Strategies for Solving Word Problems BOOK


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1 STEP BY STEP MATH Strategies for Solving Word Problems BOOK E Teaches six basic strategies for solving word problems successfully Builds on the stepbystep problemsolving process Improves problemsolving skills and strengthens mathematical reasoning Provides practice with extendedresponse problems
2 To the Student Strategies for Solving Word Problems will help you more easily solve word problems in math. In this book, you will learn six math strategies plans for finding solutions to word problems. The strategies are taught as part of a sixstep process. You will learn how to choose and use the best strategy, step by step, to solve a word problem. This book has six lessons. In each lesson, you will see how one strategy can be used to solve word problems. With help, you will practice the strategy. After the lessons, you will use the six strategies to solve word problems on your own. Ask your teacher any time you have questions about your work. Table of Contents An Introduction to the Program...1 Strategy One: Draw a Diagram...Modeled Practice...2 Guided Practice...4 Independent Practice...5 Strategy Two: Find a Pattern...Modeled Practice...6 Guided Practice...8 Independent Practice...9 Strategy Three: Act It Out...Modeled Practice...10 Guided Practice...12 Independent Practice...13 Strategy Four: Make a Table...Modeled Practice...14 Guided Practice...16 Independent Practice...17 Strategy Five: Write an Equation...Modeled Practice...18 Guided Practice...20 Independent Practice...21 Strategy Six: Guess and Check...Modeled Practice...22 Guided Practice...24 Independent Practice...25 Mixed Practice...26 Glossary...36 ISBN X 2006 Curriculum Associates, Inc. No part of this book may be reproduced by any means without written permission from the publisher. All Rights Reserved. Printed in USA
3 An Introduction to the Program Strategies for Solving Word Problems provides practice using six math strategies: Draw a Diagram, Find a Pattern, Act It Out, Make a Table, Write an Equation, and Guess and Check. These strategies can help you find solutions to word problems, but you need to know when to use each strategy and how to use it. This chart gives an overview of the six strategies. Strategy When to Use It How to Use It 1. Draw a Diagram The problem gives information that can be shown in a diagram. The question asks for a solution that can be found by using the diagram. 2. Find a Pattern The problem gives information that follows a pattern. The question asks for a solution related to the pattern. 3. Act It Out The problem gives information that can be acted out. The question asks for a solution that can be found by acting something out. 4. Make a Table The problem gives more than one set of data. The question asks for the data to be continued. 5. Write an Equation The problem tells about a situation. The question asks for an unknown amount. 6. Guess and Check The problem gives a total amount. The question asks for the kind and number of items in the total. 1. Find the information needed for the diagram. 2. Draw and label the diagram with information from the problem. 3. Use the diagram to answer the question. 1. Find the information that follows a pattern. 2. Find the rule for the pattern. 3. Use the rule to solve the problem. 1. Find the information that can be acted out. 2. Act out the information in as many ways as possible. 3. Choose the way that answers the question. 1. List the sets of data. 2. Make a table of the data. Circle the information needed to answer the question. 1. Write what the situation is. 2. Write what the unknown is. 3. Choose a letter for the unknown. 4. Write an equation, and solve for the unknown. 1. Find the total amount. 2. Find the different items that make up the total. 3. Make a reasonable guess about the kind and number of items; then check it. Continue guessing and checking until the guess is correct. The first page of each lesson shows you when and how to use a strategy to solve a word problem. You will study an example problem that has been solved using the strategy. You will follow this model as you complete the lesson. In the last part of the book, you will use the six strategies to solve word problems on your own. A glossary is provided on page 36. 1
4 STUDY IT! Modeled Practice Strategy Three: Act It Out Study how Owen used the strategy Act It Out to solve the model word problem. He used this strategy because the problem gives information that can be acted out. Read why Owen chose Act It Out and how he found and checked his solution. PREVIEW and READ Model Word Problem Bart is tiling a floor in his house. He has 24 tiles that are a different color from the rest. He plans to use the 24 tiles in equal rows to make a rectangle in the middle of the floor. Bart wants the perimeter of the rectangle to be as small as possible. What arrangement of the 24 tiles has the smallest perimeter? Explain Why: I chose Act It Out because the problem gives information that I can act out with math tiles. The question asks for the smallest perimeter. I can find that information by trying different rectangles formed by 24 tiles. 1. Find the information that can be acted out: 24 tiles to be made into a rectangle with smallest perimeter 2. Act out the information: 3. Choose: the 6 x 4 rectangle PLAN and SOLVE Perimeter = Perimeter = 22 Perimeter = Explain How: I acted out the information and found 3 possible rectangles that can be made with 24 tiles in equal rows: 12 x 2; 8 x 3; 6 x 4. I counted the tiles in the perimeter of each rectangle and got 28, 22 and 20. The 6 x 4 square has the smallest perimeter. The arrangement of tiles with the smallest perimeter is a rectangle of 6 tiles by 4 tiles CHECK and REVIEW I used the formulas for area and perimeter to check my solution. Each rectangle has an area of 24 tiles (12 x 2 = 24; 8 x 3 = 24; 6 x 4 = 24). I used 2 x length + 2 x width to find the perimeter: (2 x 12) + (2 x 2) = 28; (2 x 8) + (2 x 3) = 22; (2 x 6) + (2 x 4) = 20.
5 TRY IT! Read the practice word problem. Explain why Act It Out can be used to solve the problem. Then solve the problem. Check your solution. HINTS PREVIEW and READ Practice Word Problem Taneka wants to make a table. She has 8 boards that are 72 inches long and 4 inches wide. Taneka can place the boards side by side and make a table that is 72 inches long. She could also cut the boards in half and place 16 boards side by side. Which plan would produce a table with a larger perimeter? The problem gives information that can be acted out. The question asks for a solution that can be found by acting something out. Explain Why: PLAN and SOLVE 1. Find the information that can be acted out. 2. Act out the information in as many ways as possible. 3. Choose the way that answers the question. Explain How: CHECK and REVIEW Check your solution by solving the problem another way. 11
6 TRY IT! Guided Practice Strategy Three: Act It Out Use the strategy Act It Out to solve the word problem. Show your work. Then check your solution. REMEMBER 1. Find the information that can be acted out. 2. Act out the information in as many ways as possible. 3. Choose the way that answers the question. PREVIEW and READ These students in Mr. Torres s class are lining up to play a math game: Julie, Amy, Cheryl, James, Pablo, Daniel. The students must alternate girlboygirlboy. A girl must go first. James can play only if he goes second. Two people who have names that begin with the same letter cannot be next to each other. Amy has to go before James, and Pablo cannot go last. How should the students line up from first to sixth? PLAN and SOLVE Explain How: CHECK and REVIEW 12
7 TRY IT! Independent Practice Strategy Three: Act It Out Use the strategy Act It Out to solve each word problem. Show your work. Then check your solution. 1. Colby is using two differentsize blocks to make an 8foot walkway. The large blocks are 12 inches long, and the short blocks are 6 inches long. He plans to leave an equal space between the blocks. Colby started with a long block and alternated with a short block. How much space should Colby leave between the blocks? 2. Benita has 36 sports cards. She says that 1 3 of the cards are baseball cards. Of the remaining cards, 1 4 are hockey cards. Benita says that 1 2 of the remaining cards are football cards. The rest of the cards are basketball cards. How many of each kind of card does Benita have? 13
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