SMART TO THE CORE 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 (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
OF
CONTENTS
Grade 4 SMART TO THE CORE LESSONS
CCSS Code
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 5: Investigating FACTORS AND MULTIPLES Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
Bootcamp STRATEGY 1: Use arrays to find the factors of a whole number. Example: Eliminate the numbers that are not factors of 18. 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Factor Pairs
1
3
18
1
and
18
2
2
and
9
3
and
6
9 6
Bootcamp STRATEGY 2: Use the divisibility rules to find factors. Dividing by 2: All even numbers are divisible by 2, e.g., all numbers ending in 0, 2, 4, 6, or 8. Dividing by 3 : Add up all the digits in the number. Find out what the sum is. If the sum is divisible by 3, so is the number. For example, 12,123 (1+2+1+2+3=9); 9 is divisible by 3, therefore, 12,123 is, too. Dividing by 4: Are the last 2 digits in your number divisible by 4? If so, the number is, too. For example: 35,8912 ends in 12 which is divisible by 4; thus, so is 358,912. Dividing by 5: Numbers ending in a 5 or 0 are always divisible by 5. Dividing by 6: If the number is divisible by 2 and 3, it is divisible by 6, also. Dividing by 9: It is almost the same rule as dividing by 3. Add up all the digits in the number. Find out what the sum is. If the sum is divisible by 9, so is the number. For example, 43,785 (4+3+7+8+5=27); 27 is divisible by 9, therefore, 43,785 is, too. Dividing by 10: If the number ends in a 0, it is divisible by 10.
Bootcamp STRATEGY 3: Use skip counting or multiply to find multiples of a number. Example: Skip count by 3s: 3, 6, 9, 12, 15, 18, 21 ... ×1 ×2 ×3 Example: Find the multiples of 3: 3 3 6 9
×4
×5
×6
×7
12
15
18
21
Bootcamp STRATEGY 4: Finding prime and composite numbers. A prime number is a whole number greater than 1 that is only divisible by 1 and itself. A composite number is a number greater than 1 that has more factors than 1 and itself. Example 1: 3 is a PRIME number 1×3=3
Example 2: 4 is a COMPOSITE number 1 × 4 = 4 and 2 × 2 = 4 45 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 4.OA.4 (4.OA.2.4) Eliminate the numbers below that are not factors of 24.
1 1
2
3
4
5
6
7
8
9
10
11
12
13
14 15
16 17
18
2
Identify the numbers below as either prime or composite by placing a check mark in the appropriate box. 15
Prime
Composite
27
Prime
Composite
43
Prime
Composite
33
Prime
Composite
19
20 21 22 23
DIRECTIONS: Identify the factors for the following whole numbers. Whole Number
Circle the Factors
3
144
2
3
4
5
6
9
10
4
200
2
3
4
5
6
9
10
5
405
2
3
4
5
6
9
10
6
160
2
3
4
5
6
9
10
7
288
2
3
4
5
6
9
10
8
Multiply to find the first 7 multiples of 4. ×1
×2
×3
×4
×5
×6
×7
4 9
Skip count to find the first 7 multiples of 6.
6 , ____, ____, ____, ____, ____, ____ 46 I Smart to the Core I Educational Bootcamp
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Target PRACTICE 1 1
3
5
Krishna made a list of all the factors of 81. Which of the following could be Krishna’s list?
2
Which of the following groups below include only prime numbers?
A
1, 3, 9, 27, 81
A
Group 1: 2, 3, 6, 90, 112
B
1, 3, 9, 27
B
Group 2: 2, 3, 5, 7 , 9
C
2, 3, 9, 27, 81
C
Group 3: 17, 19, 23, 29, 31
D
1, 2, 3, 9, 27, 81
D
Group 4: 15, 17, 11, 18, 21
Select all of the prime numbers from the list below.
Select all of the composite numbers from the list below.
9
27
15
91
33
13
5
27
28
45
39
22
59
49
57
41
83
75
78
88
Joy is in a drama club that meets the same number of times each month. After a number of months, Joy’s drama club had met 32 times. Which of the following could be the number of times the club meets each month? A
4
6
Which of the following statements below best describe the relationship between the numbers 4 and 6? A
4 is a factor of 6
B
4 is a multiple of 6
C
20 is a common multiple of 4 and 6
D
The greatest common factor of 4 and 6 is 2
2, 5, or 8 times per month
B
2, 4, or 8 times per month
C
4 or 6 times per month
D
2, 4, 6 or 8 times per month
47 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 4.OA.4 (4.OA.2.4) Eliminate the numbers below that are not factors of 20.
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Identify the numbers below as either prime or composite by placing a check mark in the appropriate box.
2
51
Prime
Composite
71
Prime
Composite
26
Prime
Composite
85
Prime
Composite
DIRECTIONS: Identify the factors for the following whole numbers. Whole Number
Circle the Factors
3
135
2
3
4
5
6
9
10
4
305
2
3
4
5
6
9
10
207
2
3
4
5
6
9
10
6
440
2
3
4
5
6
9
10
7
.261
2
3
4
5
6
9
10
5
8
.
Multiply to find the first 7 multiples of 7. ×1
×2
×3
×4
×5
×6
×7
7 9
Skip count to find the first 7 multiples of 8.
8 , ____, ____, ____, ____, ____, ____ 48 I Smart to the Core I Educational Bootcamp
Target PRACTICE 2 1
3
Reece made a list of all the factors of 72. Which of the following could be Reece’s list? A
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
B
1, 2, 3, 6, 9, 18, 24, 36, 72
C
2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
D
1, 2, 3, 4, 6, 8, 9, 12, 16, 24, 36, 72
Select all of the statements that are true of the numbers 24 and 30.
2
4
Common factors of 24 and 30: 1, 2, 3, 6, and 8
A
4 or 6 weeks
B
7 or 8 weeks
C
9 or 10 weeks
D
7 or 9 weeks
Group 1: 22, 33, 24, 15, 50
B
Group 2: 5, 11, 15, 18, 31
C
Group 3: 2, 3, 13, 29, 41
D
Group 4: 5, 7, 11, 17, 21
Select all of the statements that are true of the numbers 12 and 20.
Factors of 12: 1, 2, 3, 4, 6, and 12 12 is a composite number. Common factors of 12 and 20: 1, 2, and 4 Factors of 20: 1, 2, 3, 4, 6, 12, and 20
30 is a composite number. Factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24 Factors of 30: 1, 2, 3, 5, 6, 8, 10, 15, and 30
During baseball season, Dave’s team practiced the same number of times each week. They practiced 63 times in all. Which of the following could be the length of the baseball season?
A
Factors of 12: 1, 2, 3, 6, 8, 10, and 12
24 is a prime number. Common factors of 24 and 30: 1,2,3, and 6
5
Which of the following groups include only composite numbers?
Factors of 20: 1, 2, 4, 5, 10, and 20
6
Which of the statements below best describe the relationship between the numbers 7 and 42? A
7 is a factor of 42
B
42 is a factor of 7
C
42 is a common multiple of 4 and 7
D
The greatest common factor of 7 and 42 is 14
49 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 3 4.OA.4 (4.OA.2.4) DIRECTIONS: Use drawings and equations to solve the following problems. 1 What is the least common multiple for 3 and 8? (Show your work)
2 What are the multiples of 8 that are less than 50? (Show your work)
3 What whole number is between 45 and 50 that has exactly 10 factors including 1 and itself? (Show your work)
4 What numbers are both a factor of 100 and a multiple of 5?
5 Identify the numbers below as either prime or composite by placing a check mark in the appropriate box. 89
Prime
Composite
37
Prime
Composite
52
Prime
Composite
21
Prime
Composite
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THINK TANK QUESTION After learning about factors and multiples, Jane concluded that the number 40 is a multiple of 9. She also stated that all of the factors of 10 are factors of 40.
Is Jane’s first statement accurate? (Show your work)
YES
NO
Is Jane’s second statement accurate? (Show your work)
YES
NO
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FOUR-STAR CHALLENGE - 4.OA.4 (4.OA.2.4) 1
3
5
Ryan made a list of all the factors of 24. Which of the following could be Ryan’s list? A
2, 3, 4, 6, 8, 12, 24
B
1, 2, 3, 4, 6, 8
C
1, 2, 3, 4, 6, 8, 12, 24
D
2, 3, 4, 6, 9, 12
Which of the following lists of numbers show multiples of 7? Select all of the options that apply.
Which of the following groups below include only prime numbers?
2
4
A
Group 1: 12, 13, 14, 15, 50
B
Group 2: 5, 11, 15, 18, 31
C
Group 3: 5, 3, 13, 29, 41
D
Group 4: 5, 7, 11, 17, 21 Which of the following lists of numbers show the multiples of 9? Select all of the options that apply.
17, 27, 37, 47, 57, 67, and 77
27, 36, 45, 54, 63, 72, and 81
14, 21, 28, 35, 42, 49, and 56
19, 29, 39, 49, 59, 69, and 79
14, 17, 24, 27, 34, 37, and 44
14, 19, 24, 29, 34, 39, and 44
21, 24, 28, 31, 35, 42, and 47
18, 28, 38, 48, 58, 68, and 78
14, 28, 56, 112, 224, and 448
27, 46, 55, 64, 73, 82, and 91
7, 14, 21, 28, 35, 56, and 63
54, 63, 72, 81, 90, 99, and 108
Which statement below best describes the relationship between the numbers 6 and 24?
6
At the store, T-shirts are stored in bins. There are 72 T-shirts to store in bins and each has an equal number of T-shirts. Which of the following could be the number of bins used to store the T-shirts?
A
24 is a factor of 6
B
6 is a multiple of 24 A
2, 5, or 7
C
24 is a common multiple of 6 and 24
B
2, 4, 8, or 9
C
2, 5, 8, or 9
D
48 is the least common factor of 6 and 24
D
2, 3, 4, or 10
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The host of the annual Math Bowl asked a contestant to name all of the prime numbers between 15 and 40. Part I: What numbers should the contestant have named?
Part II: Explain how you identified the prime numbers between 15 and 40.
8
9
Circle the numbers that are multiples of both 4 and 6.
40
12
16
30
24
8
28
18
48
Ms. Perez, the fourth grade math teacher, starts each class with a problem of the day. Monday’s question was, “If I am the number 32, and the number I am hiding in my hand is an even number and a factor of 32, then what number might I be holding?”
List the possible numbers that Ms. Perez might be holding in her hand. (Show your work)
53 I Copying is strictly prohibited
1
2
3
THINK TANK QUESTION DIRECTIONS: Solve the problem below and show your work.
10
A teacher gave clues to the students to help build their investigative skills. The goal was to use the clues to identify 2 specific leaves.
• Each of the leaves needed are factors of 24. • 36 is a multiple of both leaves • 30 is a multiple of the first leaf, but not the second leaf. • The sum of the 2 leaves is 10. Use the teacher’s clues and the space below to help figure out which 2 leaves are being described. (Show your work)
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MISSION 14: Using Models to compare fractions Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Bootcamp STRATEGY 1: Use fraction models to compare fractions. Example: Compare the fractions 3 and 1 using fraction models. 5 2 3 Step 1: Create a model to represent . (Shown in Step 2) 5 Step 2: Create a second model directly below the first model to represent 1 . 2 3 5 1 2 Step 3: Draw a line through the shaded region of both rectangles. 3 5 1 2 Step 4: The longer line represents the greater fraction. 3 5
1 2
>
Bootcamp STRATEGY 2: Use common denominators to compare fractions. Example: Compare 3 and 1 by writing equivalent fractions using common denominators. 5 2 Step 1: Find the common denominator by finding the least common multiple. 3 5 1 2
5 10 15 20 25 2
4 6 8 10
Step 2: To determine which fraction is larger, create equivalent fractions with common denominators. 6 3 × 2 1 × 5 = 5 = 2 10 5 10 5 2 6 10
>
5 3 Therefore, 10 5
>
1 2 135 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 1 4.NF.2 (4.NF.1.2) DIRECTIONS: Place the fractions below in order from least to greatest. 2
1
1 < 5
<
1 < 3
<
<
<
4
3
1 < 4
<
1 < 4
<
<
<
DIRECTIONS: Compare the fractions below (>, <, or =). 5
7
10
6
3 4
2 3
2 3
6 10
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11
4 5
1 3
3 4
4 5
9
12
1 4
2 8
1 2
4 8
Target PRACTICE 1 1
A charitable institution’s budget 4
2
allows 8 to be spent on rent and 1 utilities, 6 for food, and 34 for
1
Linda sewed 2 yard of fringe on her blouse, 64 on her scarf, and 41 on her jacket. Which fraction below has the
planting trees. Which fraction below
least value?
has the greatest value?
A
3
5
4 8
B
1 6
C
3 4
There are 2 friends debating who has done more homework. John said he 5 has done 6 of his homework and Tim 9 said he has done 12 .... Which of the statements below correctly compares the fractions? A
5 6
9 < 12
C
5 6
9 > 12
B
5 6
9 = 12
D
9 12
<
A
4
B
C
1 4
8
12 < 12 12 B 12 =
6
4 9
A recipe calls for 10 cup of lemon juice and 12 cup of water. Which 12 statement below correctly compares the fraction?
A
5 6
Select all of the statements that can be true based on the information from the table. RIBBON LENGTH 4 yards Red ribbon 5 5 yards Pink ribbon 6 2 yards Blue ribbon 3 red ribbon > pink ribbon
1 2
8 10
C
12 12
8 > 10
8 10
D
8 10
> 12 12
Select all of the statements that can be true based on the information from the table. PIPE DIAMETER 3 inches Pipe 1 8 2 inches Pipe 2 5 1 inches Pipe 3 2 Pipe 1 is larger than Pipe 2.
pink ribbon > blue ribbon
Pipe 2 is larger than Pipe 3.
red ribbon > blue ribbon
Pipe 1 is larger than Pipe 3.
pink ribbon > red ribbon
Pipe 2 is larger than Pipe 1.
blue ribbon > pink ribbon
Pipe 3 is larger than Pipe 2. 137 I Copying is strictly prohibited
TRAIN THE BRAIN PRACTICE 2 4.NF.2 (4.NF.1.2) DIRECTIONS: Place the fractions below in order from greatest to least. 2
1
1 >
>
4 > 6
>
>
>
4
3
4 > 6
>
6 > 7
>
>
>
DIRECTIONS: Compare the fractions below (>, <, or =). 5
7
10
6
1 4
1 3
2 3
4 5
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8
11
4 5
6 8
9
1 4
2 3
1 2
4 5
12
3 4
4 8
Target PRACTICE 2 1
Evangeline baked a peach pie. She
3
5
Jeff is making a rice cake. He adds
5 used 6 peaches, 1 dough, and 10
2 cup coconut milk, 3 cup rice, and 1 3 4 5
honey. Which fraction below has the
sesame seeds. Which fraction below
greatest value?
has the least value?
8
A
2
6 8
4
B
1 4
C
5 10
A
Select all of the fractions that could be true. 1 > 2 2 3 3 3 > 4 5 1 > 1 3 4 2 2 > 5 3 4 1 > 5 4
4
Select all of the fractions that could be true.
6
2 3 10 < 12
2 4
3 5
C
1 3
Lucy has a lawn. This week she mowed 4 of the lawn. Last week she 6 mowed 1 of the lawn. Which 3 inequality below correctly compares the fractions? A
1 3
<
4 6
C
1 3
>
6 4
B
1 3
=
4 6
D
4 6
<
1 3
Henry drank 35 of a glass of water. 7 Ron drank 8 of a glass of water. Which inequality below correctly compares the fractions?
4 5 8 < 6 8 10 < 10 12
1 whole 1 5 1 8
1 2 < 3 5 5 4 < 8 10
B
A B
3 5 3 5
1 5 1 8
< =
1 8
7 8 7 8
1 5 1 8
1 8
1 8
C
3 5
>
D
7 8
<
1 8
7 8 3 5
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TRAIN THE BRAIN PRACTICE 3 4.NF.2 (4.NF.1.2) DIRECTIONS: Use fraction models to compare the fractions below.
1
4 10
5 8
2
2 3
6 10
3
3 6
10 12
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THINK TANK QUESTION Jerome wants to use a number line to plot the following points from least to greatest. 1 3 4 6 4 8
Part I: Determine how you would find the best interval to use on a number line based on the fractions given.
Part II: Write the fractions for the intervals on the number line. Explain why you chose those fractions.
PART III: Plot Jerome’s fractions on the number line. What fractions on the number line
are equivalent to Jerome’s fractions?
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FOUR-STAR CHALLENGE - 4.NF.2 (4.NF.1.2) 1
10 2 mile, Silva skated 5 12 1 mile, and Lynn skated 2 mile. Who
Bryan skated
2
1
The trail mix that Grace made had 6 cup of cashews, 5 cup of almonds, 8 1 and 4 cup of walnuts. What ingre-
skated furthest?
dient did she use the least of? A Bryan
B Silva
C
Lynn A Walnuts
3
5
4
3
Ryan ate 8 of a pizza and Demi ate 6 of a pizza. Which statement below correctly compares the fractions?
A
3 8
<
B
3 8
=
4 6 4 6
C
3 8
>
4 6
D
4 6
<
3 8
Study the following sets of fractions. Select all of the fractions that are listed in the correct order either from least to greatest or greatest to least. 7 4 3 > > 10 5 4
4
11
11 < 12 11 B 12 =
9 10
C
11 12
9 10
D
9 11 > 10 12
>
9 10
Study the following sets of fractions. Select all of the fractions that are listed in the correct order either from least to greatest or greatest to least. 4 3 2 > > 5 4 3
3 7 4 < < 4 10 5 3 4 7 4 < 5 < 10
3 4 2 < < 4 5 3 4 3 2 5 < 4 < 3
4 3 7 5 > 4 > 10
2 3 4 3 > 4 > 5
7 3 4 10 < 4 < 5
2 3 4 3 < 4 < 5
142 I Smart to the Core I Educational Bootcamp
C Almonds
Kylee walks 12 mile to school each 9 day, and Mark walks 10 mile to school each day. Which statement below correctly compares the fractions?
A
6
B Cashews
7
Boxes were organized by their fraction number in order from least to greatest. The warehouse team noticed that 2 of the boxes were missing the fractions. Determine 2 possible fractions that may have been missing from the 2 boxes to maintain the order of least to greatest.
1 4
3 5
?
or
8
?
7 10
4 5
or
Draw a line to match the fractions from least to greatest on the steps of the ladder. 3 4 1 2 1 8 5 8
1 1 4
3 8 7 8
143 I Copying is strictly prohibited
1
2
3
4
THINK TANK QUESTION 9
Tia wants to use a number line to plot the following points from least to greatest. 3 1 6 1 3 2 12 12 4
Part I: Determine how you would find the best interval to use on a number line based on the fractions given.
Part II: Write the fractions for the intervals on the number line. Explain why you chose those fractions.
PART III: Plot Tia’s fractions on the number line. What fractions on the number line are
equivalent to Tia’s fractions?
144 I Smart to the Core I Educational Bootcamp
