The Percent Circle: Making Circle Graphs - Everyday … 5 11 349 Advance Preparation ... The Percent...

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Lesson 5�11 349

Advance PreparationFor Part 1, convert snack-survey data from Lesson 5�9 to percents, rounded to the nearest whole percent. List the snacks and percents in a table on the board or the Class Data Pad. Students will need Percent Circles from the Geometry Template or Math Masters, page 426 or 427. For the optional Readiness activity in Part 3, divide each circle on Math Masters, page 428 into three or four sections and label them A, B, C, and D. Write the same labels in the boxes to the left of the answer blanks before copying the master.

Teacher’s Reference Manual, Grades 4–6 pp. 44–46, 161–167, 234–236

Key Concepts and Skills• Find fraction and percent equivalents.

[Number and Numeration Goal 5]

• Measure sectors of a circle graph using the Percent Circle. [Measurement and Reference Frames Goal 1]

• Construct circle graphs from table data. [Data and Chance Goal 1]

• Interpret data presented in various forms. [Data and Chance Goal 2]

Key ActivitiesStudents use the Percent Circle to construct circle graphs. They use journal page data and the snack-survey data collected in Lesson 5�9. They practice finding fractional parts of sets by playing Fraction Of.

Ongoing Assessment: Informing Instruction See page 351.

Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip (Math Masters,page 414). [Data and Chance Goal 1]

MaterialsMath Journal 1, pp. 151, 157, and 158Student Reference Book, p. 313 Study Link 5�10Math Masters, pp. 414, 426, and 427 (optional); pp. 464–466 and 469Geometry Template � Class Data Pad (optional) � chalkboard compass, for demonstration purposes � counters

Finding Decimal Equivalents for Sevenths and EighthsMath Journal 1, inside back coverStudents fill in the decimals for sevenths and eighths in the Table of Decimal Equivalents.

Math Boxes 5�11Math Journal 1, p. 159Students practice and maintain skillsthrough Math Box problems.

Study Link 5�11Math Masters, p. 150Students practice and maintain skillsthrough Study Link activities.

READINESS

Measuring Circle GraphsMath Masters, p. 428Geometry TemplateStudents use a Percent Circle to measure sectors in a circle graph.

ENRICHMENTCalculating Percents: On the Square1 index card � 1 sheet of scrap paper � per group: masking tape, 12" by 12" paper squareStudents collect, calculate, and compare fractions and percents in statistical data.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

��

The Percent Circle:Making Circle Graphs

Objective To introduce constructing circle graphs using the Percent Circle.

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

349_EMCS_T_TLG1_G5_U05_L11_576825.indd 349 2/14/11 1:22 PM

Making Circle Graphs: Concrete RecipeLESSON

5 �11

Date Time

Concrete is an artificial stone. It is made by first mixing cement and sand with gravel orother broken stone. Then enough water is mixed in to cause the cement to set. Afterdrying (or curing), the result is a hard piece of concrete.

The cement, sand, and gravel are commonly mixed using this recipe.

Use your Percent Circle to make a circle graph for the above recipe in the circle below.Label each sector of the graph and give it a title.

sand

Recipe for Dry Mix for Concrete

cement

gravel

Recipe for Dry Mix for ConcreteMaterial Fractional Part of Mix Percent Part of Mix

Cement �16� 16�

23�%

Sand �13� 33 �

13�%

Gravel �12

� 50%

Math Journal 1, p. 157

Student Page

350 Unit 5 Fractions, Decimals, and Percents

Getting Started

1 Teaching the Lesson

▶ Math Message Follow-Up

INDEPENDENT ACTIVITY

(Math Journal 1, pp. 151 and 158)

Survey the class to verify that students have copied the data from Lesson 5-9 correctly. Ask students to write the number of votes for each snack as a fraction of the total number of votes. Students should write this fraction in the third column of the table on journal page 158.

▶ Constructing a Circle Graph

WHOLE-CLASS ACTIVITY

Using the Percent Circle(Math Journal 1, p. 157)

As a class, read the information about mixing concrete on journal page 157. Ask volunteers how they would go about constructing a circle graph for this data. Ask students questions such as the following:

● How many pieces (sectors) must the graph have? Three—one for each dry ingredient (concrete, sand, and gravel)

● How should the pieces be labeled or colored? If the graph is labeled correctly, colors might help, but they are not necessary. Some students may suggest using symbols to mark the pieces.

● How can the Percent Circle be used to make each piece the correct size? Use the tick marks on the Percent Circle to draw sectors with measures matching the percents given on the table.

Have students demonstrate their circle-graph construction methods, using a chalkboard compass and a large paper Percent Circle on the board (or a compass and transparency of the Percent Circle on the overhead). Have students take turns sketching sections of the circle. Then have them complete the circle graph on journal page 157.

Math Message Turn to Problem 2 on journal page 151. Copy the number of votes for each snack into the second column of the table on journal page 158. Leave the rest of the table blank.

Study Link 5�10 Follow-Up Briefly review answers for Problems 1 and 2. Ask volunteers to share their data sets for Problem 3.

Mental Math and Reflexes Have students rename percents as fractions. Encourage them to find fractions with denominators that are less than 100. Suggestions:

50% 1 _ 2

33 1 _ 3 % 1 _ 3

25% 1 _ 4

40% 2 _ 5

20% 1 _ 5

80% 4 _ 5

37.5% 3 _ 8

87.5% 7 _ 8

68% 17 _ 25

Mathematical PracticesSMP1, SMP2, SMP3, SMP4, SMP5, SMP6Content Standards5.NBT.7

350-354_EMCS_T_TLG1_G5_U05_L11_576825.indd 350 3/13/12 4:26 PM

Making Circle Graphs: Snack SurveyLESSON

5 �11

Date Time

Your class recently made a survey of favorite snacks. As your teacher tells you the percent of votes each snack received, record the data in the table at the right. Make a circle graph of the snack-survey data in the circle below. Remember to label each piece of the graph and give it a title.

granolabar

Favorite-Snack Survey Results

cookies

candy bar

fruit

other

�285�

�245�

�1205�

�225�

�215�

�2255�

Sample answers:

VotesSnack Number Fraction Percent

Cookies 8 32%Granola Bar 4 16%Candy Bar 10 40%Fruit 2 8%Other 1 4%Total 25 About 100%


Student Page

Lesson 5�11 351

NOTE Water is a necessary fourth ingredient in concrete. It is usually added to a dry mix of the other ingredients. About 5 to 7 gallons of water are used for a 94-pound bag of cement. When the concrete has dried (cured), the water is gone and the proportions of cement:sand:gravel are still 1:2:3.

Ongoing Assessment: Informing InstructionWatch for students who have difficulty devising a method for constructing the circle graph. Demonstrate the following.1. Use a board compass to draw a 12-inch diameter circle. Mark the center with

a dot.2. Place the center of the Percent Circle over the center of the circle on the

board and make tick marks on the chalk circle at the 0 and 1 _ 6 (16 2 _ 3 %) points.3. Remove the Percent Circle and draw a line segment from the center of the

circle through the tick marks. This 1 _ 6 section represents the proportion of cement in the mix.

4. Now place the Percent Circle 0% line along the line segment drawn at the 1 _ 6 mark. Then mark the 1 _ 3 (33 1 _ 3 %) measure. Draw a line segment from the center of the chalk circle to the tick mark to get the 1 _ 3 section. This represents the proportion of sand in the mix.

5. Measure the remaining section to verify that it is 1 _ 2 (50%) of the circle. This represents the amount of gravel in the mix.

6. Label the graph and add a title.

▶ Constructing a Circle Graph PARTNER ACTIVITY

for the Snack-Survey Data(Math Journal 1, p. 158)

Display the snack-survey percents on the board or Class Data Pad. (See Advance Preparation.) Ask students to copy the percents into column 4 of the table. Ask: Why do you think the table has About 100% in the Percent column? The total should be 100%, but it may not be exact because of rounding.

Have students check their totals, then construct a circle graph using the snack-survey data. Suggest that they draw the smallest sector of the circle graph first and work their way up to the largest. This way, slight errors in their sections will be absorbed into the largest piece at the end. Circulate and assist.

Ongoing Assessment: Exit Slip

Recognizing Student AchievementUse an Exit Slip (Math Masters, p. 414) to assess students’ understanding of how to use the data-set fractions to draw circle-graph sectors. Have students write a response to the following: How can finding the fraction of the whole for each category in the data set help you construct a circle graph? Students are making adequate progress if they relate the fractions to estimating the size of the sector before or after drawing it and/or refer to using the fraction to align the Percent Circle. [Data and Chance Goal 1]

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BBBBBBBBBBBBBBBBBBBB EELEMMMMMMMMOOOOOOOOOBBBLBLBLBLBBLBROOOOROROROROROROROROROO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGLLLLLLLLLLLLVVINVINVINVINVINNNNVINVINNVINVINVINVINGGGGGGGGGGOLOOLOLOLOLOOOO VINVINVLLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGOOOLOLOLOLOLLOOO VVVLLLLLLLLLLVVVVVVVVVSOSOSOOSOSOSOSOSOOSOSOSOOOOSOOSOSOSOSOSOSOSOOSOOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVLLLLLLLVVVVVVVVVLLLVVVVVVVLLLLLLLVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIISOLVING


Math Masters, p. 469

Game MasterName Date Time

132

4

3 counters 4 counters 5 counters 6 counters20 counters 21 counters 12 counters 28 counters15 counters 30 counters 20 counters 40 counters




Fraction Of Set Cards

Student Reference Book, p. 313

Student Page

Player 1 draws and .�110� of 28 will not result in a whole-number solution.

�110� of 28 counters is 2.8 counters.

�110� of 35 will not result in a whole-number solution.

�110� of 35 counters is 3.5 counters.

�110� of 30 will result in a whole-number solution.

�110� of 30 counters is 3 counters.

Player 1 chooses 30 counters as the set for the “fraction of ” problem.

Fraction Of

Materials � 1 deck of Fraction Of Fraction Cards (Math Masters, pp. 464 and 465)

� 1 deck of Fraction Of Set Cards (Math Masters, p. 469)

� 1 Fraction Of Gameboard and Record Sheet for each player (Math Masters, p. 466)

Players 2Skill Multiplication of fractions and whole numbersObject of the game To score more points by solving “fraction of ”problems.Directions1. Shuffle each deck separately. Place both decks number-side

down on the table.

2. Players take turns. On your turn, draw 1 card from eachdeck. Use the cards to create a “fraction of ” problem on yourgameboard.

♦ The Fraction Card indicates what fraction of the set youmust find.

♦ The Set Card offers 3 possible choices. Choose a set thatwill result in a “fraction of ” problem with a whole-number solution.

♦ Solve the “fraction of ” problem and set the 2 cards aside.The solution is your point score for the turn.

Games

110

28 counters35 counters30 counters


▶ Playing Fraction Of PARTNER ACTIVITY

(Math Masters, pp. 464–466, and 469; Student Reference Book, p. 313)

Students practice finding fractional parts of sets by playing Fraction Of. Review the directions on Student Reference Book, page 313, and then play several sample turns with the class.

2 Ongoing Learning & Practice

▶ Finding Decimal Equivalents PARTNER ACTIVITY

for Sevenths and Eighths(Math Journal 1, inside back cover)

Students continue to find and record decimal equivalents for fractions in the table on the inside back cover of the journal. Assign the denominators in rows 7 (sevenths) and 8 (eighths).

Den

omin

ator

Numerator 1 2 3 4 5 6 7 8 9 10

7 0. ⎯⎯⎯⎯ 142857 0. ⎯⎯⎯⎯ 285714 0. ⎯⎯⎯⎯ 428571 0. ⎯⎯⎯⎯ 571428 0. ⎯⎯⎯⎯ 714285 0. ⎯⎯⎯⎯ 857142 1.0 1. ⎯⎯⎯⎯ 142857 1. ⎯⎯⎯⎯ 285714 1. ⎯⎯⎯⎯ 428571 8 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1.0 1.125 1.25

Inside back cover of Math Journal 1.Completed rows 7 and 8.

Adjusting the ActivityTo make the activity a challenge to

mental math skills, encourage students to use their calculators for the first 3 or 4 columns in a row and identify the pattern. Students then use the pattern and mental math to complete the row.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

EM3cuG5TLG1_350-354_U05L11.indd 352 12/4/10 8:04 AM

paper

otherwaste

metalplastic

glass

Landfill Contents

foodandyard

waste

STUDY LINK

5�11 What’s in a Landfill?

Name Date Time

People who study landfills have estimated the percent of landfill space (volume) taken up by paper, food, plastic, and so on.

Space in landfills taken up by:

Paper . . . . . . . . . . . . . . . . 50%

Food and yard waste . . . . 13%

Plastic . . . . . . . . . . . . . . . 10%

Metal . . . . . . . . . . . . . . . . . 6%

Glass . . . . . . . . . . . . . . . . . 1%

Other waste . . . . . . . . . . . 20%

1. Cut out the Percent Circle. Use it to make a circle graph for the data in thetable. (Remember to label the graph and give it a title.)

Think of it this way:For every 100 boxes of garbagehauled to the dump, expect thatabout 50 boxes could be filled withpaper, 6 with metal, 1 with glass,and so on.

126

5%

15%

30%

35%

40%45%55%

60%

65%

70%

80%

85%

90%95% 0%

10%

20%

25%

50%

75%

1/51/6

1/10

1/8

1/3

3/4 1/4

2/3

1/2

2. 23��3�9�1� 3. 17��3�9�1�

4. 43��3�8�7� 5. 37��2�5�9� 79

2317Practice


Study Link Master

Math Boxes LESSON

5 �11

Date Time

4. Marcus had $5 to spend on lunch. Hebought a hot dog for $1.75 and someFrench fries for $0.69. How much moneydid he have left to spend on dessert?$2.56

1. Write a 5-digit number with

5 in the tens place,5 in the thousandths place, and0 in all the other places.

.

Write this number in words.Fifty and five

50005

thousandths

3. Use your Percent Circle and the information in the bar graph to complete the circle graph.

Favorite SportsTitle:

othe

r 5%

swimming15%

soccer25%

bicycling15%

basketball40%

Socce

r

Swimming

Baske

tball

Bicyclin

gOthe

r

Favorite Warm Weather Sports

5th-

Gra

de S

tude

nts

0

10

20

30

40

50

5. Cheryl has a babysitting business. In fivemonths, she made the following amounts:

$28, $42, $59, $42, $64

a. Find the range.

b. Find the mode.

c. Find the median.

d. Find the mean. $47$42

$42$36

2. Use the division rule to find equivalentfractions in simplest form.

a. �12050� �

b. �284� �

c. �2376� �

d. �1264� �

�14�

�13�

�34�

�23�

122 125

34–36 119–121

66 67

Sports

28


Student Page

Lesson 5�11 353

▶ Math Boxes 5�11


(Math Journal 1, p. 159)

Mixed Practice Math Boxes in this Lesson are paired with Math Boxes in Lesson 5-9. The skill in Problem 5 previews Unit 6 content.

Writing/Reasoning Have students write a response to the following: Describe the strategy you used to solve Problem 4 and explain your reasoning. Answers vary.

▶ Study Link 5�11


(Math Masters, p. 150)

Home Connection Students use the Percent Circle to make a circle graph. They do not have to calculate the percents because all percents are given.

3 Differentiation Options

READINESS


▶ Measuring Circle Graphs 15–30 Min

(Math Masters, p. 428)

To explore measuring sectors of a circle graph with the Percent Circle, have students complete the Math Masters page. Individualize the problems to address specific

student needs, such as using the fraction marks on the Percent Circle, or measuring smaller sectors. (See Advance Preparation.)

ENRICHMENT

SMALL-GROUP ACTIVITY

▶ Calculating Percents: 15–30 Min

On the SquareTo apply students’ knowledge of percents, have them conduct an experiment and report the results. Number index cards from 1 to the number of students in the class, and give one card to each student. Each student also needs a sheet of scrap paper wadded into a ball.

Place groups in separate areas of the room to set up for this activity. Students tape a 12-inch square to the floor and mark a tape line 6 feet from the square. The object is to see how many times a student can toss a paper ball so it lands inside of the taped square. Give students the following instructions:


Name Date Time

Use your Percent Circle to find the percent of each piece (sector) within the whole circle.

1. 2.

% % % %

% % % %

3. 4.

% % % %

% % % %

Measuring Circle-Graph Sections


Teaching Aid Master


1. Students take turns standing at the taped line. They are allowed to toss the ball as many times as the number indicated on their index cards.

2. Each student tosses the paper ball toward the taped square.

3. The group counts the number of times the ball lands inside the square.

4. At the end of a turn, the student writes how many times the ball landed inside the square as a fraction of the number of times he or she tossed the ball.

5. After every member of the group has had a turn, students convert their fractions to percents.

When students have calculated their percentages, discuss questions such as the following:

● Who had the greatest percentage in each group? Who had the greatest percentage in the class?

● Was the activity fair, or did it favor some students more than others? The activity might favor those students who had more tosses. However, some students might be more accurate with their tosses regardless of the number of tosses.

● How could students improve their percents? The more tosses they make, the greater the opportunity becomes to land in the square.

EM3cuG5TLG1_350-354_U05L11.indd 354 12/4/10 8:04 AM

The Percent Circle: Making Circle Graphs - Everyday … 5 11 349 Advance Preparation ... The Percent...

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