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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 Grade Level 25-Pack 100-Pack
C 3 4114-7 4115-4 D 4 4117-8 4118-5 E 5 4120-8 4121-5 F 6 4123-9 4124-6 G 7 4126-0 4127-7 H 8 4129-1 4130-7
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L E V E L G
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Math Solutions: Open-Ended Problem Solving • Level G
AcknowledgmentsExecutive Editor: Amy CollinsProject Manager: Edward NaselloEditors: Jeff Brannon
Linda LiDestri
ISBN 978-1-4204-4125-3R 4125-3
Copyright ©2008 RALLY! EDUCATION. All rights reserved. No part of the material protected by this copyright may bereproduced in any form by any means, electronic or mechanical, including photocopying, recording, or by any informationstorage and retrieval system, without permission in writing from the copyright owner. Printed in the U.S.A.
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Math Solutions: Open-Ended Problem Solving • Level G
Table of Contents
INTRODUCTION 4
How to Use This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4A Helpful List of Mathematical Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5How to Answer Short-Response and Extended-Response Questions . . . . . . . 6Mathematics Reference Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
INSTRUCTION 8
The 5-Step Problem-Solving Plan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
ON YOUR OWN 12
Number Sense and Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Number Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Equations and Inequalities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Units of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Statistics and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Organization and Display of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Predictions from Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
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Math Solutions: Open-Ended Problem Solving • Level G
INTRODUCTIONTo the TeacherMath Solutions: Open-Ended Problem Solving provides instructional practice in answering open-endedmath problems for both short-response and extended-response questions. This book contains the sametypes of questions students are likely to encounter on tests. Math problems are formatted so thatstudents will learn to solve problems using a logical, organized plan.
How to Use This BookWe have arranged the problems in this book by math strands. The questions for each strand have beengrouped by mathematical-concept bands. This format allows teachers and students to emphasize thoseareas where the most practice is needed. In this book, the teacher has an opportunity to model problemsolving and guide students using a 5-Step Problem-Solving Plan. This book may also be used to providestudents with an opportunity to work on problems independently. The teacher can then review withthe 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) canselect the specific strands they want to cover and proceed in any order.
Follow These Steps to Use This Book:Step 1: Model the 5-Step Problem-Solving Plan.Step 2: Choose a strand to study.Step 3: Choose a band to work on or review.Step 4: Have students solve a problem.Step 5: Review the problem and the solution.Step 6: Do another problem.
Math problems are formatted so that students can use a variety of problem-solving strategies inconjunction with the 5-Step Problem-Solving Plan. This teaches students to answer problems using alogical, organized, and thoughtful approach. This will help students answer problems even when a factscenario 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 thatyour students will be successful test takers.
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A Helpful List of Mathematical Language (Grade 7)Listed below are some commonly used mathematical terms and expressions that 7th Grade studentsshould be familiar with. You may want to review this list with your students.
Number Sense and Operationscoefficientcounting numbersexponentsintegersintegralirrational numbersmultiplenatural numbersnon-perfect squaresperfect squarepi (≠)prime factorizationrational numbersreal numbersscientific notationsquare rootwhole numbers
Algebrabinomialequationevaluatefunctioninequalityinput valueslike termsmonomialspolynomialtable of valuestrinomial
Geometryadjacentcircumferencediameterexterior anglehypotenuseinterior anglespolygonPythagorean theoremradiusright angle
Measurement
central anglecustomary units of massexchange rate tablemap scalemetric units of massprotractorrelative error
Statistics and Probability
circle graphconductdouble bar graphdouble line graphsmeasures of central tendencyrangevalidity of sample methods
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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 PlanWhen solving math problems, you need to follow a plan. This helps you to organize information andchoose a strategy to solve the problem. Follow these five steps to help you make your 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.
Use a Problem-Solving StrategyWhen 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 beststrategy for solving a problem will make you successful in math. The following is a list of somestrategies you may want to use.
• Draw a Picture• Organize—Make a Chart or List, Graph, Sort Data• Work Backwards• Use Manipulatives or Act Out• Compute—Write a Number Sentence, Use Ratio or Proportion• Use a Formula or Rule• Guess and Check• Make It Simpler• Make Estimates• Look for a Pattern
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.
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Mathematics Reference SheetFORMULAS
rd
s
r
h
hl
w
h
l
s
w
CONVERSIONS
1 centimeter � 10 millimeters
1 meter � 100 centimeters � 1,000 millimeters
1 kilometer � 1,000 meters
1 gram � 1,000 milligrams
1 kilogram � 1,000 grams
1 pound � 16 ounces
1 ton � 2,000 pounds
1 cup � 8 fluid ounces
1 pint � 2 cups
1 quart � 2 pints
1 gallon � 4 quarts
1 liter � 1,000 milliliters
1 kiloliter � 1,000 liters
Circle Area � � r2
Circumference � 2�r
Cube Total Surface Area � 6s2
Volume � s3
Right Circular Cylinder Total Surface Area � 2�rh � 2�r2
Volume � �r2h
Right Rectangular Prism Total Surface Area � 2wl � 2 lh � 2wh
Volume � lwh
Right Triangular Prism Total Surface Area � wh � lw � lh � ls
Volume � �12
�wh � l
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Math Solutions: Open-Ended Problem Solving • Level G
INSTRUCTION
The 5-Step Problem-Solving PlanDirections: 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
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 hasto choose from.
Step 2: Find what you need to know.
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-solvingstrategy called Organize: Make a Chart or List, Graph, Sort Data.
Drink
milk
juice
Snack
fruit
crackers
Sandwich
ham & cheese
peanut butter & jelly
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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.
Step 5: Check your solution and answer.
Check all of the lunch combinations in your tree diagram or list. Make sure all of the possiblecombinations appear once and that no combination appears more than once.
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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 pairof pants, and one shirt. The chart below shows the different color choices she has to choose from foreach article of clothing.
Clothes Tashi Can Choose From
How many combinations of shoes, pants, and shirts does Tashi have to choose from?
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.
Shirts
yellow
green
Pants
black
gray
brown
Shoes
blue
white
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Math Solutions: Open-Ended Problem Solving • Level G
Step 4: Solve the problem.
Step 5: Check your solution and answer.
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Math Solutions: Open-Ended Problem Solving • Level G
ON YOUR OWN
Strand: Number Sense and Operations
Band: Number Systems . . . . . . . . . . . . . . . . . . 13
Band: Operations . . . . . . . . . . . . . . . . . . . . . . . 17
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.
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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
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1 The table below shows geographic information about Africa.
Geography of Africa
Write the numbers, in standard form, for the lowest elevation and the highest elevationof Africa.
Answer lowest elevation meters
highest elevation meters
�1.56 � 102 meters
5.895 � 103 meters
Lowest Elevation
Highest Elevation
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Math Solutions: Open-Ended Problem Solving • Level G
2 Look at the table below. It shows approximate measurements for the highest and lowestpoints on Earth.
Earth Elevations
Write the elevations in standard form.
Answer highest point feet
lowest point feet
Highest Point
Lowest Point
Location
Mt. Everest, Nepal
Dead Sea, Israel/Jordan
Elevation (compared to sea level)
2.9 � 104 feet
�1.4 � 103 feet
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Math Solutions: Open-Ended Problem Solving • Level G
3 The table below shows the average distance between Earth and its moon and the averagedistance between Earth and the sun.
Distance from Earth
How much greater, in kilometers, is the distance from Earth to the sun than the distancefrom Earth to the moon? Write your answer in standard form.
Show your work.
Answer kilometers
Name
Moon
Sun
Average Distance
3.844 � 105 kilometers
1.49 � 108 kilometers
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Math Solutions: Open-Ended Problem Solving • Level G
4 The table shows the distance that each of the first 5 planets is from the sun.
Distance of Planets from the Sun
In standard form, write approximately how much farther Mars is from the sun than Earth isfrom the sun.
Show your work.
Answer miles
Planet
Mercury
Venus
Earth
Mars
Jupiter
Distance from the Sun (miles)
3.59 � 107
6.72 � 107
9.29 � 107
1.42 � 108
4.84 � 108
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Math Solutions: Open-Ended Problem Solving • Level G
5 The Broadway Middle School PTA conducted a book sale to raise money for the musicprogram. They sold 115 fiction books, 67 biographies, 91 travel books, and 36 hobbybooks. Fiction books were sold for $2 each, biographies were $4 each, and travel bookswere $5 each. The PTA raised $1,169 at the book sale.
Part AEach hobby book was sold for the same price. What was the price of each hobby book?
Show your work.
Answer $
Part BWhat is the difference between the amount of money raised from selling the type of bookthat generated the most money in sales and the type of book that generated the leastamount of money in sales?
Show your work.
Answer $
Strand: Number Sense and Operations
Band: Operations
The 5-Step Plan: 1. Decide 2. Find 3. Choose 4. Solve 5. Check
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Math Solutions: Open-Ended Problem Solving • Level G
6 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 sold62 boxes. In all, these 4 campers raised $3,562 by selling greetings cards.
Part AIf each box of greetings cards was sold for the same price, what was the cost of one box?
Show your work.
Answer $
Part BWhat was the amount raised by the 2 top selling scouts?
Show your work.
Answer $
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Math Solutions: Open-Ended Problem Solving • Level G
7 The lowest temperature ever recorded in Buffalo, New York, was �20°F (Fahrenheit) inFebruary, 1961. The average low temperature in Buffalo, New York, for the month ofFebruary is 19°F.
Part AOn the number line below, plot the lowest recorded temperature and the averagelow temperature in Buffalo, New York, for the month of February. Be sure to label bothpoints appropriately.
Part BHow many degrees colder was the coldest day in February than the average lowtemperature for February?
Show your work.
Answer °F
220222224 218 216 214 212 210 28 26 24 22 0 2 4 6 8 10 12 14 16 18 20 22 24
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Math Solutions: Open-Ended Problem Solving • Level G
8 Over a period of 26 years, the average high temperature in Antarctica during the month ofMarch was 6°F, and the average low temperature was �4°F.
Part AOn the number line below, plot and label the average high and low temperatures inAntarctica for the month of March during this 26-year period.
Part BHow many degrees colder was the average low temperature than the averagehigh temperature?
Show your work.
Answer °F
210 29 28 27 26 25 24 23 22 21 0 1 2 3 4 5 6 7 8 9 10
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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.
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Math Solutions: Open-Ended Problem Solving • Level G
9 Isabel and her friend, Hannah, go to the movies. A movie ticket costs $9. Snacks at themovies 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
Using the equation above, find the number of snacks Isabel can buy.
Show your work.
Answer snacks
Strand: Algebra
Band: Equations and Inequalities
The 5-Step Plan: 1. Decide 2. Find 3. Choose 4. Solve 5. Check
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Math Solutions: Open-Ended Problem Solving • Level G
10 Inez does landscaping in her community. She charges $140 for materials and $15 per hourfor labor. Write an equation that can be used to determine the number of hours, h, sheplans 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.
Answer hours
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Math Solutions: Open-Ended Problem Solving • Level G
Strand: Geometry
Band: Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . 25
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.
Strand: Geometry
Band: Shapes
The 5-Step Plan: 1. Decide 2. Find 3. Choose 4. Solve 5. Check
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Math Solutions: Open-Ended Problem Solving • Level G
11 Brian’s tool chest is shaped like a rectangular prism, as shown below.
[not drawn to scale]
Determine the volume of the tool chest. Round your answer to the nearest tenth.
Show your work.
Answer cubic feet
6 ft.
3.6 ft.
2.4 ft.
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Math Solutions: Open-Ended Problem Solving • Level G
12 Lydia took the measurements of a can of soup and drew a picture of it.
[not drawn to scale]
Find the volume of the can of soup to the nearest tenth of a cubic centimeter.
Show your work.
Answer cubic centimeters
7 cm.
11 cm.
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Math Solutions: Open-Ended Problem Solving • Level G
13 Steven uses rust-proof paint to cover the cylindrical tank shown below.
[not drawn to scale]
Part AWhat is the surface area of the entire tank to the nearest square foot?
Show your work.
Answer square feet
Part BOne can of rust-proof paint will cover 20 square feet. How many cans of paint must Stevenpurchase to cover the entire surface area of the tank?
Show your work.
Answer cans of paint
h = 10 ft.
r = 4 ft.
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Math Solutions: Open-Ended Problem Solving • Level G
14 Julie ships a present to her grandmother in a box. The dimensions of the box areshown below.
[not drawn to scale]
What is the total surface area of the box?
Show your work.
Answer square inches
16 in.
8 in.
10 in.
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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.
Step 5: Check your solution and answer.
Math Solutions: Open-Ended Problem Solving • Level G
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Math Solutions: Open-Ended Problem Solving • Level G
15 England’s Paradise Amusement Park requires each person to weigh at least 25 kilograms inorder to ride its roller coaster. What is the minimum amount of weight, in grams, a personmust weigh to be allowed to ride the coaster?
Show your work.
Answer grams
Strand: Measurement
Band: Units of Measurement
The 5-Step Plan: 1. Decide 2. Find 3. Choose 4. Solve 5. Check
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16 Brett weighed some pebbles he had found at the beach. He found a brown pebble thatweighed 1,824 milligrams and a pearl-colored pebble that weighed 2.75 grams. How muchmore did the pearl-colored pebble weigh, in milligrams, than the brown pebble?
Show your work.
Answer milligrams
Math Solutions: Open-Ended Problem Solving • Level G
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Math Solutions: Open-Ended Problem Solving • Level G
17 Use your protractor to help you solve this problem.
Maninder was asked to keep track of the amount of time he spent on different activitiesduring a typical day. The chart below shows the amount of time he spent doing eachactivity.
Maninder’s Typical Day
Use your protractor to create a circle graph that properly displays the information shown inthe chart. Be sure to label each section and indicate a title for the graph.
Show your work.
1
2
90
80
70
60
50
40
30
20
10
8 07 0 6 0 5 0 4 0 3 0 2 0
1 0100
110 120 130 140 150 160170
100
110
120
130
140
150
160
170
Activity
Sleeping
School
Homework and Chores
Other Activities
Percent of the Day
30%
25%
15%
30%
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Math Solutions: Open-Ended Problem Solving • Level G
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18 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
Create a circle graph to display the data Jason collected. Be sure to label each section on thegraph and to give it a title.
Show your work.
Type of Book
Biography
Mystery
Science Fiction
Other
Number of Students
48
42
18
12
1
2
90
80
70
60
50
40
30
20
10
8 07 0 6 0 5 0 4 0 3 0 2 0
1 0100
110 120 130 140 150 160170
100
110
120
130
140
150
160
170
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Math Solutions: Open-Ended Problem Solving • Level G
19 The fish tank below contains 4 liters of water.
Estimate the capacity of the fish tank when the fish tank is completely filled with water.
Estimation liters
On the lines below, describe how you can estimate the capacity of the fish tank withoutusing a ruler.
Strand: Measurement
Band: Estimation
The 5-Step Plan: 1. Decide 2. Find 3. Choose 4. Solve 5. Check
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Math Solutions: Open-Ended Problem Solving • Level G
20 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 is7,200 pounds.
Estimate what the weight of the water would be if the pool was completely filled.
Estimation pounds
On the lines below, describe how you arrived at your estimate without using a ruler orknowing the measurements.
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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.
Step 4: Solve the problem.
Step 5: Check your solution and answer.
Strand: Statistics and Probability
Band: Organization and Display of Data
The 5-Step Plan: 1. Decide 2. Find 3. Choose 4. Solve 5. Check
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Math Solutions: Open-Ended Problem Solving • Level G
21 At the Mather Middle School, there are 46 students in the Computer Club and 39 students inthe Science Club. Of these students, 10 are in both the Computer Club and the Science Club.
Part AUsing the information provided above, complete the Venn diagram. Be sure to indicate atitle, label each circle, and place the appropriate number in each section of the diagram.
Part BWhat is the total number of students who participate in the clubs at Mather Middle School?
Answer students
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Math Solutions: Open-Ended Problem Solving • Level G
22 The list below shows the number of students in Mr. Kelly’s class who participate in bandand 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 AUse the list above to complete a Venn diagram that shows how many of Mr. Kelly’s studentsparticipate in these activities. Be sure to indicate a title, label each circle, and write theappropriate numbers in each section of the diagram.
Part BWhat is the total number of students who participate in these activities?
Answer students
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Math Solutions: Open-Ended Problem Solving • Level G
23 Vijay was looking at his bank statement to see how his savings has grown. The chart belowshows his savings account balance over the last several months.
Vijay’s Savings Account Balance
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 displaythis data.
Month
January
February
March
April
May
June
Amount
$100
$115
$125
$145
$170
$165
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Math Solutions: Open-Ended Problem Solving • Level G
24 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
What type of graph would be best to display this data?
Answer
In the space provided, indicate why the graph you chose would be the best graph todisplay this data.
City, State
New York, NY
Miami, FL
Phoenix, AZ
Chicago, IL
Anchorage, AK
Average High Temperature
51° F
76° F
82° F
50° F
41° F
Average Low Temperature
38° F
61° F
46° F
36° F
30° F
Math Solutions: Open-Ended Problem Solving • Level G
25 Larry sells several different newspapers at his newsstand on weekdays. During one week hecompared sales for the Gazette News and the Sun Times. He compiled the sales data andrecorded it in the chart below.
Newspaper Sales
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.
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Gazette News
65
58
72
70
65
Sun Times
62
54
65
70
60
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Math Solutions: Open-Ended Problem Solving • Level G
26 A new company recorded the number of visitors to its website. The table below showsthe number of visits each day during the first and second weeks the website was availableto customers.
Visits to Website
On the grid below, create a double-bar graph that shows the number of visits to the websiteeach 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
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Week 1 (number of visits)
15
16
18
20
25
33
43
Week 2 (number of visits)
55
69
84
99
115
125
134
Strand: Statistics and Probability
Band: Predictions from Data
The 5-Step Plan: 1. Decide 2. Find 3. Choose 4. Solve 5. Check
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Math Solutions: Open-Ended Problem Solving • Level G
27 Lloyd recorded the number of sesame bagels sold each day at his store during one week.He graphed the data in two different ways.
Which one of the two graphs is misleading?
Answer
On the lines below, explain why the graph you chose is misleading.
Day of the Week
Day of the Week
Graph A
Graph B
Num
ber
ofSe
sam
eBa
gels
Sold
Num
ber
ofSe
sam
eBa
gels
Sold
0
25
50
100
Sat.Fri.Thur.Wed.Tues.Mon.Sun.
0
10
20
30
40
50
60
70
80
90
100
Sat.Fri.Thur.Wed.Tues.Mon.Sun.
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Math Solutions: Open-Ended Problem Solving • Level G
28 Mrs. Jones and Mr. Smith are managers at the Big A Amusement Park. Each of themrecorded and graphed the park attendance for a period of one week. Their graphs areshown below.
Whose graph is misleading?
Answer
In the space provided below, explain why the graph you chose is misleading.
Day of the Week
1000
1100
1200
1300
900
800
700
15001000
5000
Day of the Week
Mrs. Jones’ Graph Mr. Smith’s Graph
Att
enda
nce
Att
enda
nce
Sat.Fri.Thur.Wed.Tues.Mon.Sun. Sat.Fri.Thur.Wed.Tues.Mon.Sun.
Strand: Statistics and Probability
Band: Probability
The 5-Step Plan: 1. Decide 2. Find 3. Choose 4. Solve 5. Check
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Math Solutions: Open-Ended Problem Solving • Level G
29 Ms. Wilson opened a pet store in September. She advertised and worked hard to build asuccessful business. The table below shows the number of pets she sold in her store duringthe first several months she was in business.
Pets Sold in Ms. Wilson’s Store
Between which 2 months did pet sales increase by the greatest amount?
Answer between and
Based on the data in the table, predict pet sales for May and June and explain yourreasoning on the lines provided below.
Month
October
November
December
January
February
March
April
Number of Pets Sold
12
15
18
22
26
33
39
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Math Solutions: Open-Ended Problem Solving • Level G
30 Marisol opened a small restaurant. The table below shows the number of dinners she servedduring the first 5 weeks her restaurant was open.
Dinners Served at Marisol’s Restaurant
Between which 2 weeks did the number of dinners served increase the most?
Answer between and
Based on the information provided in the table, how many dinners should Marisol planto be able to serve during the 7th week? On the lines below, explain how you arrived atyour prediction.
Number of Dinners
210
255
300
352
407
Week
1
2
3
4
5
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Math Solutions: Open-Ended Problem Solving • Level G
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Math Solutions: Open-Ended Problem Solving • Level G
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