Math solutions g sample by RALLY! Education

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

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Open-Ended Math Problem Solving ………….. Math Solutions Grade Levels 3–8 • Provides instruction for answering open-ended math problems on tests. • Students are taught to use a 5-Step Problem-Solving Plan when answering open-ended math questions.

Level C D E F G H

Grade Level 3 4 5 6 7 8

25-Pack 4114-7 4117-8 4120-8 4123-9 4126-0 4129-1

100-Pack 4115-4 4118-5 4121-5 4124-6 4127-7 4130-7

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LEVEL G

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Math Solutions: Open-Ended Problem Solving • Level G

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y Acknowledgments T P K O K IS C R THIS BOO O O B Executive Editor: Amy Collins N FO MPLE E A V S I G S I T Project Manager: Edward Nasello TH IS NO Editors: Jeff Brannon ISSION PERM Linda LiDestri

ISBN 978-1-4204-4125-3 R 4125-3 Copyright ©2008 RALLY! EDUCATION. All rights reserved. No part of the material protected by this copyright may be reproduced in any form by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the copyright owner. Printed in the U.S.A. 1008 RALLY! EDUCATION 22 Railroad Avenue Glen Head, NY 11545 (888) 99-RALLY

Math Solutions: Open-Ended Problem Solving • Level G

Table of Contents INTRODUCTION

How to Use This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 A Helpful List of Mathematical Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 How to Answer Short-Response and Extended-Response Questions . . . . . . . 6 Mathematics Reference Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 INSTRUCTION

The 5-Step Problem-Solving Plan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 ON YOUR OWN

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Number Sense and Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Number Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Equations and Inequalities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

ER.

Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .N.E. M . .A.S.T. 24 Y. I L Y WA Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . .B. L.A.C.K. . . . . . N . .A .N . 25

OT ED I N C U S I D O T TED. I . O. . B. E. .R.E.P.R. . . . . . . . . . . . 29 Measurement . . . . . . . . . . . . . .P.Y.R.I.G.H. . . . . . . T C. O. . . . . . . I.S. B. .O.O.K. . . . . . . . . . . . . . . . . . . . . . . 30 S I Units of Measurement . . . . . K O BO . . . . F.O. R. . T. H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Estimation S.A.M. P . .LE. . . . . . .IV G EN T O THIS N N IS O I S S I Statistics PERM and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Organization and Display of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Predictions from Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Math Solutions: Open-Ended Problem Solving â&#x20AC;˘ Level G

I NT RODUCTION To the Teacher Math Solutions: Open-Ended Problem Solving provides instructional practice in answering open-ended math problems for both short-response and extended-response questions. This book contains the same types of questions students are likely to encounter on tests. Math problems are formatted so that students will learn to solve problems using a logical, organized plan.

How to Use This Book We have arranged the problems in this book by math strands. The questions for each strand have been grouped by mathematical-concept bands. This format allows teachers and students to emphasize those areas where the most practice is needed. In this book, the teacher has an opportunity to model problem solving and guide students using a 5-Step Problem-Solving Plan. This book may also be used to provide students with an opportunity to work on problems independently. The teacher can then review with the students each problem and the strategies used by students to solve these problems. In addition, students do not need to solve these problems in the order presented here. The students (or teacher) can select the specific strands they want to cover and proceed in any order.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Follow These Steps to Use This Book: Step Step Step Step Step Step

1: 2: 3: 4: 5: 6:

Model the 5-Step Problem-Solving Plan. STER. . A M Choose a strand to study. E ACKLIN IN ANY WAY L Choose a band to work on or review. B A S NOT PRODUCED Have students solve a problem. I T I . Review the problem and theRsolution. GHTED BE RE I O Y T P K O Do another problem. K IS C IS BOO

BOO R TH E O L F P N M E can use a variety of problem-solving strategies in A so that students Math problems are formatted THIS S IS NOT GIV Plan. This teaches students to answer problems using a conjunction with the 5-StepOProblem-Solving SI N approach. This will help students answer problems even when a fact S I M logical, organized,Pand thoughtful R E

scenario is presented in a new or unusual way. Finally, students will have had an opportunity to learn, perform, and practice the kinds of problems that are on actual math tests. All of this is designed so that your students will be successful test takers.

ÂŠ R A LLY! EDU CATION. NO PART OF THIS DOCUMENT MAY BE REPRODUCED WITHOUT WRITTEN PERMISSION OF THE PU B L I S H E R .

Math Solutions: Open-Ended Problem Solving • Level G

A Helpful List of Mathematical Language (Grade 7) Listed below are some commonly used mathematical terms and expressions that 7th Grade students should be familiar with. You may want to review this list with your students.

Number Sense and Operations

Geometry

coefficient counting numbers exponents integers integral irrational numbers multiple natural numbers non-perfect squares perfect square pi (≠) prime factorization rational numbers real numbers scientific notation square root whole numbers

adjacent circumference diameter exterior angle hypotenuse interior angles polygon Pythagorean theorem radius right angle

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Algebra

Measurement

central angle customary units of mass ER. exchange rate table E MAST LIN WAY. Y map scale BLACK N A A OTunits ED IN N C metric ofOmass U S I D T REPR TED. I protractor H E G B I R O T COPY BOOKrelative error

OK IS OR THIS F GIVEN

binomial PLE BO M A S equation THIS NOT S I N evaluate ISSIO PERM function inequality input values like terms monomials polynomial table of values trinomial

Statistics and Probability circle graph conduct double bar graph double line graphs measures of central tendency range validity of sample methods

Math Solutions: Open-Ended Problem Solving • Level G

To the Student How to Answer Short-Response and Extended-Response Questions: Use the 5-Step Problem-Solving Plan When solving math problems, you need to follow a plan. This helps you to organize information and choose a strategy to solve the problem. Follow these five steps to help you make your plan. Step Step Step Step Step

1. 2. 3. 4. 5.

Decide what you are being asked to do. Find what you need to know. Choose a strategy for solving the problem. Solve the problem. Check your solution and answer.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Use a Problem-Solving Strategy

When solving problems throughout this book, you will need to use different problem-solving strategies. Sometimes more than one strategy can be used to solve a problem. Knowing how to choose the best strategy for solving a problem will make you successful in math. The following is a list of some strategies you may want to use. • • • • • • • • • •

Draw a Picture Organize—Make a Chart or List, Graph, Sort Data STER. . A M Work Backwards E ACKLIN IN ANY WAY L Use Manipulatives or Act Out B A UCED S NorOTProportion Compute—Write a Number Sentence, Use Ratio I D O T I R . P Use a Formula or Rule GHTED BE RE I R O Y T P K O Guess and Check K IS C R THIS BOO O O B Make It Simpler N FO MPLE E A V S I G S I T Make THEstimatesIS NO ON Look for ISaSIPattern

PERM

Helpful Tips for Answering Questions in This Book: • You can use your calculator to help solve any of the questions. • You can use the Mathematics Reference Sheet to help solve some questions.

Math Solutions: Open-Ended Problem Solving • Level G

Mathematics Reference Sheet FORMULAS Area r 2

Circle

Circumference 2 r

Total Surface Area 6s 2

Cube

Volume s 3 s r

E L P SAM ATION C U D E ! Y L Y L L RAL A R . 9 9 . 888

Right Circular Cylinder

Volume r 2 h

Right Rectangular Prism h

h s w

Total Surface Area 2 rh 2 r 2

Total Surface Area 2wl 2lh 2 wh

STER. A M E ACKLIN ANY WAY. L B A IS NOT ODUCED IN T I . D EPR lw lh ls GHTE AreaBE Rwh ISurface R Right Triangular Prism Total Y P O O K IS C HIS BO1OK T O O B R T 2 wh l AMPLE IVEN FOVolume S S I H T NOT G S I N ISSIO PERM Volume lwh

CONVERSIONS 1 centimeter 10 millimeters

1 cup 8 fluid ounces

1 meter 100 centimeters 1,000 millimeters

1 pint 2 cups

1 kilometer 1,000 meters

1 quart 2 pints 1 gallon 4 quarts

1 gram 1,000 milligrams 1 kilogram 1,000 grams

1 liter 1,000 milliliters 1 kiloliter 1,000 liters

1 pound 16 ounces 1 ton 2,000 pounds © R A L LY ! ED U C AT I ON. NO PART OF THIS DOCUMENT M AY BE REPRODUCED WITHOUT WRITTEN PERMISSION OF THE PUB L I S H E R.

Math Solutions: Open-Ended Problem Solving • Level G

I N STRUCTION The 5-Step Problem-Solving Plan Directions: Use the 5-Step Problem-Solving Plan to help you solve Question A. QUESTION A Charles must pack a lunch to bring on the school picnic. He must choose one sandwich, one snack, and one drink. The chart below shows all of his choices. Lunch Choices Sandwich

Snack

Drink

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

ham & cheese

fruit

milk

peanut butter & jelly

crackers

juice

How many lunch combinations does Charles have to choose from?

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

This problem asks you to determine the number of possible lunch combinations Charles STERhas . A M E Y N to choose from. NY WA LACKLI

AB IN A T D O E N C U . IT IS E REPROD D E T H G B OPYRI S BOOK TO C S I BOOK R THI E O L F P N M E A THIS S IS NOT GIV N know. SIOto S I Step 2: Find what you need M R PE You need the following information to solve this problem: There are 2 sandwiches to choose from (ham & cheese, peanut butter & jelly). There are 2 snacks to choose from (fruit, crackers). There are 2 drinks to choose from (milk, juice).

Step 3: Choose a strategy for solving the problem. In order to solve problems that ask “how many combinations,” it is helpful to use the problem-solving strategy called Organize: Make a Chart or List, Graph, Sort Data.

Math Solutions: Open-Ended Problem Solving • Level G

Step 4: Solve the problem. In the space below, make a tree diagram or a list of all the possible lunch combinations. Count how many lunch combinations are possible.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY Step 5: Check your solution and answer. L B A T UCEofD the possible S NOMake I D O T I R . Check all of the lunch combinations in your tree diagram or list. sure all P RE TED GHappears BEthan I R O Y combinations appear once and that no combination more once. T P K CO OO S B I S K I O H PLE BO IVEN FOR T M A S THIS NOT G S I N ISSIO PERM

Math Solutions: Open-Ended Problem Solving • Level G

Directions: Use the 5-Step Problem-Solving Plan to solve Question B on your own. QUESTION B Tashi needs to choose what to wear to her friend’s house. She must choose one pair of shoes, one pair of pants, and one shirt. The chart below shows the different color choices she has to choose from for each article of clothing. Clothes Tashi Can Choose From Shoes

Pants

Shirts

blue

black

yellow

white

gray

green

brown

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

How many combinations of shoes, pants, and shirts does Tashi have to choose from?

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

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B E Step 2: Find what you need M toPLknow. N FO E A V S I G S I T TH IS NO N O I S IS PERM

Step 3: Choose a strategy for solving the problem.

Math Solutions: Open-Ended Problem Solving • Level G

Step 4: Solve the problem.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Step 5: Check your solution and answer.

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Math Solutions: Open-Ended Problem Solving • Level G

O N YOUR OWN Strand: Number Sense and Operations Band: Number Systems . . . . . . . . . . . . . . . . . . 13 Band: Operations . . . . . . . . . . . . . . . . . . . . . . . 17

The 5-Step Problem-Solving Plan

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 Step 1: Decide what you are being asked to do.

Step 2: Find what you need to know.

Step 3: Choose a strategy for solving the problem.

Step 4: Solve the problem.

Step 5: Check your solution and answer.

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Math Solutions: Open-Ended Problem Solving • Level G

Strand: Number Sense and Operations Band: Number Systems The 5-Step Plan:

1. Decide

2. Find

3. Choose

4. Solve

5. Check

The table below shows geographic information about Africa. Geography of Africa Lowest Elevation

1.56 102 meters

Highest Elevation

5.895 103 meters

Write the numbers, in standard form, for the lowest elevation and the highest elevation of Africa.

Answer

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

lowest elevation

meters

STER. . A M E ACKLIN IN ANY WAY highest elevation meters L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Math Solutions: Open-Ended Problem Solving • Level G

Look at the table below. It shows approximate measurements for the highest and lowest points on Earth. Earth Elevations Location

Elevation (compared to sea level)

Highest Point

Mt. Everest, Nepal

2.9 104 feet

Lowest Point

Dead Sea, Israel/Jordan

1.4 103 feet

Write the elevations in standard form.

Answer

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

highest point

lowest point

feet

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Math Solutions: Open-Ended Problem Solving • Level G

The table below shows the average distance between Earth and its moon and the average distance between Earth and the sun. Distance from Earth Name

Average Distance

Moon

3.844 105 kilometers

Sun

1.49 108 kilometers

How much greater, in kilometers, is the distance from Earth to the sun than the distance from Earth to the moon? Write your answer in standard form. Show your work.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM Answer

kilometers

Math Solutions: Open-Ended Problem Solving • Level G

The table shows the distance that each of the first 5 planets is from the sun. Distance of Planets from the Sun Planet

Distance from the Sun (miles)

Mercury

3.59 107

Venus

6.72 107

Earth

9.29 107

Mars

1.42 108

Jupiter

4.84 108

In standard form, write approximately how much farther Mars is from the sun than Earth is from the sun. Show your work.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Answer

miles

Math Solutions: Open-Ended Problem Solving • Level G

Strand: Number Sense and Operations Band: Operations The 5-Step Plan:

1. Decide

2. Find

3. Choose

4. Solve

5. Check

The Broadway Middle School PTA conducted a book sale to raise money for the music program. They sold 115 fiction books, 67 biographies, 91 travel books, and 36 hobby books. Fiction books were sold for $2 each, biographies were $4 each, and travel books were $5 each. The PTA raised $1,169 at the book sale.

Part A Each hobby book was sold for the same price. What was the price of each hobby book? Show your work.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L Answer $ B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O Part B K IS C R THIS BOO O O B PLE theIVamount N FO of money raised from selling the type of book Mbetween E A S What is the difference G S I T TH S NO in sales and the type of book that generated the least Imoney that generated the Smost N O I amount of Pmoney ERMISin sales? Show your work.

Answer $

Math Solutions: Open-Ended Problem Solving • Level G

Jacob’s scout troop sold boxes of greetings cards to raise money for their camping trips. Jacob sold 75 boxes, Frank sold 86 boxes, Dashawn sold 51 boxes, and Harjinder sold 62 boxes. In all, these 4 campers raised $3,562 by selling greetings cards.

Part A If each box of greetings cards was sold for the same price, what was the cost of one box? Show your work.

Answer $

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A Part B S NOT PRODUCED I T I . ED GHTscouts? BE RE I R O What was the amount raised by the 2 top selling Y T P K O K IS C R THIS BOO O O Show your work. B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Answer $

Math Solutions: Open-Ended Problem Solving • Level G

The lowest temperature ever recorded in Buffalo, New York, was 20°F (Fahrenheit) in February, 1961. The average low temperature in Buffalo, New York, for the month of February is 19°F.

Part A On the number line below, plot the lowest recorded temperature and the average low temperature in Buffalo, New York, for the month of February. Be sure to label both points appropriately.

224 222 220 218 216 214 212 210 28

Part B

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

How many degrees colder was the coldest day in February than the average low temperature for February? Show your work.

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Answer

°F

Math Solutions: Open-Ended Problem Solving • Level G

Over a period of 26 years, the average high temperature in Antarctica during the month of March was 6°F, and the average low temperature was 4°F.

Part A On the number line below, plot and label the average high and low temperatures in Antarctica for the month of March during this 26-year period.

210 29

Part B

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

How many degrees colder was the average low temperature than the average high temperature? Show your work.

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Answer

°F

Math Solutions: Open-Ended Problem Solving • Level G

Strand: Algebra Band: Equations and Inequalities. . . . . . . . . . . 22

The 5-Step Problem-Solving Plan Step 1: Decide what you are being asked to do. Step 2: Find what you need to know. Step 3: Choose a strategy for solving the problem. Step 4: Solve the problem. Step 5: Check your solution and answer.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Math Solutions: Open-Ended Problem Solving • Level G

Strand: Algebra Band: Equations and Inequalities The 5-Step Plan:

1. Decide

2. Find

3. Choose

4. Solve

5. Check

Isabel and her friend, Hannah, go to the movies. A movie ticket costs $9. Snacks at the movies cost $3 each. Write an equation Isabel can use to determine the number of snacks, s, she can buy if she has $27 before she buys tickets for herself and her friend.

Equation

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Using the equation above, find the number of snacks Isabel can buy. Show your work.

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Answer

snacks

Math Solutions: Open-Ended Problem Solving • Level G

Inez does landscaping in her community. She charges $140 for materials and $15 per hour for labor. Write an equation that can be used to determine the number of hours, h, she plans to work for a job she estimated to cost $230.

Equation

Use your equation, to find the number of hours, h, she plans to work on this job. Show your work.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Answer

hours

Math Solutions: Open-Ended Problem Solving • Level G

Strand: Geometry Band: Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . 25

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Math Solutions: Open-Ended Problem Solving • Level G

Strand: Geometry Band: Shapes The 5-Step Plan:

1. Decide

2. Find

3. Choose

4. Solve

5. Check

Brian’s tool chest is shaped like a rectangular prism, as shown below.

3.6 ft.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 2.4 ft.

6 ft.

[not drawn to scale]

Determine the volume of the tool chest. Round your answer to the nearest tenth.

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Show your work.

Answer

cubic feet

Math Solutions: Open-Ended Problem Solving • Level G

Lydia took the measurements of a can of soup and drew a picture of it.

7 cm.

11 cm.

[not drawn to scale]

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Find the volume of the can of soup to the nearest tenth of a cubic centimeter. Show your work.

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Answer

cubic centimeters

Math Solutions: Open-Ended Problem Solving • Level G

Steven uses rust-proof paint to cover the cylindrical tank shown below. h = 10 ft. r = 4 ft.

[not drawn to scale]

Part A What is the surface area of the entire tank to the nearest square foot? Show your work.

Answer

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 square feet

STER. . A M E ACKLIN IN ANY WAY L B A Part B S NOT PRODUCED I T I . E of paint must Steven ED How many One can of rust-proof paint will cover 20 square GHTfeet. BE Rcans I R O Y T P K CO of the Itank? purchase to cover the entire surface BOO S K ISarea O H O T B Show your work. SAMPLE N FOR E V I G S I T TH IS NO N O I S IS PERM

Answer

cans of paint

Math Solutions: Open-Ended Problem Solving • Level G

Julie ships a present to her grandmother in a box. The dimensions of the box are shown below.

8 in.

10 in. 16 in. [not drawn to scale] What is the total surface area of the box? Show your work.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Answer

square inches

Math Solutions: Open-Ended Problem Solving • Level G

Strand: Measurement Band: Units of Measurement . . . . . . . . . . . . . . 30 Band: Estimation. . . . . . . . . . . . . . . . . . . . . . . . 34

The 5-Step Problem-Solving Plan Step 1: Decide what you are being asked to do. Step 2: Find what you need to know. Step 3: Choose a strategy for solving the problem. Step 4: Solve the problem.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 Step 5: Check your solution and answer.

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Math Solutions: Open-Ended Problem Solving • Level G

Strand: Measurement Band: Units of Measurement The 5-Step Plan:

1. Decide

2. Find

3. Choose

4. Solve

5. Check

England’s Paradise Amusement Park requires each person to weigh at least 25 kilograms in order to ride its roller coaster. What is the minimum amount of weight, in grams, a person must weigh to be allowed to ride the coaster? Show your work.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Answer

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM grams

Math Solutions: Open-Ended Problem Solving • Level G

Brett weighed some pebbles he had found at the beach. He found a brown pebble that weighed 1,824 milligrams and a pearl-colored pebble that weighed 2.75 grams. How much more did the pearl-colored pebble weigh, in milligrams, than the brown pebble? Show your work.

Answer

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A milligrams S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

130 140 150 120 160 110 0 40 30 17 60 5 0 20 0 10 70 10 80

40 50 60 30 70 2 0 150 140 130 120 110 8 0 1 0 160 10 0 0 9 17

Math Solutions: Open-Ended Problem Solving • Level G

Use your protractor to help you solve this problem.

Maninder was asked to keep track of the amount of time he spent on different activities during a typical day. The chart below shows the amount of time he spent doing each activity. Maninder’s Typical Day Activity

Percent of the Day

Sleeping

30%

School

25%

Homework and Chores

15%

Other Activities

30%

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Use your protractor to create a circle graph that properly displays the information shown in the chart. Be sure to label each section and indicate a title for the graph. Show your work.

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

130 140 150 120 160 110 0 40 30 17 60 5 0 20 0 10 70 10 80

40 50 60 30 70 2 0 150 140 130 120 110 8 0 1 0 160 10 0 0 9 17

Math Solutions: Open-Ended Problem Solving • Level G

Use your protractor to help you solve this problem.

Jason surveyed 120 students in the 7th grade to find out their favorite kinds of books. The table below shows the results of his poll. 7th Graders’ Favorite Books Type of Book

Number of Students

Biography

Mystery

Science Fiction

Other

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Create a circle graph to display the data Jason collected. Be sure to label each section on the graph and to give it a title. Show your work.

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Math Solutions: Open-Ended Problem Solving • Level G

Strand: Measurement Band: Estimation The 5-Step Plan:

1. Decide

2. Find

3. Choose

4. Solve

5. Check

The fish tank below contains 4 liters of water.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Estimate the capacity of the fish tank when the fish tank is completely filled with water.

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K Estimation liters O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T On the lines below, describe how you can estimate the capacity of the fish tank without TH NO S I N using a ruler. ISSIO PERM

Math Solutions: Open-Ended Problem Solving • Level G

The Casey family has an above ground pool that is in the process of being filled with water. The diagram shows how much water is in the pool so far. The weight of the water shown is 7,200 pounds.

Estimate what the weight of the water would be if the pool was completely filled.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O Estimation BOO K IS C R THISpounds O O B N FO MPLE E A V S I G S I T O you arrived at your estimate without using a ruler or TH describe On the lines below, IS Nhow N O I S knowing the measurements. IS PERM

Math Solutions: Open-Ended Problem Solving • Level G

Strand: Statistics and Probability Band: Organization and Display of Data . . . . . 37 Band: Predictions from Data . . . . . . . . . . . . . . 43 Band: Probability . . . . . . . . . . . . . . . . . . . . . . . 45

The 5-Step Problem-Solving Plan Step 1: Decide what you are being asked to do. Step 2: Find what you need to know. Step 3: Choose a strategy for solving the problem.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 Step 4: Solve the problem.

Step 5: Check your solution and answer.

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Math Solutions: Open-Ended Problem Solving • Level G

Strand: Statistics and Probability Band: Organization and Display of Data The 5-Step Plan:

1. Decide

2. Find

3. Choose

4. Solve

5. Check

At the Mather Middle School, there are 46 students in the Computer Club and 39 students in the Science Club. Of these students, 10 are in both the Computer Club and the Science Club.

Part A Using the information provided above, complete the Venn diagram. Be sure to indicate a title, label each circle, and place the appropriate number in each section of the diagram.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B Part B N FO MPLE E A V S I G S I T O TH ISofNstudents N What is the total number who participate in the clubs at Mather Middle School? O I S S I M R PE

Answer

students

Math Solutions: Open-Ended Problem Solving • Level G

The list below shows the number of students in Mr. Kelly’s class who participate in band and chorus. • A total of 65 students participate in the band. • A total of 78 students participate in the chorus. • There are 18 students who participate in both activities.

Part A Use the list above to complete a Venn diagram that shows how many of Mr. Kelly’s students participate in these activities. Be sure to indicate a title, label each circle, and write the appropriate numbers in each section of the diagram.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P Part B K O K IS C R THIS BOO O O B What is the total number who N FOparticipate in these activities? MPLofE students E A V S I G S I T TH IS NO N O I S IS PERM

Answer

students

Math Solutions: Open-Ended Problem Solving • Level G

Vijay was looking at his bank statement to see how his savings has grown. The chart below shows his savings account balance over the last several months. Vijay’s Savings Account Balance Month

Amount

January

$100

February

$115

March

$125

April

$145

May

$170

June

$165

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Based on the chart, which kind of graph would be most appropriate to display the data?

Answer

Use the space provided below to explain why the graph you chose is best to display STER A M E Y. N this data. NY WA LACKLI

AB IN A T D O E N C U . IT IS E REPROD D E T H G B OPYRI S BOOK TO C S I BOOK R THI E O L F P N M E A THIS S IS NOT GIV SION S I M R PE

Math Solutions: Open-Ended Problem Solving • Level G

High and low temperatures were recorded for five cities during the month of March. The table shows the average high and low temperatures during the month. Average High and Low Temperatures City, State

Average High Temperature

Average Low Temperature

New York, NY

51° F

38° F

Miami, FL

76° F

61° F

Phoenix, AZ

82° F

46° F

Chicago, IL

50° F

36° F

Anchorage, AK

41° F

30° F

What type of graph would be best to display this data?

Answer

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E KLIN graphAtoNY WAY In the space provided, indicate why the graph you chose would beBthe ACbest L A OT ED IN display this data. N C U S I D O T TED. I O BE REPR H G I R COPY IS BOOK T S I K O BO R TH E O L F P N M E A THIS S IS NOT GIV SION S I M R PE

Math Solutions: Open-Ended Problem Solving • Level G

Larry sells several different newspapers at his newsstand on weekdays. During one week he compared sales for the Gazette News and the Sun Times. He compiled the sales data and recorded it in the chart below. Newspaper Sales Day

Gazette News

Sun Times

Monday

Tuesday

Wednesday

Thursday

Friday

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

On the grid provided, draw a double-bar graph that properly reflects the data in the table. Remember to provide a title, a key, an appropriate scale, and to label the axes.

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Math Solutions: Open-Ended Problem Solving • Level G

A new company recorded the number of visitors to its website. The table below shows the number of visits each day during the first and second weeks the website was available to customers. Visits to Website Day

Week 1 (number of visits)

Week 2 (number of visits)

Monday

Tuesday

Wednesday

Thursday

Friday

115

Saturday

125

134

Sunday

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

On the grid below, create a double-bar graph that shows the number of visits to the website each day during the first week and the second week. Be sure to • • • • •

title the graph label the axes provide an appropriate key for the graph provide a scale for the graph graph all the data

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Math Solutions: Open-Ended Problem Solving • Level G

Strand: Statistics and Probability Band: Predictions from Data The 5-Step Plan:

1. Decide

2. Find

3. Choose

4. Solve

5. Check

Lloyd recorded the number of sesame bagels sold each day at his store during one week. He graphed the data in two different ways. Graph B 100

Graph A

Number of Sesame Bagels Sold

90 100 50 25 0

80 70 60

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Sun. Mon. Tues. Wed. Thur.

Day of the Week

Fri.

Sat.

50 40 30 20 10 0

Sun. Mon. Tues. Wed. Thur. Fri.

Sat.

Day of the Week

STER. . A M E Which one of the two graphs is misleading? ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B Answer N FO MPLE E A V S I G S I T TH IS NO N O I S IS On the lines Ebelow, P RM explain why the graph you chose is misleading.

Math Solutions: Open-Ended Problem Solving • Level G

Mrs. Jones and Mr. Smith are managers at the Big A Amusement Park. Each of them recorded and graphed the park attendance for a period of one week. Their graphs are shown below. Mrs. Jones’ Graph

Mr. Smith’s Graph

1300

Attendance

1200 1100 1000 900 800 700 Sun.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Mon. Tues. Wed. Thur.

Day of the Week

Fri.

Sat.

1500 1000 500 0

Sun.

Mon. Tues. Wed. Thur.

Fri.

Sat.

Day of the Week

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S Answer I T TH IS NO N O I S RMIS below, explain why the graph you chose is misleading. PEprovided In the space Whose graph is misleading?

Math Solutions: Open-Ended Problem Solving • Level G

Strand: Statistics and Probability Band: Probability The 5-Step Plan:

1. Decide

2. Find

3. Choose

4. Solve

5. Check

Ms. Wilson opened a pet store in September. She advertised and worked hard to build a successful business. The table below shows the number of pets she sold in her store during the first several months she was in business. Pets Sold in Ms. Wilson’s Store Month

Number of Pets Sold

October

November

December

January

February

March

April

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B Between which 2 months did pet sales increase by the greatest amount? A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O Answer between OO K IS C R THIS Band O O B E FO sales for May and June and explain your Npet MPLtable, E A V S Based on the data in the predict I G S I T TH IS NO below. reasoning on the lines provided N O I S IS PERM

Math Solutions: Open-Ended Problem Solving • Level G

Marisol opened a small restaurant. The table below shows the number of dinners she served during the first 5 weeks her restaurant was open. Dinners Served at Marisol’s Restaurant Week

Number of Dinners

210

255

300

352

407

Between which 2 weeks did the number of dinners served increase the most?

Answer

between

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 and

Based on the information provided in the table, how many dinners should Marisol plan. STERat . A arrived to be able to serve during the 7th week? On the lines below, explain how you M E WAY KLIN your prediction. A BLAC N ANY

OT ED I N C U S I D O T TED. I O BE REPR H G I R COPY IS BOOK T S I K O BO R TH E O L F P N M E A THIS S IS NOT GIV SION S I M R PE

Math Solutions: Open-Ended Problem Solving • Level G

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

Math Solutions: Open-Ended Problem Solving • Level G

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. . A M E ACKLIN IN ANY WAY L B A S NOT PRODUCED I T I . GHTED BE RE I R O Y T P K O K IS C R THIS BOO O O B N FO MPLE E A V S I G S I T TH IS NO N O I S IS PERM