SMART TO THE CORE Teacher’s Edition GRADE 4
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—Teacher’s Edition(Grade 4) 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 CCSS Code
OF CONTENTS Grade 4
SMART TO THE CORE LESSONS
FOUR STAR CHALLENGE—SCORING RUBRIC
PAGE NUMBER 4
4.OA.1 (4.OA.1.1)
MISSION 1: Making Multiplicative Comparisons
5—14
4.OA.2 (4.OA.1.2)
MISSION 2: Making Multiplicative and Additive Comparisons
15—24
4.OA.3 (4.OA.1.3)
MISSION 3: Solving Multi-Step Word Problems
25—34
4.O.A.1.a & 4.OA.1b
MISSION 4: Using Comparative Relational Thinking
35—44
4.OA.4 (4.OA.2.4)
MISSION 5: Investigating Factors and Multiples
45—54
4.OA.5 (4.OA.3.5)
MISSION 6: Finding Number and Shape Patterns
55—64
4.NBT.1 (4.NBT.1.1)
MISSION 7: Understanding Place Value Relationships
65—74
4.NBT.2 (4.NBT.1.2)
MISSION 8: Reading, Writing, and Comparing Numbers
75—84
4.NBT.3 (4.NBT.1.3)
MISSION 9: Rounding Whole Numbers
85—94
4.NBT.4 (4.NBT.2.4)
MISSION 10: Adding and Subtracting Whole Numbers
95—104
4.NBT.5 (4.NBT.2.5)
MISSION 11: Multiplying Whole Numbers
105—114
4.NBT.6 (4.NBT.2.6)
MISSION 12: Dividing Whole Numbers
115—124
4.NF.1 (4.NF.1.1)
MISSION 13: Finding Equivalent Fractions
125—134
4.NF.2 (4.NF.1.2)
MISSION 14: Using Models to Compare Fractions
135—144
4.NF.3 (4.NF.2.3)
MISSION 15: Adding Fractions with Like Denominators
145—154
4.NF.4 (4.NF.2.4)
MISSION 16: Multiplying Fractions by a Whole Number
155—164
4.NF.5 (4.NF.3.5)
MISSION 17: Adding Fractions with Denominators of 10 & 100
165—174
4.NF.6 (4.NF.3.6)
MISSION 18: Converting Decimals and Fractions
175—184
4.NF.7 (4.NF.3.7)
MISSION 19: Comparing Decimals & Fractions to the 100th Place
185—194
4.MD.1 (4.MD.1.1)
MISSION 20: Using Custom and Metric Measurements
195—204
4.MD.2 (4.MD.1.2)
MISSION 21: Solving Problems Involving Measurement
205—214
4.MD.3 (4.MD.1.3)
MISSION 22: Calculating Area and Perimeter
215—224
4.MD.4 (4.MD.2.4)
MISSION 23: Solving Problems Presented in Line Plots
225—234
4.MD.5 (4.MD.3.5)
MISSION 24: Recognizing Angles
235—244
4.MD.6 (4.MD.3.6)
MISSION 25: Using a Protractor to Measure Angles
245—254
4.MD.7 (4.MD.3.7)
MISSION 26: Adding and Subtracting Angles
255—264
4.G.1 (4.G.1.1)
MISSION 27: Identifying Lines and Angles
265—274
4.G.2 (4.G.1.2)
MISSION 28: Classifying Two-Dimensional Figures
275—284
4.G.3 (4.G.1.3)
MISSION 29: Identifying Lines of Symmetry
285—294
ALL
Student Grids
295
SMART TO THE CORE Recommended Classroom Regimen (Includes all components of the classroom package)
DAY/ TIME
MATH BOOTCAMP: 5-Day Regimen DOK 1: BASIC RECALL & RECOGNITION
Day 1 (60 min.)
Benchmark Power Drill: Gradual Release of Basic Skills (10 min.) Hands On Math: Activity by Benchmark (20 min.) Smart to the Core Booklet: Train the Brain Practice 1 (Basic Skills) (15 min.) Smart to the Core Booklet: Target Practice 1 (Basic Application) (15 min.) DOK 1 & 2: BASIC APPLICATION
Day 2 (60 min.)
Rock Climbing Review: Mixed Daily Review - Day 2 (10 min.) Benchmark Power Drill: Gradual Release of Basic Application (20 min.) Smart to the Core Booklet: Train the Brain Practice 2 (Basic Skills) (15 min.) Smart to the Core Booklet: Target Practice 2 (Basic Application) (15 min.)
DOK 2 & 3: APPLYING SKILLS & CONCEPTS/STRATEGIC THINKING Day 3 (60 min.)
Rock Climbing Review: Mixed Daily Review - Day 3 (10 min.) Company Drill Game: Review by Benchmark (10 min.) Mathables® by Benchmark: Foldable Activity (20 min.) Mathables® by Benchmark: Think Tank Journaling (20 min.) DOK 3 & 4: STRATEGIC & EXTENDED THINKING
Day 4 (60 min.)
Day 5 (60 min.)
Rock Climbing Review: Mixed Daily Review - Day 4 (10 min.) Benchmark Power Drill: Modeling Strategic Thinking (25 min.) Smart to the Core Booklet: Train the Brain Practice 3 (Application) (15 min.) Smart to the Core Booklet: Think Tank Question (Strategic Thinking) (10 min.) ASSESSMENT BY BENCHMARK & DIFFERENTIATED INSTRUCTION Smart to the Core Booklet: Four-Star Challenge (20 min.) Smart to the Core Booklet: Review the Assessment (10 min.) Differentiated Instruction: Based on the Four-Star Challenge Results (30 min.) Group 1 - Hands On Math Activity with DOK Worksheet - 1 Star (Intensive) Group 2 - Hands On Math Activity with DOK Worksheet - 2 Stars (Strategic) Group 3 - Hands On Math Activity with DOK Worksheet - 3 Stars (Prevention) Group 4 - Triathlon Game and/or Company Drill Game (Enrichment)
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 50 - 69%.
The student earns THREE stars for correctly answering 70 - 89%.
The student earns FOUR stars for correctly answering 90 - 100%.
1
1
1
2
3
Tier 3 In need of Intensive Support
4
2
3
Tier 2 In need of Strategic Support
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2
3
4
Tier 1 * Proficient, but in need of Benchmark
1
2
3
4
Tier 1 Proficient Target for Enrichment
MISSION 3: Solving MULTI-STEP WORD PROBLEMS Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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: Draw bar models to represent multi-step problems. Example: Mr. Gomez bought his son a game for $45 and his daughter a doll for $26. He paid with a $100 bill. How much change did he get? $45
$45 + $26 $71
$26 ?
$100 $71
?
$100 ‒ $ 71 $ 29
Bootcamp STRATEGY 2: Use a grid to solve word problems involving rows and columns. Example: A parking lot has 15 rows with 8 parking spaces in each row. In each of the first 6 rows, 5 parking spaces are reserved for staff. How many parking spaces are not marked reserved for staff? Answer: 120—30 = 90
Bootcamp STRATEGY 3: Use key words to interpret multiplication sentences. KEY WORD
is
less than
times
each
each row
and
more
left
of
MEANING
Equals (=)
Subtract (‒)
Multiply (×)
Divide/ Multiply (÷) or (×)
Multiply (×)
Add (+)
Add (+)
Subtract (‒)
Multiply (×)
Example: How many stamps are needed for 21 small envelopes and 17 medium-sized envelopes if each envelope needs 2 stamps? Step 1: Remember PEDMAS when solving multi-step problems. P (Parenthesis and Grouping), E (Exponents, Powers, and Square Roots), MD (Multiplication and Division from left to right), and AS (Addition and Subtraction from left to right)
n = (21 + 17) × 2 n = 38 × 2 n= 76
Step 2: In the problem, 21 and 17 must be added first. Step 3: The sum must then be multiplied by 2.
25 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 4.OA.3 (4.OA.1.3) 1
Caesar bought a box of copy paper for $48 and an ink cartridge for $31. He paid with a $100 bill. How much change did he receive?
Solve USING BAR MODELS (Show your work)
Answer: $21.00
$100 $48
2
$31 ?
There are 10 rows of seats in a gymnasium with 9 seats in each row. Students fill in the 9 seats of the first 8 rows. How many empty seats are in the gymnasium?
Solve USING A Grid (Show your work)
Answer: 18 seats
3
A flower garden has 10 plots of tulip plants. There are 25 plants in each plot. There are also 15 rose bushes. How many tulip plants and rose bushes are there?
Solve USING EQUATIONS (Show your work)
Answer: (10 × 25) + 15 = 265 tulip plants and rose bushes
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Target PRACTICE 1 1
3
What is the total cost of 4 meals at $12 each and 3 desserts at $10 each?
2
How many stamps are needed for 15 small envelopes and 19 medium-sized envelopes if each envelope needs 2 stamps?
A
$90
B
$78
A
68
C
$29
B
53
D
$22
C
49
D
34
Select all of the expressions below that equal to 21.
4
✓ (5 × 5) - 4 (80 ÷ 4) + (7 - 2 )
(50 ÷ 5) + (3 × 11) (7 × 9) - 44
(10 ÷ 5) + (12 × 2)
(50 ÷ 2) - (9 × 2)
✓ (9 × 7) - 42 (16 - 9) + (6 × 2)
5 A bakery has 41 cookies left. The owner made 14 more cookies. Each cookie gives a profit of $2. What will be the profit for all of the cookies once they are sold? Grid your answer. Gridded Answer: 110
Select all of the expressions below that are equal to 35.
✓ (5 × 5) + 10 ✓ (24 ÷ 2) + (51 - 28)
6
A restaurant has 226 bagels and 145 freshly baked cookies. Within a few minutes, the restaurant sold 112 freshly baked cookies. How many bagels and cookies are left? Grid your answer. Gridded Answer: 259
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TRAIN THE BRAIN PRACTICE 2 4.OA.3 (4.OA.1.3) 1
Mr. Bermudez bought a drill for $57 and a hammer for $9. He paid with a $100 bill. How much change did he get?
Solve USING BAR MODELS (Show your work)
Answer: $34.00
$100 $57
2
$9
?
A parking lot has 8 rows with 16 parking spaces in each row. In each of the first 7 rows, 4 parking spaces are marked handicapped. How many parking spaces are not marked handicapped?
Solve USING A Grid (Show your work)
Answer: 100 parking spaces
3
A school cafeteria has 5 trays of food with 15 sandwiches on each tray. The cafeteria also has 4 trays of fruit cups with 15 fruit cups on each tray. If 30 fruit cups are sold, how many sandwiches and fruit cups are left?
Solve USING EQUATIONS (Show your work)
Answer: [(4 × 15) − 30] + (15 × 5) = 105 sandwiches and fruit cups
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Target PRACTICE 2 1
3
What is the total cost of 3 movie tickets at $9 each and 2 buckets of popcorn at $8 each?
2
A
$42
A
32
B
$11
B
36
C
$36
C
8
D
$43
D
28
Which of the following equations are correct? Select all of the equations that apply.
4
✓ (9 3) + (5 − 2) = 6 ✓ (27 9) − 1 = 2
35 − (4 × 7) = 12 (24 8) − 2 = 5
✓ (4 × 2) + (6 − 2) = 12 19 − (5 × 3) = 42
✓ (5 × 3) + (12 4) = 18 ✓ (2 + 8) × (16 8) = 20
(4 × 8) − (36 6) = 8 Vanady made 34 bracelets to sell at a yard sale. Her sister made 17 more bracelets for her to sell. Each bracelet will be sold for $7. What is the value of all of the bracelets Vanady has to sell? Grid your answer. Gridded Answer: 357
Which of the following equations are correct? Select all of the equations that apply. ✓ (28 4) + (7 − 5) = 9 10 + (2 × 5) = 17
8 + (6 × 3) = 42
5
How many sky lifts are needed for 18 ladies and 14 men if 4 people can ride each lift at a time?
6
A bicycle shop had 210 trail bikes and 84 beach cruisers for sale. Last week, the store sold 110 trail bikes. How many bikes are left in the store in all? Grid your answer. Gridded Answer: 184
29 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 4.OA.3 (4.OA.1.3) DIRECTIONS: Solve the problems below.
1 Daniel had 5 boxes of nails. Each box had 63 nails. If he used 105 nails, how many nails does Daniel have left? Answer: 210 nails
2 Mrs. Miller has 262 shampoo samples from the company she works for. She kept 57 of them for herself. She wants to use the rest of the samples to divide equally into 15 gift bags. How many samples will be in each gift bag? How many are left over? Answer: Each bag will have 13 samples, with 10 samples left over.
3 Valerie has 26 brown pocketbooks and 43 black ones in stock at her store that she wants to put in storage. She wants no more than 7 pocketbooks in each storage box. How many boxes will she need? Answer: 10 boxes
4 A chemist has 88 mls of water. He wants to pour an equal amount of water into 8 beakers. Then he will add 73 mls of solution to each beaker. How much liquid will be in each beaker? Answer: 84 milliliters
30 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION Saniya wants to buy herself a new tablet that costs $289. Saniya has saved $74, but needs to save the same amount of money (x dollars) each month for the next 5 months. Part I: Write an equation that helps Saniya determine the amount of money she .needs to save each month.
x = ($289 - $74) ÷ 5 Equation _______________________________________________
Part II: Solve the equation to find the amount of money Saniya must save each .month to meet her goal of buying a new tablet. (Show your work)
Answer: $43.00
31 I Copying is strictly prohibited
FOUR-STAR CHALLENGE - 4.0A.3 (4.0A.1.3) 1
3
What is the total cost of 4 hotdogs at $4 each and 6 buckets of popcorn at $4 each?
How many taxicabs are needed for 14 ladies and 13 men if 6 people can ride in each taxicab?
2
A
$40
A
122
B
$38
B
168
C
$30
C
128
D
$22
D
162
Michelle bought 6 plates and 4 cups during the mall sale. Each plate cost $12 while each cup cost $9. Select all of the statements that are true.
She spent $120 for all the items. (6 × 4) + (12 + 9) = 108
Jordan found 3 boxes of baseballs and 7 bags of tennis balls in the storage closet. Each box had 9 baseballs while each bag had 4 tennis balls. Select all of the statements that are true.
4
✓ Jordan found 27 baseballs. ✓ Jordan found 55 balls in all.
✓ She spent $108 for all the items. (6 × 4) + (12 × 9) = 120
Jordan found 63 tennis balls.
✓ (6 × 12) + (4 × 9) = 108
(3 + 7) × (9 + 4) = 39
5
Jameson made 46 dream catchers to sell at a fair. He already had 17 dream catchers leftover from the last sale. Each dream catcher will be sold for $5. What is the value of all of the dream catchers that Jameson has to sell? Grid your answer. Gridded Answer: 315
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Jordan found 39 balls in all.
6
A jewelry store has 61 gold watches and 49 silver watches for sale. This weekend, the store sold 19 silver watches. How many watches are left at the jewelry store in all? Grid your answer. Gridded Answer: 91
7
Mr. Bermudez took his wife to a restaurant and spent $31 for his wife's meal and $24 for his meal. He paid with a $100 bill. How much change did he get back?
Solve USING BAR MODELS (Show your work)
Answer: $45.00
$100 $31
8
$24
?
A farmer has 9 rows of corn with 14 corn stalks in each row. In each of the first 3 rows, 7 stalks are gathered and sold. How any corn stalks are remaining?
Solve USING A Grid (Show your work)
Answer: 105 corn stalks
9
A hardware store has 3 shelves with 11 boxes of screws on each shelf. They also have 4 shelves with 26 boxes of nails on each shelf. If 80 boxes of nails are sold, how many boxes of screws and nails are left?
Solve USING EQUATIONS (Show your work)
Answer: [(4 × 26) − 80] + (3 × 11) = 57 boxes of screws and nails
33 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 10 Boy scouts from 4 troops at Camp Boogaloo are planning a hike to Pikes Peak. In each troop, there will be 20 boy scouts. There will also be a total of 12 scout leaders and 11 chaperones. Part I: Write an equation that can be used to determine the number of tents (t), they will need if 6 people sleep in each tent.
[(4 × 20) + (12 + 11)] ÷ 6 Equation: t =______________________________________
Part II: How many tents will be needed if 6 people sleep in each tent? (Show your work) Answer: At least 18 tents will be needed.
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MISSION 15: Adding Fractions with like denominators Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
Bootcamp STRATEGY 1: Use fraction strips to find the sum of fractions with like denominators. Example: Add 2 fractions with common denominators. 1
17
+
3
17
=
Step 1: Create fraction strips that reflect the fractions being added. 1 1 7
1 7
1 7
1 7
1 7
1 7
+
1 7
1 1 7
1 7
1 7
1 7
1 7
1 7
1 7
Step 2: Add the wholes together, and then add the fraction pieces to get the sum. 1 1 1 1 + + + = 7 7 7 7
2+
2
4 7
Bootcamp STRATEGY 2: Use fraction strips to find the difference of mixed numbers with like denominators. Example: Subtract 2 fractions with common denominators. 3
‒
27
1 17
=
Step 1: Create fraction strips that reflect the fractions being subtracted. 1 1 1 7
1 7
1 7
1 7
1
‒ 1 7
1 7
1 7
1 7
1 7
1 7
1 7
1 7
1 7
1 7
Step 2: Eliminate the numbers being subtracted by canceling out the matching sides as demonstrated above. 2 Step 3: List the remaining parts. remaining parts 1 7 145 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 4.NF.3 (4.NF.2.3) DIRECTIONS: Use models to add and subtract the following fractions. 3 1 + 4 4 =
1
3
2 85 +
4 4
1 81 =
9 3 ‒ = 100 100
5
or 1
2 5 + 6 6 =
2
4 6 38
6 100
6
7 6
9 ‒ 3 = 10 10
2 81
‒
1 87
1
or 1 6
6 10
=
2 8
DIRECTIONS: Find 2 ways to decompose the following fractions into the sum of their fractions.
7
5 1 + 4 6 = 6 6
5 2 3 + 6 = 6 6
Answers may vary.
8
3 6 9 + = 12 12 12
9 5 4 12 = 12 + 12
Answers may vary.
146 I Smart to the Core I Educational Bootcamp
Target PRACTICE 1 1
7
Ben hiked 10 mile on Saturday. He 2 hiked 10 mile more on Sunday.
2
4
Chris had a piece of wire 5 inch long. 1 He used 5 inch.
1
1
1 5
1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10
2
A package of ground beef weighs 3 9 pounds. A package of ground pork 1 weighs 2 9 pounds more than the beef. What is the combined weight of the packages?
B
5
2
11 9
A
1
1 6
C
3
1 6
3 9
D
8
5 9
B
2
3 6
D
5
9 6
5
1 4 9 3 12 7 42 8 4 10 1 31
+ 3 43 = 10
6
Select all of the equations below that are correct. ✓ 4 84 - 2 82 = 2 82 9 43 - 7 41 = 1 42
7 =74 + 412 12
+ 2 42 = 9 46
3 8 4 6 12 2 63
✓ 5
7 9 + 110 = 6 10
+ 7 32 = 9
1 5
Joni bought 9 yards of fabric. She 5 used 5 6 yards for a dress. How much fabric does she have left?
C
✓ 6
✓
4
10 9
Select all the equations below that are correct.
✓
1 5
Gridded Answer: 3 5
Gridded Answer: 9 10
A
1 5
How much wire does he have left? Grid your answer.
How many miles did he hike in all? Grid your answer.
3
1 5
✓
- 4 86
=
5 8
5 - 5 11 = 1 12 12
-1
4 6
=
5 6
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TRAIN THE BRAIN PRACTICE 2 4.NF.3 (4.NF.2.3) DIRECTIONS: Use models to add and subtract the following fractions. 4 5 = + 10 10
1
2 43 + 1 41
3
9 10
4 =
2 7 ‒ 8 = 8
5
4 2 5 + 5 =
2
6 5 ‒ = 12 12
4
5 8
6
1 6 or 1 5 5
2
2 5 ‒ 1 54
1 12
=
3 5
DIRECTIONS: Find 2 ways to decompose the following fractions into the sum of their fractions.
7 8
3 1 + 2 4 = 4 4 14 = 10 + 4 100 100 100
148 I Smart to the Core I Educational Bootcamp
3 = 1 + 1 +1 4 4 4 4 14 7 + 7 = 100 100 100
Answers may vary.
Answers may vary.
Target PRACTICE 2 1
5
To paint a room, Tim mixed 8 quarts of blue paint and 3 quarts of green 8 paint.
2
9
Jeffrey promised to do 12 hours of volunteer work this week. So far, he 3 has done 12 hours.
1 1 8
1 8
1 8
1 8
1 1 8
1 8
1 8
1 8
1 1 1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 12 12 12
How much paint did Tim mix? Grid your answer.
How many more hours must he work this week? Grid your answer.
Gridded Answer: 1
Gridded Answer: 6 12 1
3
5
Benjamin spent 1 5 hours on math homework and 2 15 hours on history homework. How many hours did Benjamin spend on homework?
A
1
2 5
C
B
2
1 5
D
4
Paul and Max each travel to school 4 by bicycle. Paul’s house is 3 6 miles 1 from school. Max’s house is 5 6 miles from school. How much longer does Max travel than Paul?
3
2 5
A
1
C
2
3 5
9 6
B
1
3 6
D
Select all of the decomposed frac8
tions that have a sum of 12 . 1 2 3 4 12 + 12 + 12 + 12 3 2 3 ✓ 12 + 12 + 12 1 2 3 2 ✓ 12 + 12 + 12 + 12 1 1 1 1 1 1 1 1 ✓ 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 2 2 3 2 12 + 12 + 12 + 12
6
2
3 6
3
Select all of the decomposed frac7
tions that have a sum of 10 . 2 2 2 2 10 + 10 + 10 + 10 1 1 1 1 1 1 1 ✓ 10 + 10 + 10 + 10+ 10 + 10+ 10 1 2 1 2 1 ✓ 10 + 10 + 10 + 10 + 10 1 2 3 10 + 10 + 10 2 4 3 4 10 + 10 + 10 + 10
149 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 4.NF.3 (4.NF.2.3) DIRECTIONS: Use fraction models or equations to solve the following problems.
1
Catherine has a blue string that is 1 4 meters long and a green string that is 10 4 5 10 meters long. How much longer is the green string than the blue string?
Answer: 4 meters
2
2
4
A tree in a backyard is 11 10 feet tall. A nearby rosebush is 2 10 feet tall. How much taller is the tree than the rosebush?
8 Answer: 8 10 feet
DIRECTIONS: Solve the fractions and convert into a mixed number when possible.
3
3 4
4
8 5
5
3 6
+
+
−
3 4
2 5
2 6
+
+
−
2
= 8 =2 4 4
10 = 20 = 4 5 5
1
=0 6 =0 6
150 I Smart to the Core I Educational Bootcamp
THINK TANK QUESTION Part I: A softball player threw 3 pitches. He threw the first pitch 2 second pitch 1
4 10
yards, and the third pitch 3
5 10
1 10
yards, the
yards. Use a fraction
model to illustrate each distance.
2
1 10
1
4 10
3
5 10
Part II: Which addition problem can be used to determine the total distance of all 3 pitches? What is the total distance? 1
4
5
Answer: 2 10 + 1 10 + 3 10 = 7 yards
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FOUR-STAR CHALLENGE - 4.NF.3 (4.NF.2.3) 1
Heather added the fractions below.
5
Taylor has a green rope that is 9…. 8
Which expression below shows a
inches long and an orange rope that is
way she might have grouped the
6 58 inches long. How much longer is
addends to find the sum?
the orange rope than the green rope?
5 8
3
2
6 8
1 8
A
12 8
+
1 8
C
8 8
+
B
11 8
1 + 8
D
7 8
4 + 8
7 8 inches
A
3
B
3 inches
1
C
3 8 inches
D
3 8 inches
1 8
7 An apple tree in a backyard is 1... 10
feet tall. A nearby pear tree is 4…5
4
10
3
1
Trevor drove 10 6 miles from home 5 to the store. Then he drove 7 6 miles
feet tall. How much shorter is the
from the store to his mother’s house.
apple tree than the pear tree? Grid
How many miles did Trevor drive
your answer.
from his house to his mother’s house? Grid your answer.
Gridded Answer: 28 10
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Lynn bought 1 13 gallons of milk at 2 the market. She used 3 gallons of the milk to make a cake. Select all of the correct phrases below that tell how much milk was left.
She has 13 gallon of milk left.
✓ She has 23 gallon of milk left.
Gridded Answer: 108 6 6
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Carl bought a pipe 4 8 feet long. He used 2 58feet of the pipe for his crafts project. Select all of the correct phrases below that tell how much pipe he had left.
26
He has 8 feet of pipe left. 6 He has 2 8 feet of pipe left. 6
She has 1 + 1 gallon of milk left.
✓ He has 1 8 feet of pipe left.
She has 2 gallons of milk left.
✓ He has 8 feet of pipe left. He has 1 38 feet of pipe left.
✓ She has 13 + 13 gallon of milk left. 152 I Smart to the Core I Educational Bootcamp
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DIRECTIONS: Shade in the circles of all addends were the sums are greater than 1.
1 2 3 + 3
5 4 7 + 7
2 1 + 5 5
2 2 + 3 3
3 1 4 + 4
1 5 8 + 8
4 8 10 + 10
1 7 12 + 12
The Cumberland family ordered 2 pizzas that were both cut in 8 slices each. 6 Mr. Cumberland ate 8 of the pizza, and Mrs. Cumberland ate 84 of the pizza. The 2 daughters shared the pizza that was left over equally.
Part I: How much pizza did Mr. Cumberland and Mrs. Cumberland eat in all? (Show your work) 10
1
Answer: 8 of the pizzas, or 1 4 of the pizzas
Part II: How much of the pizza did the girls eat? (Show your work) 6
Answer: 8 of the pizzas
Part III: How much of the pizza did the girls and Mr. Cumberland eat in all? (Show your work) 12
1
Answer: 8 of the pizzas, or 1 2 of the pizzas
153 I Copying is strictly prohibited
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THINK TANK QUESTION 9
1 percent interest rate on his home. What will Miguel's 5 interest rate be if he lowers his rate by 4 percent? 5
Part I: Miguel has a 5
2
Answer: 4 5 percent
4 percent interest rate on her home. What will Lidia's 5 interest rate be if she lowers her rate 2 percent? 5
Part II: Lidia has a 4
2
Answer: 4 5 percent
Part III: How much greater is Miguel's new interest rate than Lidia’s new rate? Answer: Miguel’s new interest rate is equal to Lidia’s new interest rate.
154 I Smart to the Core I Educational Bootcamp
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