Math sbs g stats sample

G MAT H

S T R A N D - B Y- S T R A N D

STATISTICS PROBABILITY — AND —

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO C ON NEC TE D T O T H E

C OM M ON C OR E STA N D AR D S

RALLY! EDUCATION 22 Railroad Avenue Glen Head, NY 11545 888-99-RALLY Fax: 1-516-671-7900 www.RALLYEDUCATION.com LESLIE@RALLYEDUCATION.com …………………………………………………………………………………………………………………………

Math Problem-Solving Skills & Strategies by Strand

…………..

Math Strand-by-Strand Aligned to the Common Core State Standards Grade Levels 3–8

• Focuses on 5 specific math strands Number Sense & Operations, Measurement, Geometry, Statistics & Probability, Algebra

• Guided & independent practice with hints Each book provides math problem-solving practice.

Hints offer strategies to help students solve the problem

Class Set: 10 Copies of each Strand Book – Total of 50 books Level C D E F G H

Grade 3 4 5 6 7 8

______ 6002-5 6003-2 6004-9 6005-6 6006-3 6007-0

----------------------------------------------

888-99-RALLY www.RALLYEDUCATION.com

LEVEL MAT H

G

S T R A N D - B Y- S T R A N D

STATISTICS PROBABILITY — AND —

E L P SAM ATION C U D E !

Y L L Y L L RA A R .

9 9 888.

TER. S A M KLINE C A L B NOT A K TO BE S I T I HTED. R THIS BOO G I R Y IS COP T GIVEN FO WAY. K O O PLE B SION IS NO CED IN ANY M A S S IS DU THI PERM REPRO C O NNE CT ED T O T HE

C OM MON C OR E S TA N D AR D S

1 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

To the Teacher Math Strand-by-Strand prepares students to succeed on the student expectations that appear on math tests. The program is organized into five books: • Number Sense and Operations • Algebra • Geometry • Measurement • Statistics and Probability Each student expectation has Guided Practice and Independent Practice math problems. The Guided Practice math problems have a hint for every problem. The hints offer strategies to help students solve the problem. Students are introduced to several different problem-solving strategies:

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Draw a Picture or Diagram Use Manipulatives or Act it Out

Make a Chart or List, Graph, Sort Data Write a Number Sentence, Use Ratio or Proportion Guess and Check Look for a Pattern

Use a Formula or Rule Make it Simpler

ER.each In the Independent Practice section, students respond to four math problems STfor A M E N student expectation on their own.

LACKLI

OT A B TO BE N S I In each book, there are student expectationsTfrom ED. ITthe particular BOOKgrade level as well as, S H I G H I T R when appropriate, student expectations the previous grade that are important COPY from N FOR S E I V Y. I K A G O W building blocks for students to review.NOT O Y B N E A L IS P N S SAM ERMISSION RODUCED I I H T The RALLY! Math Strands P are connected REP to the Common Core State Standards: • Operations & Algebraic Thinking • Number & Operations in Base Ten • Number & Operations—Fractions • Measurement & Data • Geometry

ISBN 978-1-4204-6288-3 R 6288-3 Copyright ©2012 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. 0811.MAQ RALLY! EDUCATION • 22 Railroad Avenue, Glen Head, NY 11545 • (888) 99-RALLY

2 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Contents – Statistics and Probability Collection of Data . . . . . . . . . . . 4

Predictions from Data . . . . . . . 61

Grade 6

Grade 7

Student Expectation

Guided Practice

Independent Practice

Student Expectation

6.S.1. . . . . . . . . . . . . . 5 . . . . . . . . . 6 Guided Practice

Probability . . . . . . . . . . . . . . . . 73

Independent Practice

Grade 7

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

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7.S.1. . . . . . . . . . . . . . 8. . . . . . . . . 10

Student Expectation

Organization and Display of Data. . . . . . . . . . . . . 15

7.S.8 . . . . . . . . . . . . . 74 7.S.9 . . . . . . . . . . . . . 80 7.S.10 . . . . . . . . . . . . 83 7.S.11 . . . . . . . . . . . . 86 7.S.12 . . . . . . . . . . . . 89

Grade 6 Student Expectation

Guided Practice

Independent Practice

7.S.7 . . . . . . . . . . . . . 62 . . . . . . . . 64

Grade 7 Student Expectation

Guided Practice

Independent Practice

Guided Practice

Independent Practice

. . . . . . . . 76 . . . . . . . . 81 . . . . . . . . 84 . . . . . . . . 87 . . . . . . . . 90

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I Grade 7 R Y P IS CO Student Guided OKIndependent IVEN F Y WAY. G T O O B Expectation Practice PLE MPractice N IS N UCED IN AN A O I S S S S I I D 7.S.2 . . . . .T.H. . . . . . . 36 PER. .M. . . . . . 38 REPRO 6.S.2 . . . . . . . . . . . . . 16 . . . . . . . . 18 6.S.3 . . . . . . . . . . . . . 24 . . . . . . . . 26 6.S.4 . . . . . . . . . . . . . 30 . . . . . . . . 32

7.S.3 . . . . . . . . . . . . . 42 . . . . . . . . 44

Analysis of Data . . . . . . . . . . . . 48 Grade 7 Student Expectation

Guided Practice

Independent Practice

7.S.4 . . . . . . . . . . . . . 49 . . . . . . . . 50 7.S.5 . . . . . . . . . . . . . 52 . . . . . . . . 53 7.S.6 . . . . . . . . . . . . . 55 . . . . . . . . 56

3 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Collection of Data E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

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Student Expectation

6.S.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Develop the concept of sampling when collecting data from a population and decide the best method to collect data for a particular question

ER.

7.S.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E . 8MAST N I L K Identify and collect data using a variety of methods A BLAC

S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

4 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 6.S.1

1

Collection of Data Develop the concept of sampling when collecting data from a population and decide the best method to collect data for a particular question

A radio station wants to find the time of day that most students ages 11-15 listen to the radio. Which sample best represents the population?

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

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HINT

Guess and Check. Look at each answer choice. First eliminate any choices that include students other than ones ages 11-15. Then eliminate any choices that include just one gender of student.

A B C D

STER. A M E CKLIN A L B A a random sample of 100 girls, ages 11-15 S NOT OK TO BE I T I . a random sample of 100 students GHTED OR THIS BO I R Y P O F a random sample ofK100 ages IS Cstudents, IVEN11-15 AY. G O W T O Y O B N N E A L IS P a random of 100 AMsample D IN ONadults THIS S PERMISSI EPRODUCE R

5 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

The cafeteria manager at Cartwright Middle School wants to find out the types of food most students prefer for lunch. Which sample best represents the population?

A a random sample of 100 students at Cartwright Middle School B a random sample of 20 teachers at Cartwright Middle School C a random sample of 100 boys at Cartwright Middle School

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

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D a random sample of 100 seventh-grade students at Cartwright Middle School

3

Emily wants to find out how many hours most seventh-grade students at her school spend studying each week. Which sample best represents the population?

STER. A M E KLIN a random sample of 40 students at Emily’s school A BLAC OT O BE S NEmily’s I T T K I a random sample of 40 seventh-grade boys at school O .

GHTED OR THIS BO I R Y P a random sample of 40S seventh-grade students at Emily’s school O IVEN F Y WAY. KI C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

A a random sample of 40 students at the park B C D

6 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

The owner of a sports store wants to find out the favorite running shoe of his customers. Which sample best represents the population?

A a random sample of 100 people in the mall B a random sample of 100 customers in the sports store C a random sample of 100 female customers in the sports store D a random sample of 100 runners at a track meet

5

Kevin wants to find out the favorite video game of the seventh-grade boys at his school. Which sample best represents the population?

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

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A a random sample of 30 seventh-graders at Kevin’s school B a random sample of 30 students at Kevin’s school

C a random sample of 30 seventh-grade boys at Kevin’s school D a random sample of 30 adults at Kevin’s school

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

7 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.S.1 1

Collection of Data Identify and collect data using a variety of methods

Ricco used an almanac to collect data about the areas of certain state capitals.

He recorded the data in a table. Then he used the data to make the bar graph below.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Total Area (in square miles)

TOTAL AREAS OF STATE CAPITALS

70,000 60,000 50,000

STER. A M E 30,000 ACKLIN L B A S NOT OK TO BE I T I 20,000 .

GHTED OR THIS BO I R Y P O 10,000 IVEN F Y WAY. K IS C G O T O O B PLE N IS N UCED IN AN O I 0S SAM S S I I TH Frankfort, PERKYM Albany,RENYPRODAtlanta, GA Richmond, VA Madison, WI 40,000

State Capitals Which table shows the data Ricco used to make his graph?

HINT Organize—Make a Chart or List. Look at the bar graph. Make a list of the state capitals and the approximate total area shown in the graph. Then compare your list to the answer choices.

8 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

A

B

TOTAL AREAS OF STATE CAPITALS

C

WATER AREAS OF STATE CAPITALS

State Capital

Total Area (in square miles)

State Capital

Water Area (in square miles)

Frankfort, KY

40,409

Frankfort, KY

681

Albany, NY

54,556

Albany, NY

7,342

Atlanta, GA

59,425

Atlanta, GA

1,519

Richmond, VA

42,774

Richmond, VA

3,180

Madison, WI

65,498

Madison, WI

11,188

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

TOTAL AREAS OF STATE CAPITALS

D

AREAS OF STATE CAPITALS

State Capital

Total Area (in square miles)

State Capital

Frankfort, KY

40,409

Frankfort, KY

Albany, NY

54,556

Total Area (in square miles) 48,430TER.

S NE MA E OT A N O B59,425 S I T T Atlanta, GA 59,425 Atlanta, GA K I O .

GHTED OR THIS BO I R Y P O Pierre, SD 77,116 42,774 Y.VA IVEN FRichmond, K IS C A G O W T O Y O B AN Madison, WI WI 65,498 MPLE S65,498 N IS N UCED INMadison, A O I S S S I I D M TH O P ER REPR Albany, NYBLACKLI 54,556

9 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Selina surveyed her classmates about their favorite fruit. She recorded her results in the table below.

FAVORITE FRUIT Fruit

Tally

Frequency (Number of Students)

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 Apple

5111

8

Banana

4

4

Grapes

51

6

Orange

54

9

Selina used the data in her table to make a bar graph. Which bar graph could R. be Selina’s?

MASTE Number of Students

Number of Students

A

LINE K C A L B FAVORITE FRUIT C EFRUIT OT A FAVORITE B N O S I T T 10 10BOOK TED. I S H I G H I T R 8 8 COPY GIVEN FOR S I Y. K A O W T O Y O B 6 6 N N E A L AMP D IN ON IS 4 THIS S 4 PERMISSI EPRODUCE R 2 0

Orange Banana Grapes Apple

Fruit

D

Apple Banana Grapes Orange

FAVORITE FRUIT Number of Students

10 8 6 4 2 0

0

Fruit

FAVORITE FRUIT Number of Students

B

2

Apple Grapes Banana Orange

Fruit

10 8 6 4 2 0

Apple Banana Grapes Orange

Fruit

10 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

3

Armand surveyed four of his friends about their travel time to get to school. He recorded the data in a table. Then he used the data to make the bar graph below.

TRAVEL TIME

Time (in minutes)

35 30 25 20 15 10 5 0

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 Abe

Theresa

Julie

Grant

Friend

Which table shows the data Armand used to make his graph?

A

STER. A M E ACKLIN Time L B Friend Time Friend A BE minutes) S NOT OK TO(in I (in minutes) T I .

S BO IGHTED FOR THIAbe Theresa 20COPYR 30 N S E I .

V Y I K A G O W T Abe 25 PLE BO SIO25N IS NO CED IN ANYTheresa M A S THISJulie PERMIS 15 EPRODU Julie 15 R TRAVEL TIME

Grant B

C

30

TRAVEL TIME

Grant

TRAVEL TIME

D

20

TRAVEL TIME

Friend

Time (in minutes)

Friend

Time (in minutes)

Abe

20

Abe

20

Theresa

25

Theresa

15

Julie

15

Julie

25

Grant

30

Grant

30

11 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Leticia recorded the high temperatures for the week in a table. Then she used the data to make the line graph below.

Temperature (in °F)

DAILY HIGH TEMPERATURE 60 50 40 30 20 10 0

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 Mon

Tue

Wed Day

Thu

Fri

Which table shows the data Leticia used to make her graph?

A

DAILY HIGH TEMPERATURE Day

C

Temperature (in °F)

DAILY HIGH TEMPERATURE Day

Temperature TER. S°F) A (in M E N

CKLI A L B A Monday 35 OT O BE S NMonday I T T K I O .

Tuesday 35 IS BO GHTED OR THTuesday I R Y P CO IVEN F Wednesday AY. Wednesday BOOK IS45 G W T Y O N N E A L P N IS CED IN Thursday S SAM ERMISSIO42 U D THIThursday O P REPR Friday

B

30

Friday

DAILY HIGH TEMPERATURE

D

30 42 45 57 35

DAILY HIGH TEMPERATURE

Day

Temperature (in °F)

Day

Temperature (in °F)

Monday

35

Monday

35

Tuesday

57

Tuesday

57

Wednesday

45

Wednesday

45

Thursday

35

Thursday

42

Friday

30

Friday

30

12 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

Sheila, Ramiro, and Portia each rolled two number cubes 50 times. They recorded how many times a sum of 6 was rolled. Their data is shown in the table below.

SUM OF SIX Student

Number of Times Rolled

Sheila

8

Ramiro

12

Portia

7

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Portia used the data in the table to make a bar graph. Which bar graph could be Portia’s?

14 12 10 8 6 4 2 0

Number of Times Rolled

SUM OF SIX

14 12 10 8 6 4 2 0

14 12 10 8 6 4 2 0

Number of Times Rolled

C

Number of Times Rolled

B

SUM OF SIX

Number of Times Rolled

A

14 12 10 8 6 4 2 0

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BOSheila Ramiro Portia I Sheila Ramiro Portia R Y P O Student Student IVEN F Y WAY. K IS C G O T O O B N N E A L AMP ION IS ODUCED DIN OF SIX SUM OF SIX S S I M THIS S SUM R P P ER RE

Sheila

Ramiro Student

Portia

Sheila

Ramiro Student

Portia

13 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

14 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Organization and Display ofE Data

L P M SA N O I T Student Expectation UCA D E !

Y L L Y L A L R A R .

9 9 .

888

6.S.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Record data in a frequency table

STER. A M E LIN 6.S.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. .B.L.A.C.K. . . 24 T O BE Construct Venn diagrams to sort dataIT IS NO T K O .

GHTED OR THIS BO I R Y P 6.S.4 . . . . . . . . . . I.S. C. O . . . . . . . . .V.E.N. F. . . . . . . . .Y.. . . . . . . . 30 I K O WA to display O Ygraph OT Gappropriate B N N E Determine and justify the most A L S I P N I M N SA set ofMdata CEDgraph, line graph, Ubar ISSIO(pictograph, D THIaS given O R P P ER RE histogram, or circle graph) 7.S.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Display data in a circle graph 7.S.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Convert raw data into double-bar graphs and double-line graphs

15 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 6.S.2 1

Organization and Display of Data Record data in a frequency table

Evan surveys the students in two seventh-grade math classes about their favorite meal. The tally table below shows his results.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 FAVORITE MEAL

Meal

Tally

Pizza

55511

Spaghetti

55111

Chicken

5511

Meatloaf

511

STER. A M E ACKLIN L B A OTtally table?

Which frequency table best represents the data in O BE S Nthe I T T K I O .

GHTED OR THIS BO I R Y P O HINT IVEN F Y WAY. K IS C G O T O O B Organize—Make Next IN toANthe Tally column in the table MPLE SSaIOChart N IS Nor List.

A D S E C S U I I D THabove, make PERaMthird column REPROfor the frequency. Count up the tallies for each meal, and place the total in the new column. Compare your frequencies to the ones in the answer choices.

16 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

A

B

FAVORITE MEAL

C

FAVORITE MEAL

Meal

Frequency

Meal

Frequency

Pizza

16

Pizza

18

Spaghetti

13

Spaghetti

13

Chicken

11

Chicken

12

Meatloaf

7

Meatloaf

8

FAVORITE MEAL

D

FAVORITE MEAL

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Meal

Frequency

Meal

Frequency

Pizza

17

Pizza

17

Spaghetti

13

Spaghetti

14

Chicken

12

Chicken

11

Meatloaf

7

Meatloaf

7

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

17 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

This week, Mr. Ortiz makes the table shown below to show how many books are checked out of the library each day.

LIBRARY BOOKS CHECKED OUT Day

Number of Books

Monday

5555555554

Tuesday

555555555511

Wednesday

5555555

Thursday

5555511

Friday

5555555555555

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

18 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Which frequency table best represents the data in the tally table?

A

LIBRARY BOOKS CHECKED OUT

LIBRARY BOOKS CHECKED OUT

Day

Frequency

Day

Frequency

Monday

49

Monday

49

Tuesday

52

Tuesday

53

Wednesday

35

Wednesday

30

Thursday

27

Thursday

27

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Friday B

C

65

Friday

LIBRARY BOOKS CHECKED OUT

D

70

LIBRARY BOOKS CHECKED OUT

Day

Frequency

Day

Frequency

Monday

48

Monday

44

STER. A M E Tuesday 52 Tuesday ACKLIN 53 L B A NOT Wednesday 35 O BE35 SWednesday I T T K I O .

GHTED OR TThursday HIS BO I Thursday 28 27 R Y P O F C N S E I .

V Y K WA OT GI IN ANY Friday Friday PLE BOO 60 60 N S I M N A D O I S E ISS DUC THIS PERM REPRO

19 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

3

The seventh-grade students at Valerie’s school are collecting cans to recycle. The tally table below shows the number of cans each class collected last week.

CANS COLLECTED Class

Tally

Mr. Harper

555

Ms. Lee

555511

Ms. Rodriguez

5555555

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8 8 8

Mr. Sanders

5555554

Ms. Duran

555555551

Which frequency table best represents the data in the tally table?

A

CANS COLLECTED

C

CANS COLLECTED

Class

Frequency

Class

Mr. Harper

10

K Mr. Harper A BLAC

Ms. Duran

41

Ms. Duran

.

Frequency ASTER

LINE M15 T O BE 22 S NOMs. I T T K I O .

Ms. Lee 22 Lee GHTED OR THIS BO I R Y P O Ms. Rodriguez Rodriguez 35 IVEN F Ms. K IS35C AY. G O W T O Y O B N N E A L Mr. Sanders 34 AMP D IN Mr. Sanders O33N IS THIS S PERMISSI EPRODUCE R B

CANS COLLECTED

D

41

CANS COLLECTED

Class

Frequency

Class

Frequency

Mr. Harper

15

Mr. Harper

20

Ms. Lee

22

Ms. Lee

22

Ms. Rodriguez

40

Ms. Rodriguez

30

Mr. Sanders

34

Mr. Sanders

34

Ms. Duran

42

Ms. Duran

41

20 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Max surveyed 50 seventh graders about their favorite sport to watch. The tally table below shows his results.

FAVORITE SPORT Sport

Tally

Baseball

55

Basketball

5511

Football

5554

Soccer

5111

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Which frequency table best represents the data in the tally table?

A

B

FAVORITE SPORT

C

FAVORITE SPORT

Sport

Frequency

Sport

Frequency

Baseball

15

Baseball

10

Basketball

12

Basketball

Sport

Frequency

Sport

Frequency

Baseball

10

Baseball

10

Basketball

12

Basketball

17

Football

19

Football

17

Soccer

8

Soccer

8

STER. A M 12 E ACKLIN L B A Football 19 OT O BE14 S NFootball I T T K I O .

IS BO Soccer 8 9 GHTED OR THSoccer I R Y P O F C GIVEN NY WAY. OK IS T O O B N E L IN A MP SPORT N IS A D O I S E S C S S FAVORITE D FAVORITE SPORT U I I D TH PERM REPRO

21 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

The local mall surveyed 50 teenagers about the quality of food at the mall’s food court. The tally table below shows the results.

QUALITY OF FOOD Quality

Tally

Very Good

555

Good

5555111

Fair

5111

Poor

4

E L P SAM ATION C U D E !

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8 8 8

Which frequency table best represents the data in the tally table?

A

B

QUALITY OF FOOD

C

QUALITY OF FOOD

Quality

Frequency

Quality

Frequency

Very Good

20

Very Good

15

Good

23

Good

Quality

Frequency

Quality

Frequency

Very Good

10

Very Good

15

Good

22

Good

23

Fair

8

Fair

8

Poor

4

Poor

4

STER. A M 28 E ACKLIN L B A T Fair 9 O BE8 S NOFair I T T K I O .

IS BO Poor 4 9 GHTED OR THPoor I R Y P O F C GIVEN NY WAY. OK IS T O O B N E L IN A MP OF FOOD N IS A D O I S E S C S S QUALITY D QUALITY OF FOOD U I I D TH PERM REPRO

22 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E !

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8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

23 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 6.S.3 1

Organization and Display of Data Construct Venn diagrams to sort data

The list below shows the number of students who participate in hockey and speed skating at Jefferson Middle School.

E L P SAM ATION C U D E !

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8 8 8

A total of 29 students participate in hockey.

A total of 13 students participate in speed skating.

A total of 5 students participate in both sports.

Part A

Use the list above to complete the Venn diagram in the space below.

STER. A M E ACKLIN L • title the diagram B A S NOT OK TO BE • label each circle I T I .

D HTEdiagram Gthe • place a number in each sectionYof HIS BO I T R R P O O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO Be sure to

24 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

HINT Compute—Write a Number Sentence. Write two number sentences to find the number of students who participate in hockey only and the number of students who participate in speed skating only. Use your answers in the Venn diagram.

E L P SAM ATION C U D E !

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STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O Part B O B MPLE SSION IS N UCED IN AN A S S I D THis the totalPnumber What ERMI of students REPRO who participate in these sports?

Answer

students

25 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Seven boys in Mr. Zeller’s class participate in at least one school activity. Curtis and Sergio play baseball only; Mark and Tyler swim only; and Jacob, Devin, and Carlos play baseball and swim. Which Venn diagram correctly represents the data?

Play Baseball

A

Play Baseball

E L P SAM ATION C U D E !

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8 8 8

Curtis Sergio

Mark Tyler

Jacob Devin Carlos

C

Curtis Sergio

Jacob Devin Carlos

Swim

Mark Tyler

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

Mark Jacob Curtis Jacob Curtis Mark GHTEDD OR Devin HIS BOSergio I T R Y P Tyler Devin Sergio Tyler O F C N S E I .

V Y I K A G Carlos Carlos O W T PLE BO SION IS NO CED IN ANY M A S IS DU THIS PERM REPRO Play Baseball

B

Swim

Swim

Play Baseball

Swim

26 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

3

Sonya and seven of her friends take dance classes at the same dance school. Sonya and Lexi go to class on Tuesday only; Maria, Erica, and Cathy go to class on Friday only; and Amy, Leah, and Kara go to class on Tuesday and Friday. Which Venn diagram correctly represents the data?

Tuesday

A

Sonya Lexi

Friday

Maria Erica Cathy

Amy Leah Kara

C

Maria Erica Cathy

Friday

Sonya Lexi

E L P SAM ATION C U D E !

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Tuesday

B

Tuesday

Friday

Tuesday

Amy Leah Kara

Friday

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO Sonya Lexi

Amy Leah Kara

Maria Erica Cathy

D

Amy Leah Kara

Maria Erica Cathy

Sonya Lexi

27 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

The list below shows the number of students who participate in band and chorus at Liberty Middle School.

A total of 38 students participate in band.

A total of 25 students participate in chorus.

There are 10 students who participate in both band and chorus.

Part A Use the list above to complete the Venn diagram in the space below.

Be sure to

E L P SAM ATION C U D E !

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8 8 8

• title the diagram • label each circle • place a number in each section of the diagram

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

Part B What is the total number students who participate in band and chorus?

Answer

students

28 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

The Gourmet Muffin Store surveyed their customers about ingredients. The list below shows the number of customers who like fruit and nuts in their muffins.

A total of 32 customers like fruit.

A total of 35 customers like nuts.

A total of 15 customers like both fruit and nuts.

Part A Use the list above to complete the Venn diagram in the space below.

Be sure to

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

• title the diagram • label each circle • place a number in each section of the diagram

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

Part B What is the total number of customers who like fruit and nuts in their muffins?

Answer

customers

29 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 6.S.4

1

Organization and Display of Data Determine and justify the most appropriate graph to display a given set of data (pictograph, bar graph, line graph, histogram, or circle graph)

George surveys his classmates to find out their favorite exercise. The frequency table below shows this data.

E L P SAM ATION C U D E !

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8 8 8 FAVORITE EXERCISE

Exercise

Frequency

Aerobics

5

STER. A M E Bicycling 10 ACKLIN L B A T O BE Swimming 8IS NO T T K I O .

GHTED OR THIS BO I R Y P NF S CO of graph IVisEbest K Itype AY. George’s data?

G O W Based on the data, which toNY display T O O B N E A L AMP D IN ON IS THIS S PERMISSI EPRODUCE HINT R Jogging

7

Organize—Make a Chart or List. Make a list of each type of graph you could use and the type of data best displayed in each graph. Then choose the type of graph that is best for George’s data.

Answer

30 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

On the lines below, explain why the graph you chose is best to display George’s data.

E L P SAM ATION C U D E !

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8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

31 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Ms. Hamilton bought some stock and is recording the highest weekly price for the stock. The table below shows her data.

STOCK PRICES Week

Highest Price

1

$49.95

2

$65.95

3

$59.95

4

$45.95

E L P SAM ATION C U D E !

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8 8 8

Based on the data, which type of graph is best to display Ms. Hamilton’s data?

STER. A M E ACKLIN L Answer B A S NOT OK TO BE I T I .

On the lines below, explain why the graph O to display GHTED youOchose HISis Bbest I T R Y R P Ms. Hamilton’s data.

O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

32 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

3

Last week, Joel kept track of how he spent his weekly allowance. The table below shows his data.

WEEKLY ALLOWANCE Items Bought

Percent of Allowance

Snacks

50%

Games

20%

School Supplies

25%

Other

5%

E L P SAM ATION C U D E !

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8 8 8

Based on the data, which type of graph is best to display Joel’s data?

Answer

On the lines below, explain why the graph you chose is best to display Joel’s data.

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

33 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Claire is working on a science project about the heaviest marine mammals.

The table below shows her data.

HEAVIEST MARINE MAMMALS Mammal

Weight (in pounds)

Blue Whale

300,000

Right Whale

234,000

Fin Whale

140,000

Bowhead Whale

120,000

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Based on the data, which type of graph is best to display Claire’s data?

Answer

On the lines below, explain why the graph you chose is best to display Claire’s data.

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

34 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

Trey used an almanac to find the average monthly temperatures for Albany, New York, from July through December. The table below shows his data.

ALBANY’S AVERAGE MONTHY TEMPERATURE Month

Temperature (in °F)

July

71

August

69

September

61

October

49

November

39

December

28

E L P SAM ATION C U D E !

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8 8 8

Based on the data, which type of graph is best to display Trey’s data?

STER. A M E IN Trey’s data.

On the lines below, explain why the graph you chose is best ACtoKLdisplay L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO Answer

35 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.S.2 1

Organization and Display of Data Display data in a circle graph

Tyra surveyed 20 of her classmates to determine their favorite winter Olympic sport. The survey results are shown in the table below.

E L P SAM ATION C U D E !

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8 8 8 FAVORITE WINTER OLYMPIC SPORT Sport

Number of Students

Alpine skiing

111

Speed skating

5

Bobsledding

11

Figure skating

55

STER. A M E ACKLIN L B A OT O BE S Ntable?

I T T K I Which circle graph best represents the data in the O .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O HINT T O O B N LE S N table simpler IN Aby MItPSimpler.

N Ithe A D O I S E Make Make counting the tally marks and S C S S U I I D M TH O R R E P P E writing the number of R students for each sport. Then write a fraction for each sport to show what part of the whole it is. Look at each answer choice to find the circle graph that shows those fractions.

36 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Alpine skiing

Speed skating

Alpine skiing

A

Figure skating

C Speed skating

Figure skating

Bobsledding

Bobsledding

B

E L P SAM ATION C U D E !

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Figure skating

Bobsledding

Figure skating

Alpine skiing

Alpine skiing

D

Speed skating

Bobsledding

Speed skating

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

37 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

A frozen yogurt store owner surveys 40 customers to determine their favorite flavor of frozen yogurt. The survey results are shown in the table below.

FAVORITE FROZEN YOGURT FLAVOR Flavor

Number of Customers

Chocolate

554

Vanilla

554

Strawberry

5111

Raspberry

4

E L P SAM ATION C U D E !

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8 8 8

Which circle graph best represents the data in the table?

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

Raspberry Chocolate GHTECD OR THIS BOChocolate I R Y P O IVEN FStrawberry K IS C AY. G O W T O Y O B N N E A L IS AMP D IN Strawberry VanillaON THIS S PERMISSI EPRODUCE R Raspberry

A

Vanilla

Raspberry Raspberry

Strawberry

B

Chocolate

D Strawberry

Chocolate Vanilla

Vanilla

38 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

3

Christopher spent 60 minutes doing his homework yesterday. The number of minutes he spent on each subject is shown in the table below.

TIME SPENT ON HOMEWORK Subject

Number of Minutes

Math

15

English

10

History

15

Science

20

E L P SAM ATION C U D E !

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Which circle graph best represents the data in the table?

Math

A

C

Math

STER. A M E ACKLIN L B A History English S NOT OK TO BE I T I .

History GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO Science

B

Science

Science

English

Math

Math

D

Science English

English History History

39 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Joanna has 100 music CD’s. The types of music and number of each type of music she has are shown in the table below.

JOANNA’S CDS Type of Music

Number of CDs

Rock

60

R&B/Hip-Hop

10

Country

5

Pop

25

E L P SAM ATION C U D E !

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8 8 8

Which circle graph best represents the data in the table?

Green

A

Pop

Blue

Rock

C

Pop

Rock

STER. A M E ACKLIN L B A R&B/ Country S NOT OK TO BE I Hip-Hop T I .

Red Green GHTED OR THIS BO I R Y P O IVEN F Country K IS C AY. R&B/Hip-Hop G O W T O Y O B N N E A L AMP D IN ON IS THIS S PERMISSI EPRODUCE R Blue

Green

Pop

B

Pop

D Country

Rock

Country

R&B/ Hip-Hop

Rock

R&B/Hip-Hop

40 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

Mr. Chao’s class raised $200 at the school fair. The results for each booth are shown in the table below.

MONEY RAISED BY MR. CHAO’S CLASS Booth

Amount Raised

Baked goods

100

T-shirts

35

Games

50

Drinks

15

E L P SAM ATION C U D E !

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8 8 8

Which circle graph best represents the data in the table?

Games

A

C

Games

Baked Goods

STER. A M E Drinks T-shirts ACKLIN L B A S NOT OK TO BE I T I .

T-shirts GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO Drinks

Baked Goods

Games

B Drinks

D

Baked Goods

Games

T-shirts

Baked Goods

T-shirts Drinks

41 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.S.3 1

Organization and Display of Data Convert raw data into double-bar graphs and double-line graphs

The local post office recorded the number of books of first-class stamps it sold each week. The table below shows the data recorded each day during the first week and the second week.

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8 8 8 NUMBER OF BOOKS OF STAMPS Day

Week 1

Week 2

Monday

50

40

Tuesday

41

31

STER. A M E LIN Thursday 35 25A BLACK S NOT30 OK TO BE Friday 40ED. IT I GHT HIS BO I T R Y R P O O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO Wednesday

55

45

42 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

On the grid below, create a double-bar graph that shows the number of books of stamps sold 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

HINT Organize—Make a Chart or List, Graph, Sort Data. Look at the number of books of stamps sold each day and the size of the grid for your graph. Think about what would be the best scale for the graph.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

43 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Ms. Collins recorded the monthly average price of two stocks she bought. The table below shows the data recorded each month for four months.

MONTHLY AVERAGE STOCK PRICE Stock

January

February

March

April

Stock A

$26

$38

$28

$32

Stock B

$15

$24

$32

$35

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

On the grid below, create a double-line graph that shows the monthly average stock prices for the four months.

Be sure to

• title the graph • label the axes • provide an appropriate key for the graph

• graph all the dataASTER. M LINE for • provide the graph LACaKscale

OT A B TO BE N S I T BOOK TED. I S H I G H I T R COPY GIVEN FOR S I K AY. O W T O Y O B N N E A L AMP D IN ON IS THIS S PERMISSI EPRODUCE R

44 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

3

Robert recorded the number of miles he jogged each week. The table below shows the data recorded each week during two months.

NUMBER OF MILES JOGGED Week

May

June

1

28

34

2

29

30

3

25

31

4

30

36

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 miles Robert jogged each week during the two months.

Be sure to

• title the graph • label the axes • provide an appropriate key for the graph

• graph all the data • provide a scale for the graph

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

45 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Madeleine surveyed 100 seventh graders at her school to determine their favorite color. The table below shows her data for the boys and girls in the survey.

SEVENTH GRADERS FAVORITE COLOR Color

Boys

Girls

Blue

21

18

Red

15

17

Green

9

11

Yellow

5

4

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 boys and the number of girls that chose each color.

Be sure to

• title the graph • label the axes • provide an appropriate key for the graph

• graph all the data • provide a scale for the graph

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

46 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

Kevin and Darius recorded their weekly earnings for their summer jobs. The table below shows the data recorded each week for Kevin and Darius.

SUMMER EARNINGS Week

Kevin

Darius

1

$52

$65

2

$75

$87

3

$83

$60

4

$100

$90

5

$78

$62

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 earnings for Kevin and Darius for each week.

Be sure to

• title the graph • label the axes • provide an appropriate key for the graph

• graph all the data .

STERgraph • provide a scaleE for MAthe

ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

47 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Analysis of Data E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Student Expectation

7.S.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Calculate the range for a given set of data 7.S.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Select the appropriate measure of central tendency

STER. A M E 7.S.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B.L.A.C.K.L.IN . 55 A T O Read and interpret data represented graphically O BE S N (pictograph, I T T K I O .

ED line/bar BO bar graph, histogram, line graph, GHTdouble HISgraphs, I T R Y R P O or circle graph.) K IS CO IVEN F Y WAY. G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

48 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.S.4 1

Analysis of Data Calculate the range for a given set of data

The annual salaries of the employees working at Julie’s computer store are listed below.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

$18,600.00

$25,100.00

$19,550.00

$21,900.00

$30,665.00

$42,225.00

$35,700.00

$38,300.00

What is the range for these salaries?

HINT

Use a Formula or Rule. Put the salaries in order from greatest to least.

Then use the rule Range = the greatest value – the least value. TER.

A B C

E MAS N I L K C A BLA BE T O N . IT IS IS BOOK TO D E T $23,625 H PYRIG EN FOR TH .

O C S I $22,675 AY GIV OK W T O Y O B N N E A L AMP D IN ON IS $19,700 THIS S PERMISSI EPRODUCE R

D $18,750

49 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Paul’s scores on his last six math tests are listed below.

85

92

100

77

99

75

What is the range for these test scores?

A 10 B 23 C 25 D 77

3

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

The prices of the houses sold by a real estate agent last month are listed below. $150,000

$225,300

$189,900

$178,500

$245,700

$125,500

$301,200

$276,900 LINE

BLACK E A T O What is the range for these prices?

T IS N BOOK TO B I .

D E T A $126,900 YRIGH N FOR THIS P O C IS AY. GIVE W T B $175,700 LE BOOK Y O N N A AMP D IN ON IS C $178,500 THIS S PERMISSI EPRODUCE R

R. MASTE

D $245,700

50 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Whitney’s bowling scores are listed below.

200

132

95

214

157

111

167

What is the range for these bowling scores?

A 33 B 99 C 105 D 119

5

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Jake worked on his science project last week. He worked 35 minutes on Monday, 44 minutes on Tuesday, 37 minutes on Wednesday, 91 minutes on Thursday, and 75 minutes on Friday. What is the range for the data?

A 16 minutes B 54 minutes C 56 minutes

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

D 75 minutes

51 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.S.5 1

Analysis of Data Select the appropriate measure of central tendency

Last week, a clothing store owner recorded the size of every dress sold.

The data is shown below.

6 10

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 8

8

10

1

2

8

8

8

6

1

4

4

8

8

Which measure of central tendency should the owner find to know the most popular size sold?

HINT

Guess and Check. Look at each answer choice and think about theTER. S MAnumber N definition of each one. Which measure of central tendency isEthe I L K C LA that occurs most frequently in the data? NOT A B BE

A B

. IT IS IS BOOK TO D E T H G H OPYRI IVEN FOR T Y. C S I OOK OT G IN ANY WA N median MPLE B S I A D ON THIS S PERMISSI EPRODUCE mode R

C mean D range

52 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Mr. Ventura buys his lunch every day. The amounts he spent for lunch last week are shown below. $5.65

$6.12

$4.95

$6.50

$5.35

$6.20

$5.86

Which measure of central tendency should Mr. Ventura find to know the average amount he spent per day on lunch?

A median B mode C range D mean

3

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

The annual salaries of the employees working at Amy’s restaurant are listedEbelow.

R.

MAST E N I L $15,600.00 $24,300.00 $19,550.00 $21,900.00 BLACK E A T O T IS N BOOK TO B $30,665.00 $42,225.00 $35,700.00 I .

D E GHT THIS R O OPYRIshould F C Which measure of centralIS tendency Amy find to Y know . the salary that is IVEN K A G O W T O Y O B lower than half AN of the salaries?

S NhigherEthan IN half MPLofE the salaries N Iand A D O I S S C S S U I I D TH PERM A median REPRO B mean C range D mode

53 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Liam’s scores on a video game are shown below.

20,000

8,000

50,000

15,000

25,000

Which measure of central tendency should Liam find to know his average score?

A range B mode C mean D median

5

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Audrey recorded the ages of the students in the chess club. Her data is shown below.

13

14

15

14

14

13

12

14

14

15

Which measure of central tendency should Audrey use to find the most common age of the students in the chess club?

STER. A M E ACKLIN L B A mode S NOT OK TO BE I T I . mean GHTED OR THIS BO I R Y P O median IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

A range B C D

54 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.S.6

1

Analysis of Data Read and interpret data represented graphically (pictograph, bar graph, histogram, line graph, double line/bar graphs, or circle graph.)

The pictograph below shows the number of runners who participated in a local marathon.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 MARATHON RUNNERS

Age Group 18-25 26-45

Number of Runners

KEY = 10 runners TER.

E MAS N I L K C 46-75 A BLA =B5Erunners T O N . IT IS IS BOOK TO D E T H G TH OR26-45 OPYRI were F C N How many of the marathon runners in the S E I V Y. group?

Aage GI OK W T O Y O B N N E A L IS P IN IS SAM ERMISSION RODUCED THHINT P REP

Compute—Write a Number Sentence. First count the number of symbols for the 26-45 age group. Then use that number and the information in the Key to write a number sentence.

A 40 B 60 C 100 D 105

55 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

The table below shows the grade level of 100 students who volunteered for Trash Pick-Up Day at the lake.

STUDENT VOLUNTEERS Grade

Number of Students

6

21

7

25

8

20

9

34

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Which bar graph displays this data correctly?

0

6

7

8

Number of Students

Number of Students

A

STER. A M E STUDENT VOLUNTEERS STUDENT CKLIN AVOLUNTEERS L B A 40 NOT O BE S 40 I T T K I 35 35 O .

30 GHTED OR 30THIS BO I R Y P O 25 IVCEN F 25 K IS C AY. G O 20 20 W T O Y O B N N E A L 15AMP ION IS ODUCED IN 15 S S S I 10 M THIS 10 P ER 5 5 REPR 9

0

6

Grade

D

6

7

9

STUDENT VOLUNTEERS

8

9

Grade

Number of Students

Number of Students

B

8

Grade

STUDENT VOLUNTEERS 40 35 30 25 20 15 10 5 0

7

40 35 30 25 20 15 10 5 0

6

7

8

9

Grade

56 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

3

The circle graph below shows the number of students who participate in school clubs.

NUMBER OF STUDENTS IN SCHOOL CLUBS Art Club, 16

Science Club, 30

Environmental Club, 21

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 Math Club, 25

Chess Club, 28

What percent of the total number of students in school clubs are in the Science club?

STER. A M E 20% ACKLIN L B A S NOT OK TO BE 25% I T I .

GHTED OR THIS BO I R 30% Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

A 13% B C D

57 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

The pictograph below shows the number of students who ride the school bus at Taft Middle School.

STUDENTS RIDING SCHOOL BUS Grade

Number of Students KEY

6 7

= 6 students

8

= 3 students

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

How many 8th-grade students at Taft Middle School ride the school bus?

A 42 B 45 C 48

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

D 51

58 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

The table below shows the lowest recorded temperatures, in degrees Fahrenheit (°F), in Alaska each month for four months.

LOW TEMPERATURES Month

Temperature (°F)

March

–16

April

–5

May

26

June

42

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Which line graph displays this data correctly? y LOW TEMPERATURES 50 40

50 40

30

C

Temperature (°F)

STER. A M E 20 20 CKLIN A L B A 10 10 OT O BE S0 N I T T K I O .

0 GHTED O210R THIS BO I R Y P 210 O IVEN F220 Y WAY. K IS C G O x T O 220 O B AN March April May June x SN IJune PLEApril SMay N March I M N A D O I S E DUC THIS RMIS Month PEMonth REPRO Temperature (°F)

A

y LOW TEMPERATURES

30

y LOW TEMPERATURES

50

50

40

40

30

D

20 10 0

210

Temperature (°F)

B

Temperature (°F)

y LOW TEMPERATURES

30 20 10 0

210

x

220 March

April

May

June

x

220 March

Month

April

May

June

Month

59 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

60 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Predictions from Data E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Student Expectation

7.S.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Identify and explain misleading statistics and graphs

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

61 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.S.7 1

Predictions from Data Identify and explain misleading statistics and graphs

Mr. Zamore recorded the number of people who visited the art museum each day for a week. He graphed the data in two different ways.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 GRAPH A

Number of Visitors

y

400 300 100

50

ER. x MAST E Sat Sun Mon Tues Wed Thu Fri ACKLIN L B A Day S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEBN F Y WAY. K IS C GRAPH G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PyERM REPRO 0

270

Number of Visitors

240 210 180 150 120 90 60 30 0

x Sun

Mon

Tues

Wed

Thu

Fri

Sat

Day

62 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Which one of the two graphs is misleading?

HINT Look for a Pattern. Look at the scale for each graph. Do the numbers follow a pattern? Remember that a scale must have equal intervals.

Answer On the lines below, explain why the graph you chose is misleading.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

63 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

The owner of a hot dog concession stand recorded the number of hot dogs sold by her employees. The owner graphed the data in two different ways.

GRAPH A

Number of Hot Dogs

110

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 90

70 60 50

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEBN F Y WAY. K IS C GRAPH G O T O O B MPLE SSION IS N UCED IN AN A 110 S S I D TH 100 PERMI REPRO Number of Hot Dogs

40

90 80 70 60 50 40 30 20 10 0

Jan

Lisa

Jerome Employee

Arthur

Clay

Jan

Lisa

Jerome Employee

Arthur

Clay

64 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Which one of the two graphs is misleading?

Answer On the lines below, explain why the graph you chose is misleading.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

65 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

3

Larissa recorded the number of miles she ran during the month of May. She graphed the data in two different ways.

GRAPH A y 45

Number of Miles

40 35 30 25

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 20 15 10 5 0

1

2

3

x

4

Week

Number of Miles

STER. A M E GRAPH B ACKLIN L B A S NOT OK TO BE y I T I .

GHTED OR THIS BO I R Y P 50 IS CO VEN F Y WAY. I K G O T O O B PLE M40 N IS N UCED IN AN A O I S S S S I I 22 RM D TH PE REPRO 20 10 0

x 1

2

3

4

Week

66 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Which one of the two graphs is misleading?

Answer On the lines below, explain why the graph you chose is misleading.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

67 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Katie recorded the number of tickets for the school play that she and four other students sold last week. She graphed the data in two different ways.

GRAPH A

Number of Tickets

80 75 70 65 60

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 55 0

Katie

James

Rachel Student

Jorge

Maria

GRAPH B

STER. A M E ACKLIN L 70 B A S NOT OK TO BE I 60 T I .

GHTED OR THIS BO I R Y 50 P O IVEN F Y WAY. K IS C G T 40 LE BOO O MP N IS N UCED IN AN A O I S S S S I I 30 D TH PERM REPRO Number of Tickets

80

20 10 0

Katie

James

Rachel Student

Jorge

Maria

68 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Which one of the two graphs is misleading?

Answer On the lines below, explain why the graph you chose is misleading.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

69 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

Marvin recorded his last six math test scores. He graphed the data in two different ways.

GRAPH A y 120

Score

100 80 60 40

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 20

0

1

2

3

4

5

x

6

Test

GRAPH B

y

STER. A M E ACKLIN L B 96 A S NOT OK TO BE I T I 92 .

GHTED OR THIS BO I R Y 88 P IS CO IVEN F Y WAY. G T 84 E BOOK O PL M80 N IS N UCED IN AN A O I S S S S I I D TH PERM REPRO x Score

100

0

1

2

3

4

5

6

Test

70 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Which one of the two graphs is misleading?

Answer On the lines below, explain why the graph you chose is misleading.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

71 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

72 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Probability E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Student Expectation

7.S.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Interpret data to provide the basis for predictions and to establish experimental probabilities 7.S.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Determine the validity of sampling methods to R. predict outcomes MASTE

LINE K C A L B 7.S.10 . . . . . . . . . . . . . . . . . . . . . . . . . . .S. N .O . .T. A. . . . . . .O. .B83 E I T T K I O .

Predict the outcome of an experiment GHTED OR THIS BO I R Y P EN F . . .W. .A.Y.. . . . . . . . 86 IS CO 7.S.11 . . E. .B.O. O .K . . . . . . . .N.O. T. .G.I.V. . . . . . N A Y L Sexperiment I Pand N I M N A D O I S Design conduct an to test predictions E UC ISS D THIS O R P PERM RE

7.S.12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Compare actual results to predicted results

73 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.S.8

1

Probability Interpret data to provide the basis for predictions and to establish experimental probabilities

The population of Houston, Texas, throughout the 20th century is shown in the table below.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 POPULATION OF HOUSTON

Year

Population (in millions)

1900

0.05

1920

0.1

STER. A M E ACKLIN 1960 0.9 L B A S NOT OK TO BE I T I 1980 1.4 .

GHTED OR THIS BO I R Y P F 2000IS CO IVEN1.9 K AY. G O W T O Y O B N N E A L SAMP MISSION IS ODUCED IN S I H T Between which P two ER years didRthe EPRpopulation increase the least?

1940

Answer between

0.4

and

HINT Compute—Write a Number Sentence. Write number sentences to find the differences in population from year to year. Then compare the differences.

74 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Based on the data in the table, predict the population of Houston in the year 2020.

Justify your prediction on the lines below.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

75 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

During baseball tryouts, each player is at bat 5 times. The table below shows the number of hits gotten by 60 players.

TRYOUT HITS Number of Hits

Number of Players

0

4

1

11

2

13

3

22

4

8

5

2

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E KLIN ACget L B What is the experimental probability that the next player will 3 or more hits?

A OT BE N O S I T T K I O .

22 GHTED OR THIS BO I A R Y P 60 IS CO IVEN F Y WAY. K G O T O O B 30 MPLE SSION IS N UCED IN AN B A S S I D T60H ERMI P REPRO 32 C

D

60 50 60

76 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

3

The table shows the attendance at the football games during the first 4 games of the season.

FOOTBALL GAME ATTENDANCE Game

Number of People

1

2,361

2

2,422

3

2,485

4

2,543

5

?

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Based on the data in the table, which is the best prediction for how many people attended the fifth football game?

A 2,600 B 2,800 C D

TER. S A M E 3,000 ACKLIN L B A 3,200 S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

77 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Tia has a bag containing 20 marbles. The table below shows the number of marbles of each color in the bag. As part of a probability experiment for her math class, Tia randomly picks a marble from the bag and then replaces it. She repeats this 200 times.

TIA’S BAG OF MARBLES

Part A

Marble Color

Number of Marbles

Red

4

Green

6

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8 Blue

7

Black

3

Tia randomly picks a marble from the bag. What is the probability the marble will be blue?

R.

ASTE M E N I L Show your work.

BLACK E A T O T IS N BOOK TO B I .

D E T YRIGH N FOR THIS P O C AY. GIVE OK IS W T O Y O B N N E A L AMP D IN ON IS THIS S PERMISSI EPRODUCE R

Answer

Part B Predict the number of times out of 200 Tia will pick a blue marble.

Show your work.

Prediction

times

78 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

The attendance at a regional soccer tournament from 2003 to 2008 is shown in the table below.

ATTENDANCE AT SOCCER TOURNAMENT Year

Number of People (in thousands)

2003

2.5

2004

2.8

2005

3.1

2006

3.6

2007

3.9

2008

4.2

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Between which 2 years did the attendance increase the most?

STER. A M E KLIN tournament in ACsoccer Based on the data in the table, predict the attendance at the L B A OT O BE S Nbelow. the year 2009. Justify your prediction on the Ilines I T T K O .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO Answer

79 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.S.9 1

Probability Determine the validity of sampling methods to predict outcomes

A reporter for a sports magazine surveys teenagers leaving a football game to determine which sport teens like best. Which statement best explains why the results of this survey may not be valid?

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

HINT

Guess and Check. Read each answer choice. Think about how the survey might be biased because it was done at a football game.

STER. A M E The group surveyed consisted only of teenagers.

ACKLIN L B A NOT one magazine.

The survey was conducted by a reporter from O BE S only I T T K I O .

O HTEDteenagers IS Battended Hwho The group surveyed consisted ofIGonly a T R Y R P O O F C N S E I .

V Y football game. OOK OT GI IN ANY WA B N E L S I P M A D ON THIS S PERMISSI EPRODUCE R

A The survey should have been conducted online.

B C D

80 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Juana surveyed students in one middle school about their favorite music. Of the 1,204 students in the middle school, 70 sixth-grade students were surveyed.

More than half of the 70 students said their favorite music is hard rock. Based on the survey, Juana says most middle school students’ favorite music is hard rock.

Why is Juana’s statement incorrect?

A Juana surveyed too many students.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

B Juana’s survey sample was too small.

C Juana did not survey any high school students.

D Juana did not include any teachers in the survey.

3

A marketing person for a local radio station surveys every fifth person leaving the mall to determine which radio station teens like best. Which statementTER. AS best explains why the results of this survey may not be valid? KLINE M A B C D

BLAC A T O The group surveyed did not consist only of Iteenagers.

O BE SN T T K I O .

GHTED online.

HIS BO I The survey should have beenYconducted T R R P O O F IVENfrom K IS C by aOperson AY.radio station.

G O The survey wasBconducted just one W T O Y N N E A L D IN who shopped at the mall.

ION IS only SAMPsurveyed Epeople S C The consisted of S U I D M THISgroup O P ER REPR

81 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Don surveyed students in one middle school about their favorite food. Of the 1,512 students in the middle school, 150 seventh-grade students were surveyed.

More than half of the 150 students said their favorite food is meatloaf. Based on the survey, Don says most middle school students’ favorite food is meatloaf.

Why is Don’s statement incorrect?

A Don did not include enough food types in the survey.

B Don did not survey any second-grade students C Don’s survey only included seventh-graders.

D Don surveyed too many students.

5

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Carly surveys the members of the computer club to determine how many hours middle-school students spend on the internet. Which statement best explains why the results of this survey may not be valid.

A The group surveyed consisted only of middle-school students.

B The group surveyed was too large.

STER. A M E The group surveyed consisted only of members of theBcomputer ACKLIN club.

L A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

C The group did not include any high-school students.

D

82 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.S.10 1

Probability Predict the outcome of an experiment

Rebecca has 5 silver rings and 2 gold rings in her jewelry box. Rebecca randomly picks one ring. Which statement best describes which ring she will probably pick?

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

HINT

Guess and Check. Find the probability of picking a silver ring and the probability of choosing a gold ring. Then look at each answer choice and check it against the probabilities that you found.

STER. A M E She definitely will pick a silver ring.

ACKLIN L B A She probably will pick a gold ring.

S NOT OK TO BE I T I .

GHTED OR THIS BO I She definitely will pick a gold ring.

R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

A She probably will pick a silver ring.

B C D

83 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

A spinner is divided into 9 equal sections numbered 1 through 9. Predict how many times out of 270 spins the spinner is most likely to stop on an even number.

A 60 B 90 C 120 D 150

3

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Jim has 3 green markers and 8 red markers in a box. Jim randomly picks one marker. Which statement best describes which marker he will probably pick?

A He definitely will pick a red marker.

B He definitely will pick a green marker.

STER. A M E ACKLIN L B A D He probably will pick a red marker.

S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O F IS Cequal .

IVENnumbered K five A1Ythrough G O W T O A spinner is divided into sections 5. Predict how Y O B N N E A L S I P N I M N A D O I S E S the spinner many IS out ofER250 MISspins THtimes ODUC is most likely to stop on a number greater R P P E R than 3.

C He probably will pick a green marker.

4

A 50 B 100 C 150 D 200

84 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

Nadia has 7 pairs of red socks, 3 pairs of blue socks, and 1 pair of white socks in a drawer. Nadia randomly picks one pair of socks. Which statement best describes which pair of socks Nadia will probably pick?

A She probably will pick a pair of white socks.

B She definitely will pick a pair of blue socks.

C She probably will pick a pair of red socks.

D She definitely will pick a pair of red socks.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

85 Š R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.S.11 1

Probability Design and conduct an experiment to test predictions

Arielle has a number cube numbered 1 through 6. Arielle predicts that when she rolls the number cube 20 times, she will roll a 5 ten times.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Which experiment would be best to use to test Arielle’s prediction?

HINT

Organize—Make a Chart or List. Make a list of all of the information in the problem. Then choose the answer choice that matches that information.

STER. A M E ACKLIN L roll a number cube numbered 1 through 5 twenty times B A S NOT timesOK TO BE I T I roll a number cube numbered 1 through 6 twenty .

GHTED OR THIS BO I R Y P O spin the pointer on a spinner 6 .twenty times Y IVEN1F through K IS C numbered A G O W T O Y O B N N E A L AMP D IN ON IS THIS S PERMISSI EPRODUCE R

A roll a number cube numbered 1 through 6 ten times B C D

86 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Tucker predicts that when he flips a coin 50 times, the coin will land on heads 22 times.

Which experiment would be best to use to test Tucker’s prediction?

A flip a coin 50 times B flip a coin 25 times

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

C spin the pointer on a spinner numbered 1 through 2 fifty times D roll a number cube numbered 1 through 6 fifty times

3

Cassie has two number cubes numbered 1 through 6. Cassie predicts that when she rolls the number cubes 50 times, she will get a sum of 12 ten times.

Which experiment would be best to use to test Cassie’s prediction?

LINE A B C D

R. MASTE

BLACK E A T O N roll two number cubes numbered 1 thoughIS times TO B T 6 twenty-five K I O .

D O E B spin the pointer on a spinnerYnumbered THIS 6 fifty times RIGHT 1FOthrough R P O C VEN 6 Yfifty Y. Atimes G1 Ithrough OK ISnumbered roll two number cubes W T O O B N N E A L MP N IS IOnumbered SAnumber ED IN 6 one hundred times S C roll cubes 1 through S U I D M THIStwo O P ER REPR

87 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Angelo predicts that when he flips a coin 60 times, the coin will land on tails 40 times.

Which experiment would be best to use to test Angelo’s prediction?

A flip two coins 30 times B flip a coin 60 times C spin the pointer on a spinner numbered 1 through 2 sixty times D flip a coin 100 times

5

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Tierra has a spinner that is divided into 8 equal parts which are numbered 1 through 8. She predicts that when she spins the pointer of the spinner 40 times, the pointer will land on an odd number 40 times.

Which experiment would be best to use to test Tierra’s prediction?

A spin the spinner 100 times

B spin a spinner divided into 4 equal parts numbered 1 through 4 eighty times C D

STER. A M E roll a number cube numbered 1 through 8 forty times ACKLIN A BL T O N spin the spinner 40 times O BE S I T T K I O .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

88 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.S.12 1

Probability Compare actual results to predicted results

In a basketball contest, Robin predicted she would make 75 percent of her shots.

She actually made 15 out of 20 shots. How did Robin’s prediction compare with her actual results?

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

HINT

Compute—Write a Number Sentence. Write a fraction for 15 out of 20 and write a number sentence to change the fraction to a percent. Then compare that percent to 75 percent.

A B C D

STER. A M E Her prediction was higher than her actual results.

ACKLIN L B A Her prediction was the same as her actual results.

S NOT OK TO BE I T I .

TED results.

Her prediction was lower thanRher GHactual HIS BO I T Y R P O O EN Fher actual .

IVwith Her prediction cannot K ISbeCcompared AYresults.

G O W T O Y O B N N E A L AMP D IN ON IS THIS S PERMISSI EPRODUCE R

89 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Eli predicted that when he tossed a coin 40 times, the result would be heads for 50 percent of the tosses. The coin actually landed on heads 25 times. How did Eli’s prediction compare with his actual results?

A His prediction was the same as his actual results.

B His prediction was higher than his actual results.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

C His prediction was lower than his actual results.

D His prediction cannot be compared with his actual results.

3

In a soccer contest, Jay predicted he would make 60 percent of his goal shots.

He actually made 9 out of 25 goal shots. How did Jay’s prediction compare with his actual results?

STER. A M E ACKLIN L B His prediction was the same as his actual result.

B A NOT results.K TO BE Sactual I T I C His prediction cannot be compared with his .

BOO TED S H I G H I T R D His prediction was lower OPY his actual FOR Cthan Nresults.

S E I V I K AY. G O W T O Y O B N N E A L AMP D IN ON IS THIS S PERMISSI EPRODUCE R she rolled a number cube numbered 1 through 6 Charlotte predicted that when A His prediction was higher than his actual result.

4

150 times, the number cube would land on 6 twenty percent of the time. The number cube actually landed on 6 twenty-four times. How did Charlotte’s prediction compare with her actual results?

A Her prediction was the same as her actual results.

B Her prediction was lower than her actual results.

C Her prediction was higher than her actual results.

D Her prediction cannot be compared with her actual results.

90 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

In a baseball hitting contest, Emmanuel predicted he would get a hit 55 percent of his times at bat. He actually got a hit 11 times out of 20 times at bat. How did Emmanuel’s prediction compare with his actual results?

A His prediction cannot be compared with his actual results.

B His prediction was lower than his actual results.

C His prediction was higher than his actual results.

D His prediction was the same as his actual results.

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

91 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

92 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

93 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

94 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

95 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

96 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I .

GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

G

Strand Strand BY

E L P SAM ATION C U D E !

Y L RAL 99.RALLY .

8 8 8

Math Strand-by-Strand provides instructional practice in math problem-solving. Students are taught several different problem-solving strategies.

Each of the 5 math strands are in a separate book: • • • • •

Number Sense and Operations Algebra Geometry Measurement Statistics and ProbabilityIGHTED.

STER. A M E ACKLIN L B A E OT IT IS N BOOK TO B THIS YR R P O O F C GIVEN NY WAY. OK IS T O O B N E L IN A MP N IS A D O I S E S C S S U I I D TH PERM REPRO