a line plot to represent each tally table below.
A.
B. Length of Ribbons Length (feet) 1 5 2 5 3 5 4 5
Frequency
Length of Tentacles Length (inches) 4 7 5 7 6 7 7 7
Frequency
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2
3
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THINK TANK QUESTION 9
DIRECTIONS: The list below shows the different lengths of stickers. Use the information from the list to complete the tasks. 2 1 4 5 2 3 in. in. in. in. in. in. 8 8 8 8 8 8 5 4 1 3 1 5 in. in. in. in. in. in. 8 8 8 8 8 8 3 1 5 5 3 4 in. in. in. in. in. in. 8 8 8 8 8 8 1 4 5 3 1 2 in. in. in. in. in. in. 8 8 8 8 8 8 1 2 5 3 4 5 in. in. in. in. in. in. 8 8 8 8 8 8 Part I: Create a tally table using the information from the list above.
Part II: Create a line plot graph using the tally table you created in Part I.
204 I Smart to the Core I Educational Bootcamp
MISSION 20: UNDERSTANDING CONCEPTS OF AREA MEASUREMENT Recognize area as an attribute of plane figures and understand concepts of area measurement. a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
Bootcamp STRATEGY 1: Find the area of a rectangle by counting the unit squares. Area is defined as the inside space measured in square units. Area = 18 dots = 18 square units
To calculate the area: Step 1: Dot the middle of each individual unit as the inside space of the figure is counted.
Step 2: Add the number of dots in each square unit to find the area of the rectangle.
Bootcamp STRATEGY 2: Counting the number of unit cubes to determine the volume of a prism. 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Volume = 18 cubic units
Bootcamp STRATEGY 3: Create and count the number of unit squares to determine the area of a plane figure. 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
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TRAIN THE BRAIN PRACTICE 1 3.MD.5 (3.MD.3.5) DIRECTIONS: Determine the area of the figures shown.
2
1
Area =
Area = 4
3
Area =
Area =
6
5
Area = 206 I Smart to the Core I Educational Bootcamp
Area =
Target PRACTICE 1 1
3
Which of the following could be true of the figure? Select all that apply.
2
Which of the following could be true of the figure? Select all that apply.
Area: 24 square units.
Area: less than 25 square units.
Area: less than 24 square units.
Area: 20 square units.
Area: 20 square units.
Area: more than 30 square units.
Area: more than 30 square units.
Area: 24 square units.
Area: 32 square units.
Area: less than 20 square units.
Area: more than 20 square units.
Area: 30 square units.
Devon wants to buy a carpet to cover the floor of his office. Which of the following does Devon need to find to determine how much carpet he will need?
4
Liam wants to paint the background of a stage for a show. Which of the following does Liam need to find to determine how much space he will paint?
A a
Height of the office floor
A a
Perimeter of the stage’s background
B a
Length of the office floor
B a
Height of the stage’s background
Ca
Perimeter of the office floor
C
Area of the stage’s background
D
Area of the office floor
D a
Length of the stage’s background
5
How many square units make up the area of the shaded figure below? Grid your answer.
6
How many square units make up the area of the shaded figure below? Grid your answer.
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TRAIN THE BRAIN PRACTICE 2 3.MD.5 (3.MD.3.5) DIRECTIONS: Calculate the area of the figures shown.
2
1
Area =
Area = 4
3
Area =
Area =
6
5
Area = 208 I Smart to the Core I Educational Bootcamp
Area =
Target PRACTICE 2 1
Mandy decorated a wall in her bedroom with a poster. The figure below represents the poster.
2
What is the area of the poster? Grid your answer.
3
Richard wants to buy a piece of glass to cover a rectangular desktop. Which of the following does Richard need to find to determine how much glass he will need?
Paul is trying to figure out the area of his backyard. The shaded region below represents his backyard.
What is the area of the backyard? Grid your answer.
4
A farmer plants trees in his orchard. Which of the following does the farmer need to know to determine how much land he has to plant trees?
A a
Length of the table
A a
Perimeter of the orchard
B a
Height of the table
B
Area of the orchard
C
Area of the table
Ca
Length of the orchard
D a
Perimeter of the table
D a
Height of the orchard
5
Study the figures below. Which figures below have an area of 13 square units? Select all that apply.
6
Study the figures below. Which figures below have an area of 10 square units? Select all that apply.
209 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.MD.5 (3.MD.3.5) DIRECTIONS: Solve the problems below. 1
Jennifer is planning to make a swimming pool in her house. She has some area available near the backyard of her house as shown in the shaded portion of the figure below. Explain how to determine the available area in square units and solve.
Ashton is a table designer and designed the table shown in the shaded portion of 2 the figure below. How many square units would this table cover?
3
4
A construction company makes a bridge to connect 2 parallel roads as shown below. What will be the area (in square units) of the roads and bridge?
Jay is planning to have a rectangular tennis court made in the backyard of his house, but he is not sure whether there is enough space for it. He hires a contractor to determine this. Explain what the contractor must measure to determine whether there is enough space available.
210 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: Study the figure below. Use the figure to complete the tasks.
= 1 inch2
Part I: Determine the area of the figure above.
Part II: Explain how you were able to find the area of the figure.
211 I Copying is strictly prohibited
Four-STAR CHALLENGE - 3.MD.5 (3.MD.3.5) 13 1
Randy is trying to figure out the area of his porch. He drew the shape of the porch on a piece of paper.
14 2
What is the area of the porch? Grid your answer.
3
John wants to tile the entire floor of his kitchen. Which of the following does John need to find to determine how many tiles he will need?
Ira drew the shape of a dance floor of a dance hall on a dot paper.
What is the area of the dance floor? Grid your answer.
16 4
Jim wants to buy a mattress to fit his bed frame. Which of the following does Jim need to find to buy the mattress that will fit his bed frame?
A a
Perimeter of the floor
A
Area of the bed frame
B
Area of the floor
B a
Length of the bed frame
Ca
Height of the floor
Ca
Perimeter of the bed frame
D a
Length of the floor
D a
Height of the bed frame
5
Sandy drew a figure composed of 16 identical unit squares. Select all the statements below that are true.
6
Michael found a piece of wood. He can completely cover the wood with 21 identical unit squares. Select all the statements that could be true.
Area: 20 square units.
Area: less than 25 square units.
Area: 16 square units.
Area: less than 20 square units.
Area: 24 square units.
Area: more than 22 square units.
Area: more than 18 square units.
Area: 21 square units.
Area: less than 14 square units.
Area: 18 square units.
Area: less than 22 square units.
Area: 24 square units.
212 I Smart to the Core I Educational Bootcamp
7
Find the area of the figures. Explain your answer.
A.
B.
= 1 inch2
8
= 1 inch2
Solve the word problems.
A. Melissa was able to fit 16 unit squares B. Stephan was able to fit 24 unit squares inside a rectangle without overlapping. inside a rectangle without overlapping. What might the dimensions of the What might the dimensions of the rectangle be? Explain why you think rectangle be? Explain why you think these could be the dimensions of the these could be the dimensions of the rectangle. rectangle.
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2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Study the figure below. Use the figure to complete the tasks.
= 1 inch2
Part I: Find the area of the figure.
Part II: Rearrange and draw the unit squares so that there will be 12 rows instead of just 8 rows, but the same number of squares. What could the number of columns be? Explain your answer.
Part III: Compare the area of the figure above to the area of the figure you drew in Part II. What can you say about the 2 areas?
214 I Smart to the Core I Educational Bootcamp
MISSION 21: MEASURING AREA BY COUNTING UNIT SQUARES Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
Bootcamp STRATEGY 1: Find the area of a rectangle by counting unit squares. Area is defined as the inside space measured in square units. Area = 18 dots = 18 square units
To calculate the area: Step 1: Dot the middle of each individual unit as the inside space of the figure is counted.
Step 2: Add the number of dots in each square unit to find the area of the rectangle.
Bootcamp STRATEGY 2: Find the area of a rectangle by using repeated addition of the number of columns and rows.
To calculate the area: Step 1: Count the number of columns. There are 6 columns. Step 2: Count the number of rows. There are 3 rows. Step 3: Use repeated addition to add the number of columns an equal number of times to the amount of rows there are. Add 6 + 6 + 6 to get a total of 18 units. Note: You can also find the number of rows first, and then use repeated addition to add the number of rows an equal number of times to the amount of columns there are. 3 + 3 + 3 + 3 + 3 + 3 = 18 units. 6 3
215 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 3.MD.6 (3.MD.3.6) DIRECTIONS: Use the square units to calculate the area of the rectangles below.
1
2
Area:
Area:
DIRECTIONS: Calculate the area of the shaded regions.
3
4
Area:
Area:
5
6
Area:
216 I Smart to the Core I Educational Bootcamp
Area:
Target PRACTICE 1 Use the table for Questions 1–2. Bella is tiling the floor with 1 square foot tiles. The diagram below shows the floor.
The shaded area shows the part Bella has already tiled. What is the area of the floor that Bella has already tiled?
1
2
3
Use the table for Questions 4–5. Pearl is sewing squares together to make a quilt. The diagram shows the quilt in progress. Each square is 1 square inch.
The shaded area shows the squares Pearl has already sewn together. What is the area of the quilt that Pearl has already sewn?
4
A
21 feet2
Ca 19 feet
2
A a
19 inches2
Ca 22 inches
2
B a
20 feet2
D a 18 feet
2
B a
20 inches2
D 24 inches
2
The white area shows the part Bella has left to tile. What is the area of the floor that Bella has left to tile in square feet? Grid your answer.
Study the figure below. If each square is 1 square inch, what can be said about the area of the shaded region? Select all that apply.
5
6
The white area shows the part Pearl has left to sew together. What is the area of the part that Pearl has left to sew in square inches? Grid your answer.
Study the figure below. If each square is 1 square foot, what can be said about the area of the shaded region? Select all that apply.
Area: less than 44 square inches.
Area: 30 square feet.
Area: 36 square inches.
Area: more than 30 square feet.
Area: more than 44 square inches.
Area: 24 square feet.
Area: 44 square inches.
Area: less than 40 square feet.
Area: more than 36 square inches.
Area: 20 square feet.
217 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.MD.6 (3.MD.3.6) DIRECTIONS: Use the square units to calculate the area of the rectangles below.
1
2
Area:
Area:
DIRECTIONS: Calculate the area of the shaded regions.
3 1
2 4
Area:
5
Area:
6
Area:
218 I Smart to the Core I Educational Bootcamp
Area:
Target PRACTICE 2 Use the table for Questions 1–2. A farmer is sowing seeds in a field. The diagram shows the area to be sown. Each unit square is 1 square foot.
The shaded area shows the part the farmer has already sown. What is the area of the field that the farmer has already sown?
1
2
3
Use the table for Questions 4–5. Zoe is painting her bedroom wall. The diagram shows the area of the wall. Each unit square is 1 square foot.
The shaded area shows the part Zoe has already painted. What is the area of the wall that Zoe has painted already?
4
A a
10 feet2
C
12 feet2
A
16 feet2
Ca
18 feet2
B a
11 feet2
D a
13 feet2
B a
17 feet2
D a
19 feet2
The white area shows the part the farmer has to finish sowing. What is the area of the field that the farmer has left to sow in square feet? Grid your answer.
If each square is 1 square foot, which of the following figures has an area of 12 square feet? Select all that apply.
5
6
The white area shows the part Zoe has left to paint. What is the area of the wall that Zoe has left to paint in square feet? Grid your answer.
If each square is 1 square inch, which of the following figures has an area of 16 square inches? Select all that apply.
219 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.MD.6 (3.MD.3.6) DIRECTIONS: Solve the problems below. 1
Use the information below for Parts 1−3. The county has a list of every student who requires bus services for a particular district. The shaded blocks indicate the homes of the students who require transportation. For the purposes of answering the following questions, suppose that each block can be measured as a 2×2 square. Hint: The area of 1 block = 2×2 = 4 square units.
Part I: Determine how much area is covered by the homes of students who require bus transportation. Explain how you got your answer.
Part II: Determine the area of the homes of students who do not need to take a bus. Part III: If every student in the district required bus transportation, what would be the area of the homes in the district in square units? How did you get your answer?
2
Adam has made a walkway to his garden using gray-colored tiles, as shown below. Each tile is 3 square units in size. What is the area of this walkway? Explain how you got your answer.
3
Nancy made the drawing below during art class. She colored most of the parts in class and decided to color the rest at home. Each region has an area of 2 square units. Explain how much area she has already colored in and how much she needs to do at home.
220 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: Study the figures below. Use the figures to complete the tasks.
= 1 inch2
Part I: Determine the total area of the figure above. Show your work.
Part II: Explain how you were able to find the total area of the figure.
221 I Copying is strictly prohibited
Four-STAR CHALLENGE - 3.MD.6 (3.MD.3.6) Use the table for Questions 1–2. Selma divided her garden into equal sections. She wants to plant tulips in each section. The diagram shows all the sections of the garden. Each unit section is 1 square foot.
1
The shaded area shows the part Selma has already planted. What is the area of the garden that Selma has already planted?
Use the table for Questions 4–5. Suzy is placing stamps in an album. The stamps are the same size. The diagram shows 1 page of the album. Each stamp is 1 square inch.
4
The shaded area shows the page of the album that Suzy has already put stamps in. What is the area of the page that Suzy has already put stamps in?
A a
16 feet2
Ca 18 feet
2
A
11 inches2
Ca 13 inches
2
B
17 feet2
D a 19 feet
2
B a
12 inches2
D a 14 inches
2
2
3
The white area shows the part that Selma has left to plant. What is the area of the garden that Selma has left to plant in square feet? Grid your answer.
The living room can be covered completely using 32 square tiles. If each tile is 1 square foot, which of the following statements could be true? Select all that apply.
5
6
The white area shows the page of the album Suzy has left to put stamps in. What is the area of the white portion in square inches? Grid your answer.
Ivan used 86 square shapes to make a design. If each shape is 1 square centimeter, which of the following statements could be true? Select all that apply.
Area: 32 square feet.
Area: more than 86 square cm.
Area: 24 square feet.
Area: less than 80 square cm.
Area: 28 square feet.
Area: less than 90 square cm.
Area: more than 32 square feet.
Area: 80 square cm.
Area: less than 24 square feet.
Area: 86 square cm.
Area: more than 28 square feet.
Area: 90 square cm.
222 I Smart to the Core I Educational Bootcamp
7
Solve the word problems. Show your complete solution.
A. A rectangle is formed by stacking unit B. A rectangle is formed by stacking unit squares. If the rectangle has 5 rows and squares. If the rectangle has 7 rows and each row has 7 unit squares, what is each row has 8 unit squares, what is the area of the rectangle? the area of the rectangle?
8
Solve the word problems. Show your solution.
A. Jemma was able to stack 28 unit B. Lucas was able to stack 63 unit squares. squares. If the length of the squares is If the length of the squares is 9, what 7 units, what could be the width? Use could be the width? Use the diagram to the diagram to draw lines to solve. draw lines to solve.
Width = ? units
Width = ? units
Length = 7 units Length = 9 units
223 I Copying is strictly prohibited
1
2
3
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THINK TANK QUESTION 9
DIRECTIONS: Study the figure below. Use the figure to complete the tasks.
= 1 cm2
Part I: Find the total area of the figure.
Part II: Rearrange the unit squares so that there will be only 4 rows with the same number of squares. What could the number of columns be? Draw a figure to solve.
Part III: Compare the total area of the figure above to the total area of the figure you created in Part II. What can you say about the 2 areas?
224 I Smart to the Core I Educational Bootcamp
MISSION 22: calculating area Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with wholenumber side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
Bootcamp STRATEGY 1: Find the area of a rectangle with whole-number side lengths by tiling it.
6 units
Step 1: Tile the rectangle with unit squares with a rule to ensure even dimensions according to the units provided. Step 2: Count the number of unit squares to get the area of the rectangle. 5 units Example: = 1 square unit
= 30 square units
Bootcamp STRATEGY 2: Find the area of a rectangle by multiplying the length of the rectangle by its width. The area of a rectangle is calculated by using the formula length × width. To calculate the area: Step 1: Mark each unit as the length of the rectangle is counted and record the number as the length. Step 2: Mark each unit as the width of the rectangle is counted and record the number as the width. Step 3: Multiply the length by the width to find the area of the rectangle. Example: Area = length × width = 6 units × 3 units = 18 square units 6 3
225 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 3.MD.7 (3.MD.3.7) DIRECTIONS: Determine the length of the rectangles below. 1
3
2
Length:
Length:
Length:
DIRECTIONS: Determine the width of the rectangles below. 4
6
5
Width:
Width:
Width:
DIRECTIONS: Use the unit squares to find the area of the rectangles below. 7
8
Area:
Area:
DIRECTIONS: Use the area formula to find the area of the rectangles below. 9
10
Area:
x
226 I Smart to the Core I Educational Bootcamp
=
Area:
x
=
Target PRACTICE 1 1
An architect drew the sketch shown below of a trail through a park. What is the area of the footpath in meters squared? Grid your answer.
2
The drawing below represents a tablecloth in Mila's dining room. What is the area of Mila’s tablecloth in meters squared?
9 meters
5 feet 3 meters
3
Poona is making a pattern of square tiles as shown below. If the pattern continues, the next shape will have an area of 32 square units. What will be its length?
A a
4 units
Ca
12 units
B
8 units
D a
16 units
5
What is true about the shape below? Select all that apply.
3 feet
4
6
Ruby made the pattern below. Each unit square is 1 square inch. If the pattern continues, what will be the area of the fourth block?
A
8 square inches
Ba
12 square inches
Ca
16 square inches
D a
18 square inches
What is true about the shape below? Select all that apply.
The area is 12 square inches.
There are 4 columns.
There are 5 rows.
The area is 36 square feet.
The area is 15 square inches.
The area is 30 square feet.
There are 5 columns.
The area is 42 square feet.
The area is 30 square inches.
There are 4 rows. 227 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.MD.7 (3.MD.3.7) DIRECTIONS: Determine the length of the rectangles below. 1
3
2
Length:
Length:
Length:
DIRECTIONS: Determine the width of the rectangles below. 4
6
5
Width:
Width:
Width:
DIRECTIONS: Use the unit squares to find the area of the rectangles below. 10 units
7
6 units
8
4 units 7 units
Area:
Area:
DIRECTIONS: Use the area formula to find the area of the rectangles below. 9
10
10 units
9 units
4 units
Area:
x
228 I Smart to the Core I Educational Bootcamp
=
3 units
Area:
x
=
Target PRACTICE 2 1
Hilbert wanted to lay some square tiles in his swimming pool. What is the area of the swimming pool in square feet? Grid your answer.
2
Prita colored a rectangular shape on grid paper. What area does the shape represent in square meters? Grid your answer. 7 meters
10 feet
4 meters 9 feet
3
Demetrius drew the shapes shown. If the pattern continues, the next shape will have an area of 48 square units. What will be its length?
A a
8 units
C
16 units
Ba
12 units
D a
24 units
5
Select all that can be true of the shape below. 7 inches
4
Ashley uses wooden blocks to make the pattern below. Each unit square is 1 square inch. If the pattern of shapes continues, what will be the area of the fourth shape?
A a
16 square inches
B
32 square inches
Ca
28 square inches
D a
30 square inches
6
Select all that can be true of the shape below. 5 feet 2 feet
2 inches 7 inches
5 inches 5 inches
2 inches
2 feet 3 feet
2 feet
1 foot
The area is 24 square inches.
The area is 15 square feet.
The area is 28 square inches.
The area is 13 square feet.
The area is 56 square inches.
The area is 18 square feet.
Area = (7×2) + (5×2).
Area = (5×2) + (3×1).
Area = (7×7) + (5×5).
Area = (2×2) + (2×2) + (5×1). 229 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.MD.7 (3.MD.3.7) DIRECTIONS: Solve the problems below. Use the details given below for Questions 1−3. Adam bought a chess set and its board is shown below. Each square box has an area of 2 square units.
1 Explain how to determine the area of the whole chess board and solve.
2 How much area is covered by the white squares of the chess board? Explain how you got your answer.
3 Indicate how much area is covered by both colors in 1 row and explain how you got the answer.
4 The diagram shown below represents a parking lot for an office building. Each parking space can fit only 1 car and has an area of 10 square units. How much area is used by the parking lot. How many cars can fit in the parking lot at once?
230 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION DIRECTIONS: Study the figure below. Use the figure to complete the tasks.
6 inches
10 inches Part I: Find the area of the rectangle by dividing the rectangle into unit squares.
Part II: Explain how breaking up the rectangle into square units can help to find the area of a rectangle.
Part III: Find the area of the rectangle using the formula for area.
Part IV: Compare the results in Part I and Part III.
231 I Copying is strictly prohibited
four-STAR CHALLENGE - 3.MD.7 (3.MD.3.7) 13 1
Bessy needs to find the area of the image below for a project she is doing. What is the area of the image in square feet? Grid your answer.
14 2
The drawing represents a rug in Carmen's drawing room. What is the area of Carmen’s rug in square feet? Grid your answer. 5 feet
8 feet
4 feet
3
17 5
Amanda wanted a new rug for her living room. She bought a rug 6 feet long and 4 feet wide. What is true about the area of the rug she bought? Select all that apply.
5 feet
4
Neil was asked to paint a wall. The wall is 12 feet long and 6 feet high. What is true about the area of the wall he needs to paint? Select all that apply.
Area: 20 square feet.
Area: less than 100 square feet.
Area: 10 square feet.
Area: less than 36 square feet.
Area: 24 square feet.
Area: more than 50 square feet.
Area: more than 20 square feet.
Area: 42 square feet.
Area: less than 24 square feet.
Area: 56 square feet.
Area: more than 30 square feet.
Area: 36 square feet.
Fiona drew a diagram of her kitchen as shown below. Each unit square is equal to 1 square foot. What is the total area of Fiona’s kitchen?
2
A a
13 feet
Ba
24 feet2
2
C
19 feet
D a
32 feet2
232 I Smart to the Core I Educational Bootcamp
The area of a clubhouse is shown 18 6 below. Each unit square is equal to 1 square meter. What is the total area of the clubhouse?
A
16 square meters
Ba
28 square meters
Ca
35 square meters
D a
47 square meters
7
Find the area of the rectangle by dividing it into square units.
A.
B. 5 cm 10 cm
8
5 feet 9 feet
Solve the following word problems involving area. Show your solution.
A. Marissa found a rectangle having a B. Diana found a square having a side with length of 8 inches and a width of 10 a length of 10 centimeters. What is the inches. What will be the area of the area of the square? rectangle?
233 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Study the figure below. Use the figure to complete the tasks.
6 meters
7 meters Part I: Find the area of the rectangle by dividing it into unit squares.
Part II: Explain how dividing the rectangle can help to find the area of a rectangle.
Part III: Find the area of the rectangle using the formula for area.
Part IV: Compare the results in Part I and Part III.
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MISSION 23: determining the Perimeter of A Polygon Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
Bootcamp STRATEGY 1: Find the perimeter of a rectangle by counting the lengths and widths of a two-dimensional figure. Perimeter is defined as the total distance around the edge of a figure. Perimeter = 6 + 3 + 6 + 3 = 18 To calculate the perimeter: Step 1: Mark the side of each unit of the figure as you are counting and record the 6 number.
Step 2: Add the length of each side to find the perimeter of the rectangle.
3
3 6
Bootcamp STRATEGY 2: Find the unknown side length of a rectangle when given the perimeter and width. Perimeter is defined as the total distance around the edge of the figure. To calculate the length: Step 1: Add the known sides. In this case, the width is 5; therefore, 5 + 5 = 10. Step 2: Subtract the known sides from the perimeter. In this case, 40 − 10 = 30. Step 3: Divide the subtrahend by 2 to represent the 2 unknown sides (lengths). In this case, 30 ÷ 2 = 15. ?
Example: 5
Perimeter = 40
?
5
? = 15
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TRAIN THE BRAIN PRACTICE 1 3.MD.8 (3.MD.4.8) DIRECTIONS: Calculate the perimeter of the shapes below.
1
9
2 7
Perimeter:
6
3
Perimeter:
_____________________
4
_____________________
6
7
7
3
Perimeter:
5
5
Perimeter:
_____________________
6
5
11
8 7
7
4 Perimeter:
_____________________
_____________________
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6
Perimeter:
_____________________
Target PRACTICE 1 1
Eli drew a picture with a perimeter of 26 inches. Which picture below did Eli draw?
2 in.
Ca 4 in.
4 in.
8 in. 3 in.
5 in.
3
4 in. 6 in.
5 in.
Ba 3 in.
Ken drew the shape of a playground on grid paper.
6 in.
4 in.
A a 2 in.
2
D 5 in.
What is the perimeter of the playground? A 20 units Ca 16 units
5 in. 8 in.
Ba
Bruce cut a rectangular shape with a perimeter of 34 centimeters. The width of the rectangle is 7 cm. What is the length in centimeters? Grid your answer.
4
D a
18 units
12 units
Sammy wants to put some trim around a picture he bought. How many centimeters of trim does Sammy need for the perimeter of the picture in centimeters? Grid your 6 cm answer. 8 cm
8 cm 6 cm
5
Carl bought a piece of property. The perimeter of the property is 90 yards. Select all the properties below he could have bought.
6
Diana bought a new area rug for her bedroom. The perimeter of the rug is 28 feet. Select all the rugs below she could have bought.
21 yd
15 yd
6 ft
7 ft
24 yd
28 yd
8 ft 20 yd
22 yd
4 ft
5 ft
10 ft
22 yd
25 yd
8 ft
9 ft 8 ft
26 yd 19 yd
28 yd 20 yd
6 ft 9 ft
9 ft 237 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.MD.8 (3.MD.4.8) DIRECTIONS: Calculate the perimeter of the shapes below. 3
1
2 9
9
7
8
5
Perimeter:
Perimeter:
_____________________
8
3
4
_____________________
6
5 8 5 6
Perimeter:
3
5
Perimeter:
_____________________
6
3
7
_____________________
9
9
9
9
7 4
Perimeter:
_____________________
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Perimeter:
_____________________
Target PRACTICE 2 1
Joanna has a photo album with a perimeter of 18 inches. Which of the following is Joanna’s album?
5 in.
5 in.
Ca
5 in.
3 in.
3
What is the perimeter of the shape?
8 in. 3 in.
6 in.
5 in. 5 in.
6 in.
B 3 in.
Ash drew this shape on grid paper:
5 in.
3 in.
A a
2
D a 4 in.
4 in. 8 in.
Beth uses 16 feet of railing around the perimeter of a rectangular barn. The barn is 5 feet long. What is the width of the barn in feet? Grid your answer.
4
A
16 units
Ca
11 units
Ba
12 units
D a
8 units
Flora is putting wood trim around her drawing to make a frame. How many inches of wood trim does Flora need for the perimeter of the drawing in inches? Grid your answer. 9 inches
7 inches
7 inches 9 inches
5
Mr. Green wants to place a fence around his backyard. His backyard is 5 yards long and 2 yards wide. If the fencing material costs $9 per yard, which of the following could be true? Select all that apply.
6
Jessie wants to put lace around her decorative pillow. Her pillow is 3 feet long and 2 feet wide. If the lace costs $2 per foot, which statements could be true? Select all that apply.
The perimeter is 14 yards.
The area is 5 square feet.
Total cost of fencing: $56
The area is 6 square feet.
The area is 90 square yards.
The perimeter is 10 feet.
Total cost of fencing: $90
The perimeter is 6 feet.
The area is 10 square yards.
Total cost of lace: $12
The perimeter is 10 yards.
Total cost of lace: $10
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TRAIN THE BRAIN PRACTICE 3 3.MD.8 (3.MD.4.8) DIRECTIONS: Solve the problems below. 1 An architect made a scale sketch of a house on the grid paper shown below. Each small square has a length of 1 centimeter. What is the perimeter of his sketch? Explain how you got the answer.
2 Fred decided to frame a picture of his car. He bought the square frame shown below. The length of 1 side of the square frame is 4 centimeters. Determine the perimeter of the frame.
3 Mary bought a cutting board with a width of 3 centimeters and a perimeter of 24 centimeters. Explain how to determine the length of the board.
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THINK TANK QUESTION DIRECTIONS: Study the shaded figures below. Use the figures to complete the tasks.
Figure 2
Figure 1
Figure 3
Part I: Find the perimeter of each figure. Figure 1: __________________________ Figure 2: __________________________ Figure 3: __________________________
Part II: Find the area of each figure. Figure 1: __________________________ Figure 2: __________________________ Figure 3: __________________________
Part III: Explain how you were able to find the perimeters and areas of the figures.
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Four-STAR CHALLENGE - 3.MD.8 (3.MD.4.8) 1
3
Cameron has a rectangular calendar. The perimeter of the calendar is 42 centimeters. The width of the calendar is 9 centimeters. What is the length?
2
Hamilton drew a 4-sided shape that measures 6 inches on each side. What is the perimeter of the shape?
A
12 cm
Ca
21 cm
A a
20 inches
C
24 inches
Ba
14 cm
D a
33 cm
Ba
22 inches
D a
76 inches
Bryan drew a 38-cm border around his sketch. What is the unknown side length in centimeters? Grid your answer. 6 cm
4
2 cm 4 cm
4 cm
Mrs. Hamm wants to sew lace trim around a handkerchief. How many centimeters of lace trim does Mrs. Hamm need for the perimeter of the handkerchief? Grid your answer. 7 cm
3 cm
6 cm
6 cm
a 7 cm
5
Merida wants to put new tiles on her bathroom floor. Her bathroom is 2 feet long and 2 feet wide. If each 1square foot tile costs $5, select all that could be true.
6
Sally needs a piece of cardboard for her art project. The piece of cardboard needs to be 3 feet high and 3 feet long. The cost for 1 piece of cardboard at that size is $2. Select all the statements that are true.
Area: 8 square feet
Total cost of wallpaper: $9
Area: 4 square feet
Total cost of wallpaper: $12
Perimeter: 4 square feet
Total cost of wallpaper: $18
Total cost of tiles: $16
Area: 9 square feet
Total cost of tiles: $20
Area: 12 square feet
Total cost of tiles: $9
Area: 18 square feet
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7
Solve the following word problems involving perimeter. Show your complete solutions.
A. Anthony wants to enclose a rectangular B. The perimeter of a rectangular window garden with a fence. If the garden is 8 is 18 feet. If the longer side of the feet long and 5 feet wide, how much window measures 6 feet, how long is fencing material does Anthony need? the shorter side?
8
The red shoebox is 8 inches long and 6 inches wide; a greed shoebox is 4 inches long and 10 inches wide.
Part I: Which of the 2 shoeboxes has the greater perimeter?
Part II: Which of the 2 shoe boxes has the greater area? Area of Red Shoebox 1:
Area of Green Shoebox 2:
243 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Study the shaded figures below. Use the figures to complete the tasks.
Figure 2
Figure 1
Figure 3
Part I: Find the perimeters and areas of each figure. Perimeter
Area
Figure 1:
___________________ ___________________
Figure 2:
___________________ ___________________
Figure 3:
___________________ ___________________
Part II: Arrange the figures in order from least to greatest for the perimeters and areas. Perimeter:
Figure ___ < Figure ___ < Figure ___
Area:
Figure ___ < Figure ___ < Figure ___
Part III: Explain how you were able to get the perimeters and areas of the figures.
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MISSION 24: Classifying shapes Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
Bootcamp STRATEGY 1: Identify figures based on the number of sides and the number of angles. A triangle has 3 sides and 3 angles.
A pentagon has 5 sides and 5 angles.
A quadrilateral has 4 sides and 4 angles.
A hexagon has 6 sides and 6 angles.
Bootcamp STRATEGY 2: Classify triangles based on the size of the angle. acute acute
acute acute
acute obtuse acute
right
A right triangle has one right angle.
An obtuse triangle has one obtuse angle.
An acute triangle has three acute angles.
Bootcamp STRATEGY 3: Classify quadrilaterals by the number of sides, types of lines, and the size of its angles. A trapezoid has 1 pair of parallel sides.
A rectangle has 4 right angles and 2 pairs of parallel sides.
A quadrilateral has 4 sides and 4 angles. A parallelogram has 2 pairs of parallel sides.
A square has 4 right angles, 4 equal sides, and 2 pairs of parallel sides.
A rhombus has 4 equal sides and 2 pairs of parallel sides.
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TRAIN THE BRAIN PRACTICE 1 3.G.1 (3.G.1.1) DIRECTIONS: Identify the shape and its properties using the chart below.
SHAPE
NAME OF THE SHAPE
1
2
3
4
5
6
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NUMBER OF SIDES
NUMBER OF VERTICES
NUMBER OF RIGHT ANGLES
NUMBER OF ACUTE ANGLES
NUMBER OF OBTUSE ANGLES
Target PRACTICE 1 Use this shape for Questions 1–2.
Use this Venn diagram for Questions 4–5. Part A: Polygons with Right Angles
1
2
3
Susan used line segments to draw the shape shown above. How many line segments does Susan’s shape have? A a 3
4
Andy used a Venn diagram to sort shapes. What label could he use for Part B? A a Open Shapes
B
4
B
Ca
5
Ca
D a
6
D a
How many right angles does this shape have? A a
0
B a
1
Ca
2
D
4
Marjorie drew a shape that has 4 sides and 4 interior angles. Which of the following statements could be true? Check all that apply.
5
6
Part B:
Quadrilaterals
Shapes with 1 Right angle
Andy found some more shapes to sort. Which shape below should he place on Part A of the diagram? A
B a
Ca
D a
Tom folded a piece of paper to form a shape that has 4 sides and 4 interior angles. Which statements below are true? Check all that apply.
The shape could be a trapezoid.
The shape could be a quadrilateral.
The shape could be a pentagon.
The shape could be a triangle.
The shape could be a triangle.
The shape could be a square.
The shape could be a square.
The shape could be a heptagon.
The shape could be a hexagon.
The shape could be a rectangle.
The shape could be a rectangle.
The shape could be a pentagon. 247 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 3.G.1 (3.G.1.1) DIRECTIONS: Identify the shape and its properties using the chart below.
SHAPE
NAME OF THE SHAPE
1
2
3
4
5
6
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NUMBER OF SIDES
NUMBER OF VERTICES
NUMBER OF RIGHT ANGLES
NUMBER OF ACUTE ANGLES
NUMBER OF OBTUSE ANGLES
Target PRACTICE 2 Use this shape for Questions 1–2.
Use this Venn diagram for Questions 4–5. Part A: Quadrilaterals
1
2
3
Tim used line segments to draw the shape shown above. How many line segments does Tim’s shape have? A a 3
4
Randy used a Venn diagram to sort shapes. What label should he use for Part B? A Polygons with Right Angles
B
4
B a
C
5
Ca
D a
6
D a
How many right angles does this shape have? A
0
B a
1
C
2
D a
3
Mike saw a traffic sign shaped like a hexagon. Which of the following statements could be true? Check all that apply. The shape has 5 sides.
5
Part B:
Quadrilaterals
Shapes with 1 Right Angle
Ron found some more shapes to sort. Which shape below should he place into Part A of the Venn diagram? A a
B a
Ca
D
6 A carpenter created a table in the shape of a pentagon. Which of the following statements could be true? Check all that apply. The shape has 5 sides.
The shape has 6 interior angles.
The shape has 7 sides.
The shape has 4 sides.
The shape has 6 sides.
The shape has 5 interior angles.
The shape has 7 interior angles.
The shape has 4 interior angles.
The shape has 5 interior angles.
The shape has 6 sides.
The shape has 6 interior angles. 249 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 3.G.1 (3.G.1.1) DIRECTIONS: Solve the problems below. 1 Adam was asked to make a square, but instead he made the figure shown below. Describe the properties of the shape below.
2 Audrey drew the shape and angle shown below. She asked her friend to classify the angle of the lines she drew inside the shape. Explain how her friend would classify the angle.
3 Study the figure below. How many angles in the figure are acute? Explain how you got the answer. Label each acute angle on the figure with the letter “A.”
4 Evan was asked to draw a closed shape that had fewer than 5 sides. Name any 4 shapes that Evan can draw.
5 Alex makes a shape that has 3 angles and 3 sides. There is 1 angle that is 90ᵒ and the other angle is acute. What will be the third angle in the shape?
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THINK TANK QUESTION DIRECTIONS: Jones went to a jewelry store. He saw that a jeweler crafted gems into the shapes seen below. Using these shapes, answer the following questions.
Gem 1
Gem 2
Gem 3
Gem 4
Gem 5
Gem 6
Gem 7
Gem 8 Gem 9 Part I: If Jones wants to buy a gem that has more than 4 sides, which gem(s) could he choose? Write the number that represents the gem shape(s) with more than 4 sides. Explain your answer.
Part II: If Jones does not want to buy a gem that has a right angle, which gem(s) could he choose? Write the number that represents the gem(s) that do not have right angles. Explain your answer.
Part III: If Jones wants to buy 1 triangular-shaped gem and 1 rhombus-shaped gem, determine which gem(s) he might pick by writing down the corresponding number.
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Four-STAR CHALLENGE - 3.G.1 (3.G.1.1) Use this shape for Questions 1–2.
Use this Venn diagram for Questions 4–5. Part A: Quadrilaterals
1
2
3
Anthony used line segments to draw the shape shown above. How many line segments does Anthony’s shape have? A a 2
4
Part B:
George used a Venn diagram to sort shapes. What label could he use for Part B? A a
Open Shapes
B a
4
B a
Quadrilaterals
Ca
6
Ca
Shapes with Sides of Equal Length
D
8
D
Polygons with 1 Right Angle
How many right angles does this shape have? A a
0
B a
1
Ca
2
D
4
Which statements below could be true? Check all that apply.
5
George found some more shapes to sort. Which shape below should he place into the overlap section of the Venn diagram? A
B a
Ca
D a
6 Which statements below could be true? Check all that apply.
The shape is a rectangle.
The shape has 4 interior angles.
The shape has 4 right angles.
The shape has 1 pair of equal sides.
The shape has 2 pairs of equal sides.
The shape has 2 right angles.
The shape has 4 sides.
The shape has 2 pairs of equal sides.
The shape has 2 right angles.
The shape has 4 right angles.
The shape has 1 pair of equal sides.
The shape is a trapezoid.
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7
Andy is trying to determine the similarities and differences between the 2 groups of shapes. Help Andy explain the characteristics that show how the groups are the same and how they are different.
Group 2
Group 1
8
Alice has to solve a problem in her math book. The question shows the figures below and asks her to find the figure that is different from the others. Help Alice find the figure that is different and explain the characteristics that make it different from the other figures.
Figure 1
Figure 2
Figure 3
Figure 4
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1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Kevin wants to separate the 12 shapes shown below into 4 groups: G1, G2, G3, and G4. Determine how each shape can be placed into 1 of the 4 groups. Draw each shape in the group it belongs to and write 1 sentence describing the feature of each group.
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MISSION 25: partitioning shapes into equal areas Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
Bootcamp STRATEGY: Determine the number of shapes that are congruent within the shape. STEP 1: Count the number of congruent shapes within the partitioned shape. STEP 2: Record the fractional part represented by each of the congruent shapes. Example 1: Fractional part for each congruent shape
1 2
Fractional part for each congruent shape
1 8
Example 2:
Example 3:
Fractional part for each congruent shape
1 6
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TRAIN THE BRAIN PRACTICE 1 3.G.2 (3.G.1.2) DIRECTIONS: Identify the fractional parts for the shapes shown below.
1
2
3
4
5
6
7
8
9
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Target PRACTICE 1 1
3
5
Jackie divided a quadrilateral into equal parts that each show 12 . Which figure below could be Jackie's quadrilateral? A
Ca
B a
D a
What fraction represents each equal part that is shown in the figure below? Grid your answer.
Select all the models that show the 1 fraction 3 .
2
4
6
Pico divided a rhombus into equal parts that each show 16 . Which figure below could be Pico’s rhombus? A a
C
B a
D a
What fraction represents each equal part that is shown in the figure below? Grid your answer.
Select all the models that show the 1 fraction . 6
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TRAIN THE BRAIN PRACTICE 2 3.G.2 (3.G.1.2) DIRECTIONS: Identify the fractional parts for the shapes shown below.
1
2
3
4
5
6
7
8
9
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Target PRACTICE 2 1
3
5
Luke divided a rectangle into equal parts that each show 14 . Which figure below could be Luke’s rectangle?
2
Amad divided a rhombus into equal parts that each show 18 . Which figure below could be Amad’s rhombus?
A
Ca
A a
Ca
B a
D a
B
D a
What fraction represents each equal part that is shown in the figure below? Grid your answer.
Dan drew a triangle and divided it into equal parts. Select all the triangles that Dan could have drawn.
4
What fraction represents each equal part that is shown in the figure below? Grid your answer.
6 Mike drew a rectangle and divided it into 3 equal parts. Select all the rectangles that Mike could have drawn.
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TRAIN THE BRAIN PRACTICE 3 3.G.2 (3.G.1.2) DIRECTIONS: Solve the problems below. 1
Henry made a square out of clay and then decided to divide it into 4 equal parts as shown below. What fraction names each of the 4 shapes he got after dividing the square?
2
Ellen cut a pentagon out of paper. She decided to cut it into 2 pieces as shown below. What 2 types of shapes did she create?
3
Sissy has an app on her phone that combines shapes. She input a square and a triangle and the output she got is shown below. How many triangles are shown on the output shape?
4
If the shape below was split in half, how many unit fractions would be represented in each half?
5
Paul made several triangles within a triangle as shown below. How many triangles make up the figure? Indicate how many right triangles there are.
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THINK TANK QUESTION DIRECTIONS: Use the figures below to complete the tasks below.
Figure 1 Figure 2 Part I: Explain how to divide Figure 1 into 8 equal parts. Draw the lines showing how you would divide it into 8 equal parts on the shape provided above.
Part II: Explain how you would divide Figure 2 into 4 equal parts. Draw the lines showing how you would divide it into 4 equal parts on the shape provided above.
Part III: Write the equivalent fraction for 1 part of a whole for Figure 1 and for Figure 2 in the lines provided below. Explain how you determined your answer. For Figure 1:
For Figure 2:
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Four-STAR CHALLENGE - 3.G.2 (3.G.1.2) 13 1
3
5
Tony divided a square into equal parts that each show 14 . Which figure below could be Tony’s square? A a
Ca
B a
D
What fraction represents each equal part that is shown in the figure below? Grid your answer.
Identify the shape(s) below that are divided into equal parts.
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14 2
16 4
16 6
Sandy divided a rhombus into equal parts that each show 18 . Which figure below could be Sandy’s rhombus? A a
C
B a
D a
What fraction represents each equal part that is shown in the figure below? Grid your answer.
Identify the shape(s) that are NOT divided into equal parts.
7
Consider the 2 figures given below. Explain how to divide both figures equally into 4 parts. If you cannot divide the figures into 4 parts, explain why not.
Figure 1
8
Figure 2
Consider the figures shown below. What fraction is the shaded part of the whole for each figure? Explain how you determined your answer.
Figure 1
Figure 2
Figure 1:
Figure 2:
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1
2
3
4
THINK TANK QUESTION 9
DIRECTIONS: Use the figures below to solve the questions below.
Figure 1
Figure 2
Figure 4
Figure 3
Figure 5
Part I: Find the figures that represent the same shaded portion. Write the fractions that represent the shaded regions as parts of a whole.
Part II: Do any of the figures above have more than 6 divisions? If so, which one(s)? Write the fraction of a whole that the figures with more than 6 divisions represent.
Part III: Determine the fractional value for each figure above and write different mathematical sentences that equal 1 whole. For example, 1/4 + 3/4 = 1 . Figure 1: _____________
Figure 2: __________________
Figure 3: _____________
Figure 4: _________________
Figure 5: _____________
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DIRECTIONS: Complete the two−minute drills. 2- MINUTE MULTIPLICATION CHALLENGE
2- MINUTE MULTIPLICATION CHALLENGE
7×4=
6×3=
6×4=
5×9=
7×8=
5×7=
5×5=
6×8=
9×5=
4×9=
7×4=
3×4=
8×5=
2×4=
9×6=
4×9=
7×6=
2×9=
3×6=
2×3=
8×6=
7×3=
7×5=
4×8=
4×5=
9×3=
8×8=
7×8=
5×8=
8×7=
4×7=
9×3=
4×8=
9×4=
8×9=
3×5=
3×9=
9×6=
4×3=
5×6=
TOTAL CORRECT:
1
2
3
4
YOUR SCORE HERE
TOTAL CORRECT:
1
2
3
4
YOUR SCORE HERE
265 I Copying is strictly prohibited
DIRECTIONS: Complete the two−minute drills. 2- MINUTE MULTIPLICATION CHALLENGE
2- MINUTE MULTIPLICATION CHALLENGE
6×5=
4×3=
7×4=
5×3=
6×8=
5×9=
7×7=
6×9=
7×8=
2×9=
6×5=
3×9=
4×5=
4×8=
9×7=
4×4=
5×6=
3×8=
9×6=
2×8=
6×6=
4×6=
7×5=
4×3=
5×5=
7×4=
3×5=
7×3=
8×9=
9×6=
9×8=
8×3=
5×8=
6×4=
8×6=
6×4=
3×9=
8×5=
4×9=
5×6=
TOTAL CORRECT:
1
2
3
4
YOUR SCORE HERE
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TOTAL CORRECT:
1
2
3
4
YOUR SCORE HERE
Grade 3
Lesson Number:
Name:
Target Practice 1
Target Practice 1
Question #:
Question #:
Target Practice 2
Target Practice 2
Question #:
Question #:
Four-Star Challenge Question #:
Four-Star Challenge Question #:
NOTE: For mixed numbers, write the whole number, leave a space, and write the fraction. Do not fill in a bubble for the empty space. 267 I Copying is strictly prohibited
NOTES
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