essential strategies for math success

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Level D

Essential Strategiesfor Math SuccessMath Problem Solving and Test-Taking Instruction

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Acknowledgments

2 ESSENTIAL STRATEGIES FOR MATH SUCCESS

ISBN 978-1-4204-5494-9R 5494-9

Copyright ©2011 RALLY! EDUCATIONAll rights reserved. No part of the material protected by this copyrightmay be reproduced in any form by any means, electronic or mechanical,including photocopying, recording, or by any information storage andretrieval system, without permission in writing from the copyrightowner. Printed in the U.S.A.0710.MAQ

Executive Editor: Amy CollinsEditor: Shelley WakeDesign Director: Jean-Paul Vest

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ESSENTIAL SKILLS FOR READING SUCCESS

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

PART A: The 5-Step Problem-Solving Plan . . . . . . . . . . . . . . . . .5Part A introduces students to the 5-Step Problem-Solving Plan that they will use to solve all the

problems in the book.

PART B: The 10 Problem-Solving Strategies One-by-One . . .13Part B teaches students how to follow a plan, use problem-solving strategies, and solve different types of

math problems. For each of the 10 strategies, we first use modeled instruction to model what we teach.

Then we use guided instruction to help students learn the strategy. Then we provide students with

problems to solve on their own using the strategy.

Strategy 1: Draw a Picture or Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

Strategy 2: Organize—Make a Chart or List, Graph, Sort Data . . . . . . . . . . . . . . .20

Strategy 3: Work Backwards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26

Strategy 4: Use Manipulatives or Act Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

Strategy 5: Compute—Write a Number Sentence, Use Ratio or Proportion . . . . . . .38

Strategy 6: Use a Formula or Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44

Strategy 7: Guess and Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50

Strategy 8: Make It Simpler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56

Strategy 9: Make Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62

Strategy 10: Look for a Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68

PART C: Practice Using the Strategies . . . . . . . . . . . . . . . . . . . .75Part C gives students practice in using the strategies to solve problems. This section has multiple choice,

short response, and extended response problems. Students are given a hint that tells them which strategy

to use and provides guidance on how to use the strategy.

PART D: Choose the Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . .89Part D gives students practice in selecting and using the right strategy to solve problems. This section has

multiple choice, short response, and extended response problems. Students are guided to choose the right

strategy and solve the problems on their own.

PART E: Problem Solving Practice . . . . . . . . . . . . . . . . . . . . . . .103In Part E, students select a suitable strategy for solving each problem on their own. This section has

multiple choice, short response, and extended response problems. Students solve each problem on their

own and identify the strategy they used to solve the problem.

ESSENTIAL STRATEGIES FOR MATH SUCCESS 3

Table of Contents

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Introduction | ESSENTIAL STRATEGIES FOR MATH SUCCESS

INTRODUCTION

IntroductionWelcome to Essential Strategies for Math Success: Math Problem Solving and Test-TakingInstruction. To be successful in math, students must become good problem solvers. Usingscaffolded instruction, this book teaches students problem-solving skills and shows themhow to apply those skills to different types of math problems.

Essential Strategies for Math Success is made up of five parts.

Part A: The 5-Step Problem-Solving PlanGood problem solvers always follow a plan. This section introduces students to the planthat they will use to solve all the problems in the book.

Part B: The 10 Problem-Solving Strategies One-by-OnePart B teaches students how to follow a plan, use problem-solving strategies, and solvedifferent types of math problems.

Part C: Practice Using the StrategiesPart C gives students practice in using the strategies to solve problems. Students will begiven a hint that tells them which strategy to use and provides guidance on how to usethe strategy.

Part D: Choose the StrategyPart D gives students practice in selecting and using the right strategy to solve problems.Students are guided to choose the right strategy and solve the problems on their own.

Part E: Problem Solving PracticeIn Part E, students select a suitable strategy for solving each problem on their own.

When students finish Essential Strategies for Math Success they will be better problemsolvers and better test takers.

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5

Part A introduces students to the 5-Step Problem-Solving Plan that they willuse to solve all the problems in the book.

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Step 1: DECIDE what you are being asked to do.

The problem tells you that Alek would like to give each friend an equalnumber of stamps. You must find how many stamps Alek should give to eachfriend if he keeps 8 stamps for himself.

Step 2: FIND what you need to know.

You can find the following facts in the problem:

• Number of stamps Alek has = 35• Number of stamps Alek would like to keep = 8• Number of friends Alek would like to give stamps to = 9

Step 3: CHOOSE a strategy for solving the problem.

There is often more than one way to solve a math problem. In this book youwill learn how to use several problem-solving strategies. Sometimes you cansolve a problem by drawing a picture. Looking at a picture can make it easierto find the solution.

PART A: The 5-Step Problem-Solving Plan

THE 5-STEP PROBLEM-SOLVING PLAN

Modeled InstructionWhen solving math problems, you need to follow a plan. This helps you to organizeinformation and choose a strategy to solve the problem. The example below shows howto follow the 5-Step Problem-Solving Plan. Read the math problem and follow each stepof the plan.

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1. Alek has 35 stamps. He would like to keep 8 stamps for himself and sharethe rest equally with 9 of his friends.

How many stamps should Alek give to each of his friends?

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The 5-Step Problem-Solving Plan

Step 4: SOLVE the problem.

• Draw a picture to show the total number of stamps that Alek has.• Cross out the stamps Alek will keep for himself.• Draw circles around the stamps each friend should receive.

Look at the drawing. Count how many stamps are inside each circle. Now youcan see that Alek should give each of his friends 3 stamps.

Step 5: CHECK your answer.

You can use number sentences to check your answer.

If Alek has 35 stamps and would like to keep 8, then the number of stampsleft to give to his friends is 35 – 8 = 27.

If Alek gives 3 stamps to each of his 9 friends, then the total number ofstamps he gives to his friends is 3 x 9 = 27.

Since the answer to both number sentences is the same, you know that youranswer makes sense.

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On Your OwnFollow the 5-Step Problem-Solving Plan to answer the next two questions onyour own.

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2. Marta places 7 crates in her garage. There are 5 boxes of plant seeds insideeach crate. Each box contains 24 packets of seeds. How many packets ofseeds did Marta place in her garage?

A840 B 600 C 168 D 120

DECIDE what you are being asked to do.

State what the problem is asking you to do.

FIND what you need to know.

List key facts from the problem. Remember, some problems will give extrainformation that you do not need to know.

CHOOSE a strategy for solving the problem.

Name the strategy you choose to solve this problem.

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SOLVE the problem.

Show your work for solving this problem.

CHECK your answer.

Show or explain how you know that your answer makes sense.

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List key facts from the problem.


Name the strategy you choose to solve this problem.

3. Marco needs 150 nails to build a fence around his yard. He already has66 nails. How many more nails does Marco need to build his fence?

Answer:

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SOLVE the problem.


CHECK your answer.

Show or explain how you know that your answer makes sense.

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PART B:The 10 Problem-SolvingStrategies One-by-OnePart B teaches students how to follow a plan, use problem-solving strategies, andsolve different types of math problems. For each of the 10 strategies, first we usemodeled instruction to model what we teach. Then we use guided instruction to helpstudents learn the strategy. Then we provide students with two problems to solve ontheir own using the strategy.

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PART B: One-by-One | Strategy 1: Draw a Picture or Diagram

STRATEGY 1: Draw a Picture or Diagram

Modeled InstructionNow you will learn how to solve a math problem by drawing a picture or diagram.Read the problem below. The plan that follows will explain how to use this strategy.


You must find how many tiles are needed to completely cover Mrs. Chang’sbathroom floor.


You need the following information to solve this problem:

• The floor is shaped like a rectangle.• The floor is 6 tiles wide.• The floor is 11 tiles long.


This problem gives details about the shape, width, and length of thebathroom floor. A good strategy for solving problems like this is to Draw aPicture or Diagram. A picture or diagram can help you to see the answer.

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1. Mrs. Chang would like to cover her bathroom floor with tiles. The floor isshaped like a rectangle. It takes 6 tiles to cover the width of the floor.It takes 11 tiles to cover the length of the floor. How many tiles willMrs. Chang need to completely cover her floor?

A 77 C 55

B 66 D 34

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Draw a Picture or Diagram

ONE

BY

ONE

SOLVE the problem.

Draw a picture that shows how wide the bathroom floor is and how long thebathroom floor is. Use squares to represent the tiles. Draw 11 tiles as thelength and 6 tiles as the width.

To find how many tiles it will take to cover the floor, count the number oftiles. There are 66 tiles. The correct answer to the problem is “B.”

CHECK your answer.

You can use multiplication to check your answer. The number of tiles neededis the width multiplied by the length.

6 × 11 = 66

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Guided InstructionDirections: Solve question 2 using the Draw a Picture or Diagram strategy. Remember tofollow the Problem-Solving Plan.

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You will use the Draw a Picture or Diagram strategy to solve this problem.

2. Guan would like to build a fence around his backyard. The yard is shapedlike a square. One side of the backyard measures 14 meters in length. Thefence will go around the 4 sides of the backyard. How many meters long willthe fence be?

A 18 meters C 56 meters

B 28 meters D 72 meters

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ONE

BY

ONE

SOLVE the problem.


CHECK your answer.

Show or explain how you know that your answer makes sense.Is your answer reasonable?

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On Your OwnDirections: Solve questions 3 and 4 using the Draw a Picture or Diagram strategy.

Remember to follow the Problem-Solving Plan.

3. The total distance around the sides of a square is equal to 96 centimeters.How many centimeters does one side of the square measure?

A 12 centimeters

B 16 centimeters

C 24 centimeters

D 48 centimeters


Choose the correct answer.

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ONE

BY

ONE

4. Inga walked 5 blocks north from her house to return a book at the library. Shethen walked 7 blocks east to meet her friend at the soccer field. When she wasfinished playing soccer, she walked 3 blocks south and 2 blocks west to mail aletter at the post office. How many blocks did Inga walk in all?


Write your answer.

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PART B: One-by-One | Strategy 2: Organize – Make a Chart or List, Graph, Sort Data

STRATEGY 2: Organize

Modeled InstructionNow you will learn how to solve a math problem by making a chart or list, making agraph, or sorting data. Read the problem below. The plan that follows will explain how touse this strategy.


You have to decide which answer choice is a correct statement.


The question gives you information about the ages of Lupe, Pao, and Zac.

• Lupe is twice as old as Pao.• Pao is 9.• Zac is 6 years younger than Lupe.


To solve this problem, you will need to compare the ages of the threepeople. It will be easier to compare data if you Organize – Make a Chartor List.

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1. Lupe is twice as old as Pao. Pao is 9 years old. Zac is 6 years younger thanLupe. Which statement is true?

A Pao is 3 years younger than Zac. C Lupe is 9 years older than Zac.

B Lupe is 6 years older than Pao. D Zac is older than Lupe and Pao.

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Organize – Make a Chart or List, Graph, Sort Data

ONE

BY

ONE

SOLVE the problem.

Use the information in the question to find the age of each person.

The question tells you that Pao is 9 years old.

The question tells you that Lupe is twice as old as Pao. Since Pao is 9,Lupe must be 18.

The question tells you that Zac is 6 years younger than Lupe. Since Lupeis 18, Zac must be 12.

Now list the ages of each person so you can compare them.

Pao 9Lupe 18Zac 12

You can see that Pao is 3 years younger than Zac. The correct answer ischoice “A.”

CHECK your answer.

Check your answer by working backwards.

The question tells you that Pao is 9 years old.

The answer selected states that Pao is 3 years younger than Zac.

If Pao is 3 years younger than Zac, Zac must be 12 years old.

If Zac is 6 years younger than Lupe, Lupe must be 18 years old.

If Lupe is twice as old as Pao, Pao must be 9 years old.

The information matches what the question tells you about everyone’s age.This shows that you found the correct age of Pao, Lupe, and Zac.

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Guided InstructionDirections: Solve question 2 using the Organize – Make a Chart or List, Graph,Sort Data strategy. Remember to follow the Problem-Solving Plan.

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You will use the Organize – Make a Chart or List, Graph, Sort Datastrategy to solve this problem.

2. Marleen and Hamid work at the video store. The chart below shows howmuch money they each earned during one month.

In which week did Marleen and Hamid earn the most money?

AWeek 1 C Week 3

BWeek 2 D Week 4

Marleen Hamid

Week 1 $105 $110

Week 2 $95 $105

Week 3 $125 $80

Week 4 $90 $100

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ONE

BY

ONE

SOLVE the problem.


CHECK your answer.


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On Your OwnDirections: Solve questions 3 and 4 using the Organize – Make a Chart or List, Graph,Sort Data strategy.


3. The chart below shows the heights of some of the world’s tallest buildings.

Which building is the tallest?

A Emirates Tower One

B Empire State Building

C Jin Mao Building

D John Hancock Center



Height (feet)

1,165

1,250

1,380

1,127

1,140

Building

Emirates Tower One

Empire State Building

Jin Mao Building

John Hancock Center

T & C Tower

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ONE

BY

ONE

4. Takira has $9 more than Matthew. Matthew has $8 more than Yvonne.How much money does Takira have if Yvonne has $22?


Write your answer.

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PART B: One-by-One | Strategy 3: Work Backwards

STRATEGY 3: Work Backwards

Modeled InstructionNow you will learn how to solve a math problem by working backwards. Read the problembelow. The plan that follows will explain how to use this strategy.


You must find how many apples Nancy had to begin with.



• Nancy gives 6 apples to Armando.• Nancy gives 3 apples to Mai.• After giving apples to her friends, Nancy gives half of the apples left to

Miss Haywood.• Nancy eats 1 apple.• There are 5 apples left.


The problem tells you how many apples Nancy had left, but it does NOT tellyou how many apples she had to begin with. A good strategy for solving thistype of math problem is to Work Backwards.

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1. Nancy has a bag of apples. She gives 6 apples to Armando and 3 apples toMai. When Nancy arrives at school, she gives half of the apples that are leftto Miss Haywood. At lunchtime, Nancy eats 1 apple from the bag. AfterNancy eats her apple, there are only 5 apples left in the bag. How manyapples were in the bag to begin with?

A 15 C 21

B 17 D 25

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Work Backwards

ONE

BY

ONE

SOLVE the problem.

Start with how many apples Nancy had left.

There were 5 apples left in the bag.

Find how many apples there were before Nancy ate 1 of them.

5 + 1 = 6 apples

Find how many apples there were before Nancy gave half of them toMiss Haywood.

6 + 6 = 12 apples

Find how many apples there were before Nancy gave 3 to Mai.

12 + 3 = 15 apples

Find how many apples there were before Nancy gave 6 to Armando.

15 + 6 = 21 apples

Since you have concluded that Nancy had 21 apples to begin with,the correct answer is choice “C.”

CHECK your answer.

You now know how many apples Nancy had to begin with. Read the problemagain and check to see that your answer makes sense.

Nancy had 21 apples to begin with.

She gave 6 apples to Armando. (21 – 6 = 15)

She gave 3 apples to Mai. (15 – 3 = 12)

She gave half of the apples left to Miss Haywood. (12 – 6 = 6)

Nancy ate 1 apple. (6 – 1 = 5)

Nancy has 5 apples left.

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Work Backwards

Guided InstructionDirections: Solve question 2 using the Work Backwards strategy. Remember to follow theProblem-Solving Plan.

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You will use the Work Backwards strategy to solve this problem.

2. Trevor is reading a book. On Tuesday he read 39 pages. On Wednesday heread 43 pages. When Trevor finished reading on Wednesday, he was onpage 111. What page was Trevor on when he began reading on Tuesday?

A 29 C 68

B 37 D 82

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Work Backwards

ONE

BY

ONE

SOLVE the problem.


CHECK your answer.


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Work Backwards

On Your OwnDirections: Solve questions 3 and 4 using the Work Backwards strategy.


3. Enrique has a jar filled with marbles. He removes half of the marbles from thejar. Then he places 23 marbles back into the jar. There are now 129 marblesinside the jar. How many marbles were in the jar to begin with?

A 258

B 212

C 153

D 106



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Work Backwards

ONE

BY

ONE

4. From noon to midnight, the temperature decreased by 12°C. At midnight, thetemperature was 14°C. What was the temperature at noon?


Write your answer.

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PART B: One-by-One | Strategy 4: Use Manipulatives or Act Out

STRATEGY 4: Use Manipulatives or Act Out

Modeled InstructionNow you will learn how to solve a math problem by using manipulatives or acting it out.Read the problem below. The plan that follows will explain how to use this strategy.


You must find what fraction of the shapes are triangles.


The question shows six shapes.


You can work out what fraction of the shapes are triangles by sorting theminto shapes that are triangles and shapes that are not triangles. You can UseManipulatives or Act Out to do this.

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1. Suwan cuts out several different shapes from a piece of paper. These shapesare shown below.

What fraction of the shapes are triangles?

A�13� B �16� C �12� D �23�

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Use Manipulatives or Act Out

ONE

BY

ONE

SOLVE the problem.

Copy the shapes shown on a piece of paper. Then cut out the shapes. Sortthe shapes into those that are triangles and those that are not.

Now that the shapes are sorted, you can see that there are 2 shapes that aretriangles. There are 6 shapes total. The fraction of shapes that are trianglesis �26�. This fraction can be simplified to �13�. The correct answer is choice “A.”

CHECK your answer.

Check your answer by recounting the number of triangles and the totalnumber of shapes. Write a fraction as below.

number of trianglestotal number of shapes

The fraction is:

�26�

Simplify the fraction.

�26� = �13�

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Guided InstructionDirections: Solve question 2 using the Use Manipulatives or Act Out strategy. Rememberto follow the Problem-Solving Plan.

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You will use the Use Manipulatives or Act Out strategy to solvethis problem.

2. The following cards are used to play a game.

What fraction of the cards have stars on them?

A�18� B �14� C �13� D �12�

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ONE

BY

ONE

SOLVE the problem.


CHECK your answer.


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On Your OwnDirections: Solve questions 3 and 4 using the Use Manipulatives or Act Out strategy.


3. Ethan has the following tokens.

Which number is on �15� of the tokens?

A 10

B 30

C 35

D 50



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ONE

BY

ONE

4. Two rows of cards are placed on a table.

Octavio must select one card from each row and use the number on each cardto form a 2-digit number. What is the lowest number that Octavio could make?


Write your answer.

3 5 1

326

Row A

Row B

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PART B: One-by-One | Strategy 5: Compute – Write a Number Sentence, Use Ratio or Proportion

STRATEGY 5: Compute

Modeled InstructionNow you will learn how to solve a math problem by writing a number sentence or usinga ratio or proportion. Read the problem below. The plan that follows will explain how touse this strategy.


You must find how many minutes Omar practiced in all for the last threedays of the week.


The table shows how many minutes Omar practiced on each day of the week.You only need to know how many minutes Omar practiced for on the lastthree days of the week.

• Wednesday = 30 minutes• Thursday = 25 minutes• Friday = 40 minutes

You do NOT need to know how long Omar practiced for on Monday orTuesday. This is extra information that is not needed to solve the problem.

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1. Omar practices playing the piano each day after school. He made a table toshow how much he practiced in one week.

How many minutes did Omar practice in all for the last three days of the week?

A65 B 70 C 80 D 95

Day of the Week

Monday

Tuesday

Wednesday

Thursday

Friday

Minutes Practiced

25

35

30

25

40

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Compute – Write a Number Sentence, Use Ratio or Proportion

ONE

BY

ONE


You can Compute – Write a Number Sentence to find how many minutesOmar practiced on the last three days of the week. Use facts given in thetable to write the number sentence.

SOLVE the problem.

The last 3 days of the week are Wednesday, Thursday, and Friday. Create anumber sentence that shows how many minutes Omar practiced in all onthese 3 days. On Wednesday, Omar practiced for 30 minutes. On Thursday, hepracticed for 25 minutes. On Friday, he practiced for 40 minutes.

30 + 25 + 40 = number of minutes practiced in allfor the last three days of the week

Calculate how many minutes Omar practiced in all on these 3 days.

3025

+ 4095

Choice “D” is the correct answer to the problem.

CHECK your answer.

Check that your number sentence matches the data in the table.

The minutes practiced for the last 3 days of the week are as below:

Wednesday = 30 minutesThursday = 25 minutesFriday = 40 minutes

The number sentence is as below:

30 + 25 + 40 = number of minutes practiced in allfor the last three days of the week

The number sentence does match the data in the table.

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Guided InstructionDirections: Solve question 2 using the Compute – Write a Number Sentence,Use Ratio or Proportion strategy. Remember to follow the Problem-Solving Plan.

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You will use the Compute – Write a Number Sentence, Use Ratio orProportion strategy to solve this problem.

2. John placed 98 boxes on some shelves. He placed 7 boxes on each shelf.How many shelves did John use for all the boxes?

A7 B 9 C 12 D 14

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ONE

BY

ONE

SOLVE the problem.


CHECK your answer.


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On Your OwnDirections: Solve questions 3 and 4 using the Compute – Write a Number Sentence, UseRatio or Proportion strategy.


3. Mr. Kessler is preparing for a party. He places the same number of plates oneach table as shown below.

Mr. Kessler must also place 2 napkins next to each plate. What number sentence canbe used to find how many napkins Mr. Kessler will need if there are 15 tables?

A 2 × 7 × 15 = ___

B 2 × 7 × ___ = 15

C 2 + 7 × 15 = ___

D 2 + 7 × ___ = 15



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ONE

BY

ONE

4. Jana took a survey of the students in her school to find what their favoriteseason of the year is. The results are listed in the table below.

How many more students chose spring as their favorite season than chose winter?


Write your answer.

Season

Winter

Spring

Summer

Fall

Number of Students WhoSaid It Was Their Favorite

50

95

90

65

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PART B: One-by-One | Strategy 6: Use a Formula or Rule

STRATEGY 6: Use a Formula or Rule

Modeled InstructionNow you will learn how to solve a math problem by using a formula or rule. Read theproblem below. The plan that follows will explain how to use this strategy.


You must round the number 385 to the nearest ten.


To solve this problem you must know the place value of each digit in thenumber 385.

• The digit 3 is in the hundreds place.• The digit 8 is in the tens place.• The digit 5 is in the ones place.


You must follow a rule when rounding numbers. Use a Formula or Rule isone possible strategy for solving this problem.

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1. What is 385 rounded to the nearest 10?

A 300 C 390

B 380 D 400

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Use a Formula or Rule

ONE

BY

ONE

SOLVE the problem.

To round the digit in the tens place, you must look at the digit in theones place.

Then use one of these rules:

• If the digit in the ones place is less than 5, the digit in the tens placestays the same. Then the digit in the ones place becomes zero.

• If the digit in the ones place is 5 or greater, the digit in the tens placeis rounded to the next highest ten. Then the digit in the ones placebecomes zero.

The digit in the ones place for the number 385 is 5. Follow the rule andround up the number in the tens place. Then change the digit in the onesplace to zero.

The number 385 should be rounded up to 390. The correct answer ischoice “C.”

CHECK your answer.

Check that you have used the correct rule for rounding. You have used thesecond rule for rounding. To use this rule, the number in the ones placemust be 5 or greater. The number in the ones place in the number 385 is 5.This shows that you have used the correct rule.

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Guided InstructionDirections: Solve question 2 using the Use a Formula or Rule strategy. Remember tofollow the Problem-Solving Plan.

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You will use the Use a Formula or Rule strategy to solve this problem.

2. Jack has 164 baseball cards in his collection. Rounded to the nearest 10,how many baseball cards does Jack have?

A 150 C 170

B 160 D 180

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ONE

BY

ONE

SOLVE the problem.


CHECK your answer.


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On Your OwnDirections: Solve questions 3 and 4 using the Use a Formula or Rule strategy.


3. Mike stayed at his uncle’s house for 3 weeks. There are 7 days in 1 week.How many days did Mike stay at his uncle’s place for?

A 3 days

B 10 days

C 21 days

D 28 days



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ONE

BY

ONE

4. There are 60 seconds in 1 minute. How many seconds are there in 4 minutes?


Write your answer.

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PART B: One-by-One | Strategy 7: Guess and Check

STRATEGY 7: Guess and Check

Modeled InstructionNow you will learn how to solve a math problem by guessing and checking. Read theproblem below. The plan that follows will explain how to use this strategy.

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You must find the equation that will be true if the number 8 is placed insidethe box.


You know that the number 8 must be placed inside the box.


You are given four answer choices. Only one is correct. A good strategy forsolving this type of problem is to Guess and Check. Since the number 8will make one of these equations true, you can find the correct answer byusing 8 in each answer choice.

1. Which of the following equations will be true if the number 8 is placedinside the box?

A 3 × 24 = C 3 ÷ 24 =

B × 24 = 3 D 24 ÷ = 3

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Guess and Check

ONE

BY

ONE

SOLVE the problem.

Place the number 8 in each equation. Ask yourself which equation is trueand which equations are not true.

÷A 3 × 24 =

This equation is NOT true.

÷B × 24 = 3


÷C 3 ÷ 24 =


÷D 24 ÷ = 3

This equation is TRUE.

Choice “D” is the only equation that is true when the number 8 is placedinside the box. The correct answer is choice “D.”

CHECK your answer.

Check that the equation you have chosen is correct. The equation is24 ÷ 8 = 3. To check a division equation, use multiplication towork backwards.

8 × 3 = 24

8

8

8

8

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Guess and Check

Guided InstructionDirections: Solve question 2 using the Guess and Check strategy. Remember to follow theProblem-Solving Plan.

52






You will use the Guess and Check strategy to solve this problem.

2. Look at the equation below.

– 55 =

Which pair of numbers correctly completes this equation?

A and C and

B and D and135 75 135 80

70 85130130

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Guess and Check

ONE

BY

ONE

SOLVE the problem.


CHECK your answer.


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Guess and Check

On Your OwnDirections: Solve questions 3 and 4 using the Guess and Check strategy.


3. Look at the equation below.

– 498 = 136

Which number could go in the box to make the equation true?

A 644

B 634

C 544

D 534



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Guess and Check

ONE

BY

ONE

4. A bowl of fruit contains 7 apples, 9 oranges, 5 bananas, 12 grapes, and6 pineapples. For which two fruits are there a total of 17 fruits?


Write your answer.

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PART B: One-by-One | Strategy 8: Make It Simpler

STRATEGY 8: Make It Simpler

Modeled InstructionNow you will learn how to solve a math problem by making the problem simpler. Readthe problem below. The plan that follows will explain how to use this strategy.


You must find the number of boxes of beads that the craft club needs.



• Number of beads the craft club needs = 9,000• Number of beads inside each box = 500


Very large numbers can be difficult to work with. Sometimes you can makethe numbers in a problem smaller or you can group them. This makes iteasier to solve a problem. This strategy is called Make It Simpler.

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1. There are 500 beads in a box. The craft club needs exactly 9,000 beads.How many boxes of beads does the craft club need?

Answer:

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Make It Simpler

ONE

BY

ONE

SOLVE the problem.

You can find the number of boxes of beads needed by dividing the number ofbeads needed by the number of beads in each box.

9,000 ÷ 500 = Number of boxes needed

You can make this calculation simpler by making the numbers smaller. Makeeach of the numbers in the problem smaller by removing an equal number ofzeros from each. In this problem, you can remove 2 zeros from each number.This is the same as if each number were divided by 100.

9,000 becomes 90

500 becomes 5

Next, solve the problem using these smaller numbers.

90 ÷ 5 = Number of boxes needed

90 ÷ 5 = 18

The craft club needs 18 boxes. The correct answer is “18.”

CHECK your answer.

You can check that your answer makes sense by using the original numbersin the problem.

500 × 18 = 9,000

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Make It Simpler

Guided InstructionDirections: Solve question 2 using the Make It Simpler strategy. Remember to follow theProblem-Solving Plan.

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You will use the Make It Simpler strategy to solve this problem.

2. An airplane travels 2,000 feet higher in the sky every minute. How manyminutes will it take for the plane to travel 28,000 feet higher?

Answer:

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Make It Simpler

ONE

BY

ONE

SOLVE the problem.


CHECK your answer.


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Make It Simpler

On Your OwnDirections: Solve questions 3 and 4 using the Make It Simpler strategy.


3. Marc uses 500 small plastic blocks to build a model house. How many modelhouses could Marc build if he has 4,000 blocks?

A 4

B 8

C 40

D 80



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Make It Simpler

ONE

BY

ONE

4. Clara practices playing the flute every day. The chart below shows how manyminutes she practiced each day for five days.

How many minutes did Clara practice the flute for on Day 1, Day 2, and Day 3?


Write your answer.

Day 5

20 minutes

Day 4

30 minutes

Day 3

20 minutes

Day 2

30 minutes

Day 1

20 minutes

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PART B: One-by-One | Strategy 9: Make Estimates

STRATEGY 9: Make Estimates

Modeled InstructionNow you will learn how to solve a math problem by making estimates. Read the problembelow. The plan that follows will explain how to use this strategy.


You must find about how much money in all the movie theater madeselling tickets.


You can find these facts in the problem:

• One ticket costs $6.95.• The theater sold 63 tickets.


You can multiply the cost of 1 ticket by the total number of tickets sold tofind how much money the theater made. The question is asking about howmuch money the theater made, so you can round each number to make thecalculation easier. This strategy is called Make Estimates.

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1. One ticket to see a movie costs $6.95. A movie theater sold 63 tickets.About how much money did the movie theater make selling tickets?

A $420 C $3,600

B $360 D $4,200

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Make Estimates

ONE

BY

ONE

SOLVE the problem.

To estimate $6.95 × 63, first round each number.

$6.95 can be rounded up to $7

63 can be rounded down to 60

Next, multiply using the numbers you rounded to.

$7 × 60 = $420

Choice “A” is the correct answer.

CHECK your answer.

Check that you have rounded the decimal to the nearest whole number.The nearest whole number to 6.95 is 7.

Check that you have rounded the whole number to the nearest ten.The nearest ten to 63 is 60.

Check that you have multiplied correctly.

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Make Estimates

Guided InstructionDirections: Solve question 2 using the Make Estimates strategy. Remember to follow theProblem-Solving Plan.

64






You will use the Make Estimates strategy to solve this problem.

2. It takes Victor 41.69 seconds to run around the track 1 time. About howmany seconds will it take Victor to run around the track 11 times?

A 42 seconds C 420 seconds

B 84 seconds D 840 seconds

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Make Estimates

ONE

BY

ONE

SOLVE the problem.


CHECK your answer.


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Make Estimates

On Your OwnDirections: Solve questions 3 and 4 using the Make Estimates strategy.


3. Veronica studied 22 minutes for math, 38 minutes for science, and 13 minutesfor language arts. About how long did Veronica study for in all?

A 60 minutes

B 70 minutes

C 80 minutes

D 90 minutes



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Make Estimates

ONE

BY

ONE

4. Lakecia sold 70 cups of lemonade at the county fair. She sold each cup oflemonade for $1.95. Round the decimal to the nearest whole number to findabout how much money Lakecia made.


Write your answer.

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PART B: One-by-One | Strategy 10: Look for a Pattern

STRATEGY 10: Look for a Pattern

Modeled InstructionNow you will learn how to solve a math problem by looking for a pattern. Read theproblem below. The plan that follows will explain how to use this strategy.


The question asks what the total number of cans will be after one more rowis added. First decide how many cans will be added to the next row. Thenyou can find the total number of cans.


The picture shows how many cans are in each row.

• Row 1 has 7 cans.• Row 2 has 6 cans.• Row 3 has 5 cans.• Row 4 has 4 cans.

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1. Akira stacks cans of fruit at the grocery store. She has stacked four rows ofcans as shown below.

If Akira continues to follow the pattern shown, what will be the totalnumber of cans after one more row is added?

Answer:

Row 4

Row 3

Row 2

Row 1

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Look for a Pattern

ONE

BY

ONE


You already know how many cans are in each of the first four rows. You canuse this information to Look for a Pattern. The pattern will help youdecide how many cans there will be in the next row.

SOLVE the problem.

Study how many cans are in each row. First, ask yourself what the differenceis between the number of cans in Row 1 and Row 2.

Row 1 has 7 cans.Row 2 has 6 cans.

The difference is 7 – 6 = 1.

Next, find the difference between the number of cans in Row 2 and Row 3.



Then, find the difference between the number of cans in Row 3 and Row 4.



You should be able to see a pattern. Each row that is added has 1 can fewerthan the row beneath it. If this pattern continues, the next row added willhave 1 can fewer than Row 4.

4 cans – 1 can = 3 cans

Find the total number of cans by adding how many are in each row.

7 + 6 + 5 + 4 + 3 = 25(Row 1) (Row 2) (Row 3) (Row 4) (Row 5)

The total number of cans is equal to 25.

CHECK your answer.

Check your answer by adding the next row to the diagram. The next rowshould have 3 cans in it. Then count the total number of cans. The totalnumber of cans is 25.

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Look for a Pattern

Guided InstructionDirections: Solve question 2 using the Look for a Pattern strategy. Remember to followthe Problem-Solving Plan.

70






You will use the Look for a Pattern strategy to solve this problem.

2. The pattern below is made using toothpicks.

How many toothpicks are needed for the next step in the pattern?

Answer:

Step 1 Step 2 Step 3

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Look for a Pattern

ONE

BY

ONE

SOLVE the problem.


CHECK your answer.


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Look for a Pattern

On Your OwnDirections: Solve questions 3 and 4 using the Look for a Pattern strategy.


3. Look at the picture below.

Which expression does this picture represent?

A 7 × 4

B 7 ÷ 4

C 28 + 28

D 28 – 28



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Look for a Pattern

ONE

BY

ONE

4. The picture below shows the house number of four houses on a street.

What would be the house number of the next house on the street?


Write your answer.

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75

Part C gives students practice in using the strategies to solve problems. This sectionhas 10 problems, including multiple choice, short response, and extended responseproblems. Students are given a hint that tells them which strategy to use andprovides guidance on how to use the strategy.

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PART C: Practice Using the Strategies

Practice Using the Strategies

Directions: Answer questions 1-10. The hint tells you which strategy to use and will helpyou to solve the problem. Follow the Problem-Solving Plan. Be sure to show all of your work.If you need more room, use a separate sheet of paper. Remember to check your answers.

1. There are four boxes on a scale, as shown below. The scale below is balancedwhen the total weight on each end of the scale is the same.

If the scale is balanced, how much does Box A weigh?

A 21 grams

B 18 grams

C 12 grams

D 6 grams

Guess and Check. Substitute each of the possible answer choices forthe weight of Box A. Which answer choice makes both sides of thescale equal?

Show your work.


12grams

15grams

BoxA

21grams

HINT

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PRACTICE

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STRATEGIES

2. Henrik uses yarn to make some decorations for the classroom. The chartbelow shows how many centimeters of yarn are needed to make a certainnumber of decorations.

How much yarn does Henrik need to make 16 decorations?

Use a Formula or Rule. Use the data in the table to work out the rulefor how much yarn is needed to make a certain number of decorations.Then use the rule to work out how much yarn is needed to make 16decorations.

Show your work.

Write your answer.

Number ofDecorations Made

6

8

10

12

Centimeters ofYarn Needed

48

64

80

96

HINT

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3. Dawn is thinking of a number. She adds 16 to this number and then dividesby 2. The answer she gets is 44. What number is Dawn thinking of?

A 72

B 38

C 76

D 6

Work Backwards. You can use the facts given in the problem to workbackwards from 44. You will need to reverse each step to find thenumber that Dawn is thinking of.

Show your work.


HINT

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PRACTICE

THE

STRATEGIES

4. Sigrid wrote a number on a piece of paper. The number is less than 50 butgreater than 25. The number she wrote is an odd number. Both digits in thenumber are the same. What number did Sigrid write on the piece of paper?

Organize – Make a Chart or List. List all of the numbers between25 and 50. Circle all of the odd numbers in the list. Look at the circlednumbers. Find the number with both digits that are the same.

Show your work.

Write your answer.

HINT

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5. Each figure in the answer choices below shows a fraction. Which pair offigures shows equivalent fractions?

A

B

C

D

Draw a Picture or Diagram. Draw the figures that are shown as possibleanswers. Try shading the figures differently to help you see which onesare equivalent.

Show your work.


HINT

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PRACTICE

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STRATEGIES

6. The graph below shows how many people went to a beach during certainmonths of the year.

How many people went to the beach in June?

Make It Simpler. The question is only asking about the number ofpeople who went to the beach in June. You will only need to use thesecond bar of the graph to answer the question.

Show your work.

Write your answer.

0

2,500

5,000

7,500

10,000

12,500

15,000

17,500

20,000

SeptemberAugustJulyJuneMayMonth

Number of People at the BeachN

umbe

rof

Peop

le

HINT

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7. Study the shape pattern below.

Which shape will be next in the pattern?

A

B

C

D

Use Manipulatives or Act Out. On separate pieces of paper, draw circlesand squares like the ones shown. Try placing each shape at the end ofthe pattern to see which one belongs next.

Show your work.


HINT

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PRACTICE

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STRATEGIES

8. One notebook costs $3. Edda needs 3 notebooks for school. She also needs1 notebook to use as a journal. How much will it cost for Edda to buy all ofthe notebooks that she needs?

Compute – Write a Number Sentence. Use the facts given in theproblem to write a number sentence. Remember, you need to find thecost for all of the notebooks Edda needs to buy.

Show your work.

Write your answer.

HINT

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9. Some of the students at Glendale School went on a field trip to the zoo.A total of 9 buses took students to the zoo. There were 28 students oneach bus.

Part 1. About how many students were on the buses in all?

Make Estimates. The question is asking you to find about how manystudents there were, so you can make an estimate. Round 9 and 28 tothe nearest ten. Then multiply the rounded numbers.

Show your work.

Answer:

HINT

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PRACTICE

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STRATEGIES

Part 2. The students on each bus sat in rows of 4. How many rows ofstudents were there?

Draw a Picture or Diagram. Draw a row of 4 students. Then drawanother row of 4 students. Keep adding rows until there are 28 students.Then count the number of rows.

Show your work.

Answer:

HINT

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10. Juwan placed some birdseed on the ground in his backyard each day for oneweek. He noticed a pattern for how many birds came to feed on thebirdseed each day.

Part 1. Describe the pattern for how many birds came to feed on thebirdseed each day.

Look for a Pattern. Use the art to work out the pattern for how manybirds came to feed each day. Describe how the number of birds changesfrom one day to the next.

Show your work.

Answer:

Day 1 Day 2 Day 3 Day 4

HINT

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PRACTICE

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STRATEGIES

Part 2. If the pattern continues, how many birds will come to feed on thebirdseed on Day 6?

Look for a Pattern. Use your answer to Part 1 to continue the pattern.First find the number of birds that will come on Day 5. Then find thenumber of birds that will come on Day 6.

Show your work.

Answer:

HINT

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PART D:Choose the StrategyPart D gives students practice in selecting and using the right strategy to solveproblems. This section has 10 problems, including multiple choice, short response,and extended response problems. Students are guided to choose the right strategyand solve the problems on their own.

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PART D: Choose the Strategy

CHOOSE THE STRATEGY

Directions: Answer questions 1-10. Follow the Problem-Solving Plan and choose the beststrategy for solving each problem. Be sure to show all of your work. If you need moreroom, use a separate sheet of paper. Remember to check your answers.

1. A school is buying computers. Each computer will cost $600. How manycomputers can the school buy for $3,600?

A 6

B 10

C 30

D 60

Which strategy is BEST to use to solve this problem?

• Make It Simpler• Draw a Picture or Diagram• Look for a Pattern

Explain why you chose this strategy.

Show your work.


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Choose the Strategy

CHOOSE

THE

STRATEGY

2. The chart shows how many people live in 4 towns.

List the four towns in order from the town with the fewest number ofpeople to the town with the greatest number of people.


• Organize – Make a Chart or List, Graph, Sort Data• Compute – Write a Number Sentence• Draw a Picture or Diagram


Show your work.

Write your answer.

Number of People

1,178

1,097

1,223

1,219

Town

Summerville

Lakeside

Davenport

Rivendell

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Choose the Strategy

3. Peter has the stickers shown below.

What fraction of the stickers are hearts?

A �13�

B �14�

C �16�

D �15�


• Use Manipulatives or Act Out• Work Backwards• Make Estimates


Show your work.


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Choose the Strategy

CHOOSE

THE

STRATEGY

4. The chart below shows the amount of snowfall over a four-month period forseveral cities.

Round each decimal to the nearest whole number to find the total inches ofsnowfall in Buffalo for the four-month period.


• Look for a Pattern• Make Estimates• Guess and Check


Show your work.

Write your answer.

Buffalo 3.2 18.4 26.1 21.5

Cleveland 6.1 12.6 31.8 18.3

Pittsburgh 8.7 16.3 21.3 22.6

Seattle 4.7 14.8 17.5 24.9

November December January February

Snowfall in Inches

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Choose the Strategy

5. Mrs. Estrada drove to her cousin’s house. She drove at a constant rate ofspeed. The table below shows how far she had traveled at several pointsduring her trip.

What expression shows how many hours it took for Mrs. Estrada to travel440 miles?

A 440 ÷ 8 C 440 × 8

B 440 ÷ 55 D 440 × 55


• Make It Simpler• Draw a Picture or Diagram• Look for a Pattern


Show your work.


Hours Traveled

2

3

5

?

Miles Traveled

110

165

275

440

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Choose the Strategy

CHOOSE

THE

STRATEGY

6. Angus planted roses in a garden. He planted 3 rows of roses, with 7 roses ineach row. How many roses did Angus plant?


• Work Backwards• Draw a Picture or Diagram• Make It Simpler


Show your work.

Write your answer.

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Choose the Strategy

7. What is 751 rounded to the nearest hundred?

A 700

B 750

C 760

D 800


• Draw a Picture or Diagram• Work Backwards• Use a Formula or Rule


Show your work.


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Choose the Strategy

CHOOSE

THE

STRATEGY

8. Pearl collects stamps. Her stamp album can hold 800 stamps. Yesterday sheplaced 64 new stamps in her album. Her album now has 502 stamps in it.How many stamps were in Pearl’s album before yesterday?


• Look for a Pattern• Work Backwards• Make It Simpler


Show your work.

Write your answer.

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Choose the Strategy

9. The graph below shows how long it took four horses to run one time arounda racetrack.

Part 1. Which horse took the longest amount of time to run once aroundthe track?

Which strategy is BEST to use to solve Part 1 of the problem?

• Use a Formula or Rule• Make Estimates• Organize – Make a Chart or List, Graph, Sort Data


Show your work.

Answer:

Amount of Time To Go Around the Track Once

Time (in seconds)

Hor

se’s

Nam

e

0 10 20 30 40 50 60

Fast Freddie

Prince Elwood

Crazy Legs

Ginger Girl

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Choose the Strategy

CHOOSE

THE

STRATEGY

Part 2. How many seconds longer did it take Fast Freddie to run around thetrack than it took Ginger Girl?


• Guess and Check• Compute – Write a Number Sentence• Look for a Pattern


Show your work.

Answer:

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Choose the Strategy

10. Jun Ming plays football on the school team. He made a table to showhow many points his team scored in each of the games they played sofar this season.

Part 1. In which two games did Jun Ming’s team score a total of 60 points?


• Guess and Check• Draw a Picture or Diagram• Work Backwards


Show your work.

Answer:

Game

Game 1

Game 2

Game 3

Game 4

Game 5

Number of Points Scored

20

45

30

25

35

100

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Choose the Strategy

CHOOSE

THE

STRATEGY

Part 2. How many points did Jun Ming’s team score in their first five games?


• Use Manipulatives or Act Out• Compute – Write a Number Sentence• Make Estimates


Show your work.

Answer:

101

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PART E:Problem Solving PracticeIn Part E, students select a suitable strategy for solving each problem on their own.This section has 20 problems, including multiple choice, short response, andextended response problems. Students solve each problem on their own and identifythe strategy they used to solve the problem.

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PART E: Problem Solving Practice

PROBLEM SOLVING PRACTICE

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Directions: Answer questions 1-20. Follow the Problem-Solving Plan and choose the beststrategy for solving each problem. Be sure to show all of your work. If you need moreroom, use a separate sheet of paper. Remember to check your answers.

1. There are 127 oranges on a tree. A farmer picks off 59 oranges. About howmany oranges would be left on the tree?

A 40

B 50

C 60

D 70

Show your work.


What strategy did you use to solve this problem?

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Problem Solving Practice

PROBLEM

SOLVING

PRACTICE

105

2. A box contains six different color crayons. The table below shows how manyof each color crayon are inside the box.

For which two colors are there a total of 20 crayons?

Show your work.

Write your answer.


Color

Red

Blue

Green

Yellow

Orange

Black

Quantity

11

6

15

8

10

12

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3. Jamie has a sheet of stickers. There are 6 rows of stickers and 4 stickers ineach row. How many stickers does Jamie have in all?

A 10

B 12

C 20

D 24

Show your work.



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PROBLEM

SOLVING

PRACTICE

4. The graph below shows how many questions each student in Mr. Carlino’sclass answered correctly on a science quiz.

How many questions did Ronald answer correctly?

Show your work.

Write your answer.


Chantel

Ivan

Mao

Diego

Kea

Hasan

Vera

Danny

Cassie

Ronald

0 2 4 6 8 10 12 14 16 18 20 22 24

Number of Questions Answered Correctly

Questions Answered Correctly by Students

Stud

ents

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5. The city library just purchased 98 new fiction books and 57 new nonfictionbooks. There are now a total of 832 books in the library. How many bookswere in the library before the new books were purchased?

A 677

B 734

C 930

D 987

Show your work.



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PROBLEM

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PRACTICE

6. Mr. Sheppard builds picnic tables for the county fair. The tables vary in size.The chart below shows how many pieces of wood and how many nails areneeded to build some of the tables.

How many pieces of wood are used to build a table if 144 nails are needed?

Show your work.

Write your answer.


Number of Nails

Pieces of Wood

32

4

64

8

96

12

128

?

144

?

109

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7. Betty has 500 beads. She needs 20 beads to make a bracelet. How manybracelets could Betty make?

A 15

B 25

C 50

D 250

Show your work.



110

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PROBLEM

SOLVING

PRACTICE

8. Sandra has $8.70 in savings. She spent $4.25. Round each decimal to thenearest whole number to find about how much money Sandra has left.

Show your work.

Write your answer.


111

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9. Jordan wrote a number on a piece of paper. The number is greater than24 but less than 38. The number is even and can be divided evenly by 5.What number did Jordan write on the piece of paper?

A 25

B 28

C 30

D 36

Show your work.



112

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PROBLEM

SOLVING

PRACTICE

10. The distance between two houses is shown below.

There are 3 feet in 1 yard. How many feet apart are the two houses?

Show your work.

Write your answer.


8 yards

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11. Which of the following equations will be true if the number 52 is placedinside the box?

A ÷ 4 = 13

B 4 × = 13

C – 4 = 13

D 4 + = 13

Show your work.



114

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PROBLEM

SOLVING

PRACTICE

12. Richard works at the grocery store. He earns $7 for each hour that he works.Last week he worked for 18 hours. How much did he earn last week?

Show your work.

Write your answer.


115

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13. What will be the eighth number in the pattern below?

10, 5, 12, 6, 14, 7, ___, ___

A 16

B 15

C 9

D 8

Show your work.



116

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PROBLEM

SOLVING

PRACTICE

14. Some paper clips are inside a box. Selma removes 28 paper clips from thebox. Corey places 32 paper clips inside the box. There are now 73 paper clipsinside the box. How many paper clips were inside the box to begin with?

Show your work.

Write your answer.


117

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15. Look at the shapes below.

What is the next shape in this pattern?

A

B

C

D

Show your work.



118

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PROBLEM

SOLVING

PRACTICE

16. Josephina weighed several items that were on her desk. She made a chart torecord the weight of each item.

What is the total weight of the two heaviest items?

Show your work.

Write your answer.


Item

paper clip

paper bag

pencil

marker

Weight

1 gram

6 grams

4 grams

9 grams

119

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17. Dedra would like to buy some paper clips. The table below shows how manypaper clips come in 20, 60, and 120 boxes.

Part 1. How many paper clips are in each box?

Show your work.

Answer:

What strategy did you use to solve Part 1 of the problem?

Number of Boxes

20

60

120

Number of Paper Clips

4,000

12,000

24,000

120

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PROBLEM

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Part 2. How many paper clips would Dedra have if she bought 100 boxes?

Show your work.

Answer:


121

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18. Huong built a rectangular-shaped table. The table is 8 feet long and3 feet wide.

Part 1. What is the total distance around the edge of the table?

Show your work.

Answer:


122

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PROBLEM

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PRACTICE

Part 2. Huong wants to cover the top of the table with tiles. Each tilemeasures 1 foot by 1 foot. How many tiles would Huong need?

Show your work.

Answer:


123

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19. Latrell measures the depth of a lake near his house. He ties a weight to along piece of string to help measure how deep the water is at differentdistances from the shore. He records the measurements in the table below.

Part 1. At what distance from the shore is the water the deepest?

Show your work.

Answer:


How Deep Water Is

1 meter

2 meters

4 meters

10 meters

17 meters

20 meters

18 meters

Distance from the Shore

1 meter

5 meters

10 meters

15 meters

20 meters

25 meters

30 meters

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Part 2. How much deeper is the water 20 meters from the shore comparedto 5 meters from the shore?

Show your work.

Answer:


125

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20. Jared has the seven weights shown below. The scale below is balanced whenthe total weight on each end of the scale is the same.

Part 1. Jared placed the 11 oz. weight on one end of the scale. List twoweights that could be placed on the other end of the scale to balance it.

Show your work.

Answer:


1 oz. 2 oz. 4 oz. 5 oz. 7 oz. 10 oz. 11 oz.

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PROBLEM

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PRACTICE

Part 2. Jared placed the 10 oz. and the 11 oz. weight on one end of the scale.Could Jared use the other weights to balance the scale? Explain your answer.

Show your work.

Answer:


127

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128

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