Ready Mathematics Practice and Problem Solving … · Table of Contents Ready® Program Overview A7 What’s in Ready Practice and Problem Solving A8 Lesson Practice Pages A8 Unit

Common Core State Standards © 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

Acknowledgments

ISBN 978-0-7609-9593-8©2015—Curriculum Associates, LLC

North Billerica, MA 01862

No part of this book may be reproduced by any means without written permission

from the publisher.All Rights Reserved. Printed in USA.

15 14 13 12

Rachel Adelstein, Assistant Principal, Briggs Avenue Academy, Bronx, NY

Crystal Bailey, Math Impact Teacher, Eastern Guilford Middle School, Guilford County Schools, Gibsonville, NC

Max Brand, Reading Specialist, Indian Run Elementary, Dublin City School District, Dublin, OH

Dinah Chancellor, Professional Development Mathematics Consultant, Southlake, TX

Helen Comba, Supervisor of Basic Skills & Language Arts, School District of the Chathams, Chatham, NJ

Cindy Dean, Classroom Teacher, Mt. Diablo Unified School District, Concord, CA

Leah Flynn, Classroom Teacher, Brockton Public Schools, Brockton, MA

Randall E. Groth, Ph.D, Associate Professor of Mathematics Education, Salisbury University, Salisbury, MD

Bill Laraway, Classroom Teacher, Silver Oak Elementary, Evergreen School District, San Jose, CA

Jennifer Lerner, Classroom Teacher, PS 57, New York City Public Schools, New York, NY

Susie Legg, Elementary Curriculum Coordinator, Kansas City Public Schools, Kansas City, KS

Sarah Levine, Classroom Teacher, Springhurst Elementary School, Dobbs Ferry School District, Dobbs Ferry, NY

Nicole Peirce, Classroom Teacher, Eleanor Roosevelt Elementary, Pennsbury School District, Morrisville, PA

Donna Phillips, Classroom Teacher, Farmington R-7 School District, Farmington, MO

Maria Rosati, Classroom Teacher, Harwood Elementary School, Warren Consolidated Schools, Warren, MI

Kari Ross, Reading Specialist, MN

Sunita Sangari, Math Coach, PS/MS 29, New York City Public Schools, New York, NY

Eileen Seybuck, Classroom Teacher, PS 57, New York City Public Schools, New York, NY

Mark Hoover Thames, Research Scientist, University of Michigan, Ann Arbor, MI

Shannon Tsuruda, Classroom Teacher, Mt. Diablo Unified School District, Concord, CA

Teacher Advisors

Editorial Director: Cynthia TrippCover Designers, Illustrators: Julia Bourque,

Matt PollockBook Designer: Scott Hoffman

Executive Editor: Kathy KellmanSupervising Editors: Pamela Halloran, Grace IzziDirector–Product Development: Daniel J. SmithVice President–Product Development: Adam Berkin

NOT FOR RESALE

Table of ContentsReady® Program Overview A7

What’s in Ready Practice and Problem Solving A8Lesson Practice Pages A8Unit Practice Pages A10Fluency Practice Pages A12

Correlation ChartCommon Core State Standards Practice in Ready Practice and Problem Solving A13

Lesson Plans (with Answers)

Unit 1: Operations and Algebraic Thinking, Part 1

Lesson 1 Understand the Meaning of Multiplication 1 CCSS Focus - 3.OA.A.1 Embedded SMPs - 2–4

Lesson 2 Use Order and Grouping to Multiply 4 CCSS Focus - 3.OA.B.5 Embedded SMPs - 2–4, 7

Lesson 3 Split Numbers to Multiply 9 CCSS Focus - 3.OA.B.5 Embedded SMPs - 1, 2, 4, 7, 8

Lesson 4 Understand the Meaning of Division 13 CCSS Focus - 3.OA.A.2 Embedded SMPs - 1–4, 6

Lesson 5 Understand How Multiplication and Division Are Connected 16 CCSS Focus - 3.OA.B.6 Embedded SMPs - 2, 6

Lesson 6 Multiplication and Division Facts 19 CCSS Focus - 3.OA.A.4, 3.OA.C.7 Embedded SMPs - 1, 2, 6–8

Lesson 7 Understand Patterns 23 CCSS Focus - 3.OA.D.9 Embedded SMPs - 2, 4, 6 ,7

Unit 1 Game: Fish for Factors! 26 CCSS - 3.OA.C.7, 3.OA.A.4 Embedded SMPs - 2, 6, 7

Unit 1 Practice 27 CCSS - 3.OA.A.1, 3.OA.A.2, 3.OA.A.4, 3.OA.B.5 Embedded SMPs - 1, 2, 3, 6, 7, 8

Unit 1 Performance Task 28 CCSS - 3.OA.A.2, 3.OA.A.3 Embedded SMPs - 1, 2, 3, 4, 6, 8

Student Book includes a Family Letter for every lesson and Unit Vocabulary pages.

Unit 2: Number and Operations in Base Ten

Lesson 8 Use Place Value to Round Numbers 30 CCSS Focus - 3.NBT.A.1 Embedded SMPs - 1, 5–8

Lesson 9 Use Place Value to Add and Subtract 34 CCSS Focus - 3.NBT.A.2 Embedded SMPs - 1, 2, 7, 8

Lesson 10 Use Place Value to Multiply 39 CCSS Focus - 3.NBT.A.3 Embedded SMPs - 2, 7, 8

Unit 2 Game: Tic-Tac-Times-Ten 42 CCSS - 3.NBT.A.1, 3.NBT.A.3 Embedded SMPs - 6, 7, 8

Unit 2 Practice 43 CCSS - 3.NBT.A.1, 3.NBT.A.2, 3.NBT.A.3 Embedded SMPs - 1, 2, 6, 7

Unit 2 Performance Task 44 CCSS - 3.NBT.A.1, 3.NBT.A.2 Embedded SMPs - 1, 2, 4, 5, 6, 7

Unit 3: Operations and Algebraic Thinking, Part 2

Lesson 11 Solve One-Step Word Problems Using Multiplication and Division 46 CCSS Focus - 3.OA.A.3 Embedded SMPs - 1–4, 7

Lesson 12 Model Two-Step Word Problems Using the Four Operations 51 CCSS Focus - 3.OA.D.8 Embedded SMPs - 1, 2, 4, 5

Lesson 13 Solve Two-Step Word Problems Using the Four Operations 55 CCSS Focus - 3.OA.D.8 Embedded SMPs - 1–5

Unit 3 Game: Two-Step Problems 59 CCSS - 3.OA.A.3, 3.OA.D.8 Embedded SMPs - 2, 4, 5, 7

Unit 3 Practice 60 CCSS - 3.OA.A.2, 3.OA.A.3, 3.OA.A.4, 3.OA.D.8 Embedded SMPs - 1, 2, 4

Unit 3 Performance Task 61 CCSS - 3.OA.A.3, 3.NBT.A.2 Embedded SMPs - 1, 2, 4, 6, 7

Unit 4: Number and Operations—Fractions

Lesson 14 Understand What a Fraction Is 63 CCSS Focus - 3.NF.A.1 Embedded SMPs - 2–4, 6

Lesson 15 Understand Fractions on a Number Line 66 CCSS Focus - 3.NF.A.2a, 3.NF.A.2b Embedded SMPs - 2, 3, 7

Lesson 16 Understand Equivalent Fractions 69 CCSS Focus - 3.NF.A.3a Embedded SMPs - 2–4


Unit 4: Number and Operations—Fractions (continued)Lesson 17 Find Equivalent Fractions 72 CCSS Focus - 3.NF.A.3b, 3.NF.A.3c Embedded SMPs - 1, 2, 4, 6

Lesson 18 Understand Comparing Fractions 77 CCSS Focus - 3.NF.A.3d Embedded SMPs - 2, 3, 7

Lesson 19 Use Symbols to Compare Fractions 80 CCSS Focus - 3.NF.A.3d Embedded SMPs - 2–4, 7

Unit 4 Game: Equivalent Fraction Match 83 CCSS - 3.NF.A.1, 3.NF.A.3 Embedded SMPs - 2, 3, 4, 6, 7

Unit 4 Practice 84 CCSS - 3.NF.A.1, 3.NF.A.2b, 3.NF.A.3a, 3.NF.A.3b, 3.NF.A.3c, 3.NF.A.3d Embedded SMPs - 1, 2, 3, 4, 5, 6, 7, 8

Unit 4 Performance Task 85 CCSS - 3.NF.A.3, 3.NF.A.3d Embedded SMPs - 1, 2, 3, 4, 6, 7

Unit 5: Measurement and Data

Lesson 20 Tell and Write Time 87 CCSS Focus - 3.MD.A.1 Embedded SMPs - 1, 3, 4, 6

Lesson 21 Solve Problems About Time 90 CCSS Focus - 3.MD.A.1 Embedded SMPs - 1, 3–6

Lesson 22 Liquid Volume 94 CCSS Focus - 3.MD.A.2 Embedded SMPs - 2, 4, 6

Lesson 23 Mass 98 CCSS Focus - 3.MD.A.2 Embedded SMPs - 1, 2, 4–6

Lesson 24 Solve Problems Using Scaled Graphs 102 CCSS Focus - 3.MD.B.3 Embedded SMPs - 1, 2, 4, 6, 7

Lesson 25 Draw Scaled Graphs 106 CCSS Focus - 3.MD.B.3 Embedded SMPs - 1, 2, 4, 6, 7

Lesson 26 Measure Length and Plot Data on Line Plots 110 CCSS Focus - 3.MD.B.4 Embedded SMPs - 1, 4–6

Lesson 27 Understand Area 114 CCSS Focus - 3.MD.C.5a, 3.MD.C.5b, 3.MD.C.6 Embedded SMPs - 2, 3, 5

Lesson 28 Multiply to Find Area 117 CCSS Focus - 3.MD.C.7a, 3.MD.C.7b Embedded SMPs - 4, 6–8

Lesson 29 Add Areas 121 CCSS Focus - 3.MD.C.7c, 3.MD.C. 7d Embedded SMPs - 3, 5, 7


Unit 5: Measurement and Data (continued)Lesson 30 Connect Area and Perimeter 125 CCSS Focus - 3.MD.D.8 Embedded SMPs - 1–7

Unit 5 Game: Time Match 130 CCSS - 3.MD.A.1 Embedded SMPs - 2, 4, 6

Unit 5 Practice 131 CCSS - 3.MD.A.1, 3.MD.A.2, 3.MD.B.3, 3.MD.C.5a, 3.MD.C.5b, 3.MD.C.7a, 3.MD.C.7b, 3.MD.D.8 Embedded SMPs - 1, 2, 5, 6, 7

Unit 5 Performance Task 132 CCSS - 3.MD.C.5, 3.MD.C.6, 3.MD.C.7 Embedded SMPs - 1, 2, 3, 4, 5, 6, 7

Unit 6: Geometry

Lesson 31 Understand Properties of Shapes 134 CCSS Focus - 3.G.A.1 Embedded SMPs - 5, 6, 7

Lesson 32 Classify Quadrilaterals 137 CCSS Focus - 3.G.A.1 Embedded SMPs - 3, 5, 7

Lesson 33 Divide Shapes Into Parts With Equal Areas 141 CCSS Focus - 3.G.A.2 Embedded SMPs - 2, 4, 5

Unit 6 Game: Shape Attribute Cover-Up 144 CCSS - 3.G.A.1 Embedded SMPs - 3, 5, 6, 7

Unit 6 Practice 145 CCSS - 3.G.A.1, 3.G.A.2, 3.NF.A.1, 3.NF.A.3b Embedded SMPs - 1, 3, 4, 5, 6, 7

Unit 6 Performance Task 146 CCSS - 3.G.A.2, 3.NF.A.1 Embedded SMPs - 1, 2, 3, 4, 6, 7

Fluency Practice 148

Unit Game Teacher Resource Masters 169

Teacher Resource Blacklines

Teacher Resource blackline masters are provided for use with the collaborative practice games in Ready Practice and Problem Solving. Full instructions for use of these teacher resources can be found in the Step by Step for each unit game.


©Curriculum Associates, LLC Copying is not permitted.A7

Ready® Program Overview

Ready Program Features

Built with all-new content written specifically for rigorous national and state standards for college and career readiness

Uses a research-based, gradual-release instructional model

Requires higher-order thinking and complex reasoning to solve problems

Integrates Standards for Mathematical Practice throughout every lesson

Embeds thoughtful professional development

Encourages students to develop deeper understanding of concepts and to understand and use a variety of mathematical strategies and models

Promotes fluency and connects hands-on learning with clearly articulated models throughout

For Teachers

For Students

The Ready Teacher Resource Book and Ready Practice and Problem Solving Teacher Guide support teachers with strong professional development, step-by-step lesson plans, and best practices for implementing rigorous standards.

Ready Teacher Toolbox provides online lessons, prerequisite lessons from previous grades, center activities, and targeted best-practice teaching strategies.

Ready is an integrated program of assessment and data-driven instruction designed to teach your students rigorous national and state standards for college and career readiness, including mathematical practice standards. You can use the program as a supplement to address specific standards where your students need instruction and practice, or more comprehensively to engage students in all standards.

Ready Instruction provides differentiated instruction and independent practice of key concepts and skills that build student confidence. Interim assessments give frequent opportunities to monitor progress.

Ready Practice and Problem Solving complements Ready Instruction, through rich practice, games, and performance tasks that develop understanding and fluency with key skills and concepts.

Ready Assessments provides three full-length assessments designed to show student mastery of standards.

Built for the new standards. Not just aligned.


Building on Ready Instruction, Ready Practice and Problem Solving encourages students to reason, use strategies, solve extended problems, and engage in collaborative learning to extend classroom learning. Designed for flexibility, Ready Practice and Problem Solving can be used for homework, independent classroom practice, and in after-school settings.

Lesson Practice Pages

Practice specific to each part of every Ready Instruction lesson gives students multiple opportunities to reinforce procedural fluency and synthesize concepts and skills learned in the classroom.

• Lesson practice pages can be used at the end of a lesson or after completing each part of a lesson.

• For ease of use, each part of a Ready Practice and Problem Solving lesson includes a Ready Instruction page reference indicating when they could be assigned.

What’s in Ready® Practice and Problem Solving

Prerequisite Skill Practice

• Students apply lesson prerequisite concepts or skills as they work with models that support those in the Ready Instruction lesson Introduction.

• This serves as a review of previous understandings and prepares students for the next section of the Ready Instruction lesson.

Family Letters

• Family Letters can be sent home separately before each lesson, or as part of a family communication package. They include a summary statement, vocabulary definitions, and models that help adult family members support their child’s mathematical learning.

• Each letter concludes with a simple activity that encourages students to share their math knowledge with family members while practicing skills or concepts in a fun, engaging way.

• A Spanish version of each letter is available on the Teacher Toolbox.

©Curriculum Associates, LLC Copying is not permitted. 173Lesson 16 Add and Subtract Fractions

Dear Family, Use with Ready Instruction Lesson 16

Like fractions have denominators that are the same.

like fractions: 1··4

and ··

and ··

3··

and ··

and 4 unlike fractions: 1

··2 and

·· and

··3··

and ··

and 4

To find the sum of like fractions, understand that you are just adding like units. Just as 3 apples plus 2 apples is 5 apples, 3 eighths plus 2 eighths is 5 eighths. Similarly, when you take away, or subtract, 2 eighths from 5 eighths, you have 3 eighths left.

You can also use a number line to understand adding and subtracting like fractions.

08

0 1

18

28

38

48

58

68

78

88

Remember that the denominator just names the units in the same way as “apples” names units. So,

• to add two fractions with the same denominator, the sum of the numerators tells how many of those units you have.

• to subtract two fractions with like denominators, the difference of the numerators tells how many of those units you have.

Invite your child to share what he or she knows about adding and subtracting fractions by doing the following activity together.

This week your child is learning how to add and subtract like fractions.

3··8

1 2··8

5 5··8

©Curriculum Associates, LLC Copying is not permitted. 167Lesson 15 Understand Fraction Addition and Subtraction

Name:

How do you show fractions with number lines and area models?

Study the example problem showing fractions with number lines and area models. Then solve problems 1–7.

1 Label the numbers 1, 3 ·· 8 , and 4 ·· 8 on the number line.

0 18

2 Shade the area model to show 3 ·· 8 .

3 Shade the area model to show 4 ·· 8 .

Example

How can you draw two different models to show 3 ·· 4 ?

0 114

24

34

An area model for 3 ·· 4 shows

4 equal parts, and 1 part shaded.

A number line model for 3 ·· 4 shows each whole

cut into 4 equal parts. 3 ·· 4 is the mark at the end

of the third part.

UnderstandFraction Addition and Subtraction

Lesson 15


Skills and Concepts Practice

• Worked-out examples support and reinforce students’ classroom learning, and can also serve as an explanation of the math content for adult family members if the practice pages are used as homework.

• Problems are differentiated to provide maximum flexibility when assigning practice as independent classwork or homework. The differentiation is marked in the Teacher Guide as basic B , medium

M , or challenging C .

• Vocabulary is defined at the point where terms are used in the practice problems.

• Students are encouraged to show their work and use models and strategies they learned in the Ready Instruction lesson.

• Lessons conclude with mixed practice problems that vary in type, including multiple choice, yes-no formats, and open-ended questions.

©Curriculum Associates, LLC Copying is not permitted. 169Lesson 15 Understand Fraction Addition and Subtraction

Name: Name: Lesson 15

1 Count by sixths to fi ll in the blanks:

1 ·· 6 , 2 ·· 6 , , , , , , , ,

2 Now label the number line to show sixths.

0 1

3 What is 1 ·· 6 more than 2 ·· 6 ?

4 What is 1 ·· 6 less than 2 ·· 6 ?

5 What is 1 ·· 6 more than 6 ·· 6 ?

6 What is 1 ·· 6 less than 6 ·· 6 ?

Example

You can count on or count back to add or subtract whole numbers. You can do the same to add or subtract fractions.

To add fourths, use a number line that shows fourths.

Add 3 ·· 4 1 2 ·· 4 .

0 14

24

34

44

54

Start at 3 ·· 4 . One more fourth is 4 ·· 4 , and another fourth is 5 ·· 4 .

3 ·· 4 1 2 ·· 4 5 5 ·· 4

Show Adding and Subtracting Fractions

Study how the example shows adding fractions. Then solve problems 1–12.

©Curriculum Associates, LLC Copying is not permitted.170 Lesson 15 Understand Fraction Addition and Subtraction

Solve.

7 Label the number line to show fourths.

0 44

8 Now use the number line in problem 7 to show 2

·· 4 1 2

·· 4 .

9 Label the number line to show fourths again.

0 44

10 Now use the number line in problem 9 to show 4 ·· 4 2 2 ·· 4 .

11 Use the number line and area model below to show 2 ·· 8 1 1 ·· 8 1 3 ·· 8 .

0

12 Look at the three area models. Which one would you choose to show 1 ·· 8 + 2 ·· 8 ? Explain how the denominator of the fraction helps you choose the model.

Vocabularydenominator the

number below the line

in a fraction. It tells how

many equal parts are in

the whole.

3 } 4

4 equal parts

numerator the number

above the line in a

fraction. It tells how many

equal parts are described.

3 } 4

3 parts described

©Curriculum Associates, LLC Copying is not permitted. 175Lesson 16 Add and Subtract Fractions

Name:

Model Fraction Addition and Subtraction

Study the example problem showing fraction addition with number line and area models. Then solve problems 1–8.

1 Label the number line to show eighths.

0 1

2 Use the number line in problem 1 to show 3 ·· 8 1 2 ·· 8 .

3 Divide the rectangle to show eighths.

4 Use the rectangle in problem 3 to show 3 ·· 8 1 2 ·· 8 .

Example

Adding fractions means joining or putting together parts of a whole. On the number line, each whole is divided into 6 equal sections. Each rectangle is divided into 6 equal pieces.

6 ·· 6 1

1 ·· 6 6 ·· 6 1

1 ·· 6

0 16

26

36

46

56

66

76

86

96

Add and Subtract Fractions

Lesson 16


Unit Practice Pages

Unit materials cover multiple skills and concepts, helping students make connections across standards.

Unit Game

• Unit Games are engaging collaborative experiences, designed to encourage students to use strategic thinking as they play the game with a partner.

• Students record the mathematics of each game to promote fluency and reinforce learning. The recording sheet also serves as an opportunity for informal assessment by providing a written record for teachers to monitor students’ work.

• These partner games can be used at classroom centers and/or sent home for play with an adult family member.

Unit Practice

• The Unit Practice provides mixed practice of lesson skills and concepts, and includes visual or stepped-out support for students.

• Unit Practice problems integrate multiple skills.

• These pages present problems with a variety of formats, including multiple choice and constructed response, to help students become familiar with items they will encounter on their state tests.

• The unit practice pages can be assigned as homework, used as independent or small group practice, or for whole class discussion.

©Curriculum Associates, LLC Copying is not permitted. 239Unit 4 Practice Number and Operations—Fractions

Name: Unit 4 Practice

Number and Operations—Fractions

In this unit you learned to: Lesson

find equivalent fractions, for example: 2··3 5 4··6 . 13

compare fractions with unlike denominators, for example: 2··5 . 3··10 . 14

add and subtract fractions with like denominators; add and

subtract mixed numbers, for example: 2 ·· 6 1 3 ·· 6 5 5 ·· 6 .15, 16, 17

multiply a fraction by a whole number, for example, 3 3 1··2 5 3

··2 . 18, 19

write a decimal as a fraction, for example: 0.4 5 4··10 . 20, 21

compare decimals, for example: 0.65 , 0.7. 22

Use these skills to solve problems 1–5.

1 Use ,, ., or 5 to complete each number sentence.

a. 2··41··3

b. 3··4 3 3 4··4 3 3

c. 2··10 0.20

d. 3··415··20

e. 0.5 0.09

2 Write each of the following numbers in one box below to show where on the number line it belongs.

1.03

1.4

1.34

1.3 1.36

What is another number that could go between 1.3 and 1.36?

Solution: ______________________

©Curriculum Associates, LLC Copying is not permitted. 237Unit 4 Game

Unit 4 Game Name:

Directions

• Players each choose a denominator from the list on the Recording Sheet. Players write their numbers in the Denominator Choice column of the Recording Sheet.

• Player A rolls the number cubes and makes two fractions using the numbers rolled as the numerators along with the chosen denominator.

• Player A writes and solves an addition problem with the two fractions on the Recording Sheet.

• Player B takes a turn following the same steps as Player A.

• Players compare the two fraction sums. The player with the greater sum wins the round.

• In each round, players choose a denominator that they have not used yet. The player with more wins after 5 rounds wins the game.

Fraction Sums

What you need: Recording Sheet, two 1–6 number cubes

Name:

Fraction Sums Recording Sheet

Player A Name Denominator Equation Choice

1.

2.

3.

Player B Name Denominator Equation Choice

1.

2.

Denominators

2 3 4 6 8

Denominators

2 3 4 6 8

Maya

48

3 ·· 4 1 4 ·· 4 5 7 ·· 4 4 ·· 8 1 6 ·· 8 5 10 ·· 8

Isaac

Maya

I chose fourths.

3 ·· 4 1 4 ·· 4 5 7 ·· 4 .

That ’s the same

as 14 ·· 8 . I win this

round because 14 ·· 8 is

more than your sum

of 10 ·· 8 .

31 546 2


Unit Performance Task

• Real-world Unit Performance Tasks require students to integrate skills and concepts, apply higher-order thinking, and explain their reasoning.

• Engaging real-world tasks encourage students to become active participants in their learning by requiring them to organize and manage mathematical content and processes.

• Performance Task Tips help students organize their thinking.

• Students are asked to reflect on Mathematical Practices after they have concluded their work.

Unit Vocabulary

• The Unit Vocabulary is a way for students to integrate vocabulary into their learning. Vocabulary pages provide a student-friendly definition for each new and review vocabulary term in the unit.

• Students are given space to write examples for each term to help them connect the term to their own understanding.

• After students have completed these pages, they can use them as a reference.

• Throughout the units, students are given opportunities to further personalize their acquisition of mathematics vocabulary by selecting terms they want to define.

©Curriculum Associates, LLC Copying is not permitted. 241Unit 4 Performance Task

Unit 4 Performance Task Name:

Answer the questions and show all your work on separate paper.

A grocery store sells fruit salad made with pineapples, strawberries, raspberries, blueberries, blackberries, and grapes. The store sells three different kinds of salad:

The Hawaiian: More than 1 ·· 2 of the salad is made of

pineapple. The rest is made of grapes and blueberries.

The Red Rose: Less than 1 ·· 2 of the salad is made of red

grapes. The rest is made of strawberries and raspberries.

The Berry Basket: The salad has equal parts of strawberries, blueberries, raspberries, and blackberries.

Make an ingredient list for each of the salads. Write a fraction for the fruits that are included in each salad.Explain why your lists fit the description of each salad.

The Hawaiian

—8

—8

—8

The Red Rose

—8

—8

—8

The Berry Basket

—8

—8

—8

—8

ChecklistDid you . . .

meet the given

conditions?

check your work?

reread your explanation to see if it makes sense?

Reflect on Mathematical PracticesAfter you complete the task, choose one of the following questions to answer.

1 Make Sense of Problems How did you know which fraction to fi nd fi rst for The Hawaiian and The Red Rose salads?

2 Use Structure How did you decide which fractions to use after you found the fi rst fraction?

©Curriculum Associates, LLC Copying is not permitted. 243Unit 4 Vocabulary

Use with Ready Instruction Unit 4

Unit 4 Vocabulary Name:

My Examples

equivalent fractions

two or more fractions that name the same part of a whole

denominator

the number below the line in a fraction; it tells how many equal parts are in a whole

numerator

the number above the line in a fraction; it tells how many equal parts are described

fraction

a number that names part of a whole


Fluency Practice Pages

Skills Practice

• Fluency facts practice and multi-digit computation worksheets in multiple formats provide flexibility and promote the use of grade-appropriate strategies and algorithms.

• These worksheets for grade-level facts and operations can be used any time after the skill has been taught.

Repeated Reasoning Practice

• Repeated Reasoning practice worksheets encourage students to make use of structure and look for regularity as part of their development of grade-level fluency.

• In this type of fluency practice, students identify and describe patterns in the relationship between the answers and the problems. This develops their abstract reasoning skills, mental math skills, and a deeper understanding of fractions and base ten numbers.

©Curriculum Associates, LLC Copying is permitted for classroom use. 399Fluency Practice

Name:

Form BAdd within 100,000.

Multi-Digit Addition—Skills Practice

1 10,9431 2,035

5 34,2101 1,399

9 94,6271 987

13 23,6581 8,467

17 74,8951 16,395

2 17,3421 1,340

6 72,6431 8,142

10 68,2541 2,438

14 47,6521 27,836

18 57,9181 25,896

3 12,4531 20,143

7 15,9201 63,254

11 26,5131 25,974

15 29,9991 3,999

19 42,9681 20,947

4 61,2381 24,501

8 45,8061 54,159

12 21,9421 38,657

16 84,3161 15,684

20 45,1631 27,989

400

Name:

©Curriculum Associates, LLC Copying is permitted for classroom use.Fluency Practice

Find place value patterns in the tens.

Multi-Digit Addition—Repeated Reasoning

Set B

1 1,3251 25

4 1,3251 125

7 1,3261 126

2 1,3261 25

5 1,3261 125

8 1,3271 126

3 1,3271 25

6 1,3271 125

9 1,3281 126

Set A

1 201 1 109 5

4 202 1 109 5

7 203 1 109 5

10 204 1 109 5

2 1,201 1 109 5

5 1,202 1 109 5

8 1,203 1 109 5

11 1,204 1 109 5

3 2,201 1 109 5

6 2,202 1 109 5

9 2,203 1 109 5

12 2,204 1 109 5

Describe a pattern you see in one of the sets of problems above.


Correlation Chart

Common Core State Standards © 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

The Standards for Mathematical Practice are integrated throughout the lesson practices, unit practices, and unit games.

Common Core State Standards Practice in Ready® Practice and Problem SolvingThe table below shows the standards addressed in lesson practices, unit practices, games, and performance tasks, all of which correspond to Ready Instruction lessons and units. Use this information to plan and focus meaningful practice.

Common Core State Standards for Grade 3 — Mathematics Standards

Content Emphasis

Ready® Practice and Problem Solving

Operations and Algebraic Thinking

Represent and solve problems involving multiplication and division.

3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 3 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 3 7.

MajorLesson 1 PracticeUnit 1 Practice

3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 4 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 4 8.

Major

Lesson 4 PracticeUnit 1 PracticeUnit 1 Performance TaskUnit 3 Practice

3.OA.A.3 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. Major

Lesson 11 PracticeUnit 1 Performance TaskUnit 3 Game: Two-Step ProblemsUnit 3 PracticeUnit 3 Performance Task

3.OA.A.4 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 3 ? 5 48, 5 5 4 3, 6 3 6 5 ?

Major

Lesson 6 PracticeUnit 1 Game: Fish for Factors!Unit 1 PracticeUnit 3 Practice

Understand properties of multiplication and the relationship between multiplication and division.

3.OA.B.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6 3 4 5 24 is known, then 4 3 6 5 24 is also known. (Commutative property of multiplication.) 3 3 5 3 2 can be found by 3 3 5 5 15, then 15 3 2 5 30, or by 5 3 2 5 10, then 3 3 10 5 30. (Associative property of multiplication.) Knowing that 8 3 5 5 40 and 8 3 2 5 16, one can find 8 3 7 as 8 3 (5 1 2) 5 (8 3 5) 1 (8 3 2) 5 40 1 16 5 56. (Distributive property.)

Major

Lesson 2 PracticeLesson 3 PracticeUnit 1 Practice

3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 4 8 by finding the number that makes 32 when multiplied by 8. Major Lesson 5 Practice

Multiply and divide within 100.

3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 3 5 5 40, one knows 40 4 5 5 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Major

Lesson 6 PracticeUnit 1 Game: Fish For Factors!

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

3.OA.D.8 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.

Major


3.OA.D.9 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.

Major

Lesson 7 Practice



Content Emphasis


Number and Operations in Base Ten

Use place value understanding and properties of operations to perform multi-digit arithmetic.

3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or 100. Supporting/

Additional

Lesson 8 PracticeUnit 2 Game: Tic-Tac-Times-TenUnit 2 PracticeUnit 2 Performance Task

3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Supporting/

Additional

Lesson 9 PracticeUnit 2 PracticeUnit 2 Performance TaskUnit 3 Game: Two-Step ProblemsUnit 3 Performance Task

3.NBT.A.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 3 80, 5 3 60) using strategies based on place value and properties of operations.

Supporting/Additional

Lesson 10 PracticeUnit 2 Game: Tic-Tac-Times-TenUnit 2 Practice

Number and Operations—Fractions

Develop understanding of fractions as numbers.

3.NF.A.1 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 .

Major

Lesson 14 PracticeUnit 4 PracticeUnit 6 PracticeUnit 6 Performance Task

3.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. Major Lesson 15 Practice

Unit 4 Practice 3.NF.A.2a 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.

Major

3.NF.A.2b 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.

Major

3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Major Lesson 16 Practice

Lesson 17 PracticeLesson 18 PracticeLesson 19 PracticeUnit 4 Game: Equivalent Fraction MatchUnit 4 PracticeUnit 4 Performance TaskUnit 6 Practice

3.NF.A.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Major

3.NF.A.3b Recognize and generate simple equivalent fractions, e.g., 1 ··

2

5 2 ··

4 , 4

··

6 5 2

··

3 . Explain why the fractions are equivalent, e.g.,

by using a visual fraction model.Major

3.NF.A.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 5 3

··

1 ; recognize that 6

··

1 5 6; locate 4

··

4

and 1 at the same point of a number line diagram.

Major

3.NF.A.3d 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 ., 5, or ,, and justify the conclusions, e.g., by using a visual fraction model.

Major



Content Emphasis


Measurement and Data

Solve problems involving measurement and estimation.

3.MD.A.1 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.

Major

Lesson 20 PracticeLesson 21 PracticeUnit 5 Game: Time MatchUnit 5 Practice

3.MD.A.2 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, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

Major


Represent and interpret data.

3.MD.B.3 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.



3.MD.B.4 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.


Lesson Practice: Lesson 26

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

3.MD.C.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. Major Lesson 27 Practice

Unit 5 PracticeUnit 5 Performance Task 3.MD.C.5a 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.

Major

3.MD.C.5b 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.

Major

3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). Major

Lesson 27 PracticeUnit 5 Performance Task

3.MD.C.7 Relate area to the operations of multiplication and addition. Major Lesson 28 PracticeLesson 29 PracticeUnit 5 Practice

3.MD.C.7a Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

Major

3.MD.C.7b 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.

Major

3.MD.C.7c Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b 1 c is the sum of a 3 b and a 3 c. Use area models to represent the distributive property in mathematical reasoning.

Major

3.MD.C.7d 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.

Major

Geometric measurement: recognize perimeter.

3.MD.D.8 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.


Lesson 30 PracticeUnit 5 Practice



Content Emphasis


Geometry

Reason with shapes and their attributes.

3.G.A.1 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.


Lesson 31 PracticeLesson 32 PracticeUnit 6 Game: Shape Attribute Cover-UpUnit 6 Practice

3.G.A.2 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.


Lesson 33 PracticeUnit 6 PracticeUnit 6 Performance Task

77©Curriculum Associates, LLC Copying is not permitted.

Practice Lesson 18 Understand Comparing Fractions Unit 4

Practice and Problem Solving Unit 4 Number and Operations—Fractions

Key

B

Bas

ic

M M

ediu

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C C

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198

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Shad

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ape

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how

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8 W

hich

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198

1 4 23 6 4

2 2 1

5 3 2

2

6 8 6

2 ··

6

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acti

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Prer

equ

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ow d

o y

ou

sh

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qu

ival

ent

frac

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wit

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hap

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dy

the

exam

ple

sh

owin

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qu

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ract

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s.

Then

so

lve

pro

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ms

1–8.

Wri

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qu

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s fo

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e sh

aded

par

ts.

1

1 ·· 4 5

8

2

4 ·· 4 5

3

3 ·· 4 5

Exam

ple

Both

circ

les

are

the

sam

e si

ze.

Both

circ

les

have

the

sam

e am

ount

of s

hadi

ng.

1 ·· 2 and

4 ·· 8 are

equ

ival

ent f

ract

ions

.

1 ·· 2 5 4 ·· 8

Und

erst

and

Com

par

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Frac

tion

s

Less

on 1

8

Vo

cab

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ryeq

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t fr

acti

on

s fr

actio

ns th

at n

ame

the

sam

e nu

mb

er.

1 ·· 2 and

2 ··

4

are

equ

ival

ent.

1 p

art s

hade

d2

equa

l par

ts in

the

who

le

1 ·· 2

4 p

arts

sha

ded

8 eq

ual p

arts

in th

e w

hole

4 ·· 8

197

2 8 8 6 8BBB




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ons

Wri

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frac

tio

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e sh

aded

par

ts. C

ircl

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e fr

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th

at is

less

.

4 Fr

actio

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5 Fr

actio

ns:

6 Fr

actio

ns:

Wri

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frac

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e sh

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rec

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at h

as a

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of 1

.

200

Po

ssib

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nsw

ers:

1 ··

5 , 1 ··

6 ,

1 ··

8 Poss

ible

an

swer

: 4 ··

8 . Als

o a

ccep

t 1 ··

8 ,

2 ··

8 , 3 ··

8 ,

5 ··

8 , 1 ··

2 ,

or

1 ··

4 .

1 ··

2 1 ··

4 4 ··

8

1 ··

3

1 ··

8 4 ··

6

6 ··

8

CCMMM

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Less

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Un

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Less

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8

Use

Mod

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to C

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ract

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Stu

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how

th

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ses

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s to

co

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are

frac

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ns.

Th

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olv

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rob

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s 1–

8.

Wri

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frac

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par

ts. C

ircl

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e fr

acti

on

th

at is

gre

ater

.

1 Fr

actio

ns:

2 Fr

actio

ns:

3 Fr

actio

ns:

Exam

ple

Both

rect

angl

es a

re th

e sa

me

size

.

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u m

ake

8 eq

ual p

arts

, the

par

ts a

re

smal

ler t

han

if yo

u m

ake

4 eq

ual p

arts

.

1 ·· 8 is le

ss th

an 1 ·· 4 .

1 ·· 4 is g

reat

er th

an 1 ·· 8 .

1 ·· 8 1 ·· 4

199

2 ··

3 3 ··

6 1 ··

8

1 ··

3 4 ··

6 1 ··

4

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202

Less

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18

Un

der

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omp

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acti

ons

Solv

e th

e p

rob

lem

. Use

wh

at y

ou

lear

ned

fro

m t

he

mo

del

.

Whi

ch fr

actio

n is

the

leas

t: 3 ·· 4 ,

3 ·· 6 , or

3 ·· 8 ?

Eric

sai

d, “

3 ·· 8 is th

e le

ast.”

Bob

sai

d, “

3 ·· 4 is th

e le

ast.”

Who

is ri

ght?

Who

is w

rong

? H

ow d

id y

ou d

ecid

e?

Wha

t was

the

mis

take

?

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you

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wor

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s to

ex

pla

in h

ow y

ou d

ecid

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hat t

o dr

aw.

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ou . .

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se a

pictu

re to

ex

plain?

• use

num

bers

to

expla

in?• u

se w

ords

to

expla

in?• g

ive de

tails

?

202Po

ssib

le a

nsw

er: E

ric

is c

orr

ect.

3 ··

8 is t

he

leas

t fr

acti

on

. Wh

en y

ou

div

ide

the

sam

e sh

ape

into

a

gre

ater

nu

mb

er o

f par

ts, t

he

par

ts a

re s

mal

ler.

So

1 ··

8 is le

ss t

han

1 ··

6 or

1 ··

4 , an

d 3 ··

8 is

less

th

an 3 ··

6 o

r 3 ··

4 .

The

mo

del

sh

ows

that

th

is is

tru

e.

3 83 4

3 6

Bo

b is

wro

ng

. He

may

hav

e co

mp

ared

d

eno

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ato

rs s

ince

all

of t

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nu

mer

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re t

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sam

e. H

e m

ay h

ave

pic

ked

3 ··

4 bec

ause

he

saw

th

at

4 is

less

th

an 6

or

8. H

e d

idn

’t r

eco

gn

ize

that

wh

en

the

nu

mer

ato

rs a

re t

he

sam

e, t

he

frac

tio

n w

ith

th

e g

reat

est d

eno

min

ato

r is

th

e le

ast f

ract

ion

. Th

e m

od

el t

hat

I m

ade

abov

e sh

ows

this

.

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201

Less

on

18

Un

der

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acti

ons

Nam

e:

Rea

son

and

Wri

te

Stu

dy

the

exam

ple

pro

ble

m. U

nd

erlin

e tw

o p

arts

th

at y

ou

th

ink

mak

e it

a p

arti

cula

rly

go

od

an

swer

an

d a

hel

pfu

l exa

mp

le.

Exam

ple

Whi

ch fr

actio

n is

gre

ates

t: 2 ·· 3 , 2 ·· 4 , o

r 2 ·· 8 ?

Dia

ne s

aid,

“ 2 ·· 8 is

the

grea

test

.”

Sand

ra s

aid,

“ 2 ·· 3 is

the

grea

test

.”

Who

is ri

ght?

Who

is w

rong

? H

ow d

id y

ou d

ecid

e?

Wha

t was

the

mis

take

?

Show

you

r wor

k. U

se p

ictu

res,

wor

ds, o

r num

ber

s to

ex

pla

in.

San

dra

is r

igh

t. S

he

saw

th

at 2

is t

he

nu

mer

ato

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ea

ch fr

acti

on

. Sh

e lo

oke

d a

t th

e d

eno

min

ato

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co

mp

are

the

frac

tio

ns.

I m

ade

a m

od

el to

ch

eck

the

answ

er.

2 42 3

2 8

The

mo

del

sh

ows

that

th

ird

s ar

e b

igg

er t

han

fou

rth

s an

d t

hir

ds

are

big

ger

th

an e

igh

ths.

So

tw

o t

hir

ds

is

big

ger

th

an t

wo

fou

rth

s.

Dia

ne’

s an

swer

is w

ron

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he

may

hav

e co

mp

ared

th

e d

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min

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f th

e fr

acti

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s. S

he

tho

ug

ht

that

2 ··

8 is g

reat

est b

ecau

se it

has

th

e g

reat

est

den

om

inat

or.

Sh

e m

ay n

ot h

ave

use

d a

mo

del

or

tho

ug

ht a

bo

ut t

he

size

of e

ach

of t

he

equ

al p

arts

.

Less

on 1

8

Whe

re d

oes t

he

exam

ple . .

.• u

se a

pictu

re to

ex

plain?

• use

num

bers

to

expla

in?• u

se w

ords

to

expla

in?• g

ive de

tails

?

201

Documents

Ready Mathematics Practice and Problem Solving … · Table of Contents Ready® Program Overview A7 What’s in Ready Practice and Problem Solving A8 Lesson Practice Pages A8 Unit