The Percent Circle: Making Circle Graphs



Objective To introduce constructing circle graphs using the Percent Circle.

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eToolkit

Algorithms Practice

EM Facts Workshop Game™

Teaching the Lesson 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]

Family Letters

Assessment Management

Common Core State Standards

Ongoing Learning & Practice Finding Decimal Equivalents for Sevenths and Eighths Math Journal 1, inside back cover Students fill in the decimals for sevenths and eighths in the Table of Decimal Equivalents.

Math Boxes 5 11

Curriculum Focal Points

Interactive Teacher’s Lesson Guide

Differentiation Options READINESS

Measuring Circle Graphs Math Masters, p. 428 Geometry Template Students use a Percent Circle to measure sectors in a circle graph.



Math Journal 1, p. 159 Students practice and maintain skills through Math Box problems.

Key Activities

Study Link 5 11

Students use the Percent Circle to construct circle graphs. They use journal page data and the snack-survey data collected in Lesson 59. They practice finding fractional parts of sets by playing Fraction Of.

Math Masters, p. 150 Students practice and maintain skills through Study Link activities.



ENRICHMENT

Calculating Percents: On the Square 1 index card  1 sheet of scrap paper  per group: masking tape, 12" by 12" paper square Students collect, calculate, and compare fractions and percents in statistical data.

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]

Materials Math Journal 1, pp. 151, 157, and 158 Student Reference Book, p. 313 Study Link 510 Math Masters, pp. 414, 426, and 427 (optional); pp. 464–466 and 469 Geometry Template  Class Data Pad (optional)  chalkboard compass, for demonstration purposes  counters

Advance Preparation For Part 1, convert snack-survey data from Lesson 59 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 Lesson 5 11 

349

Mathematical Practices

SMP1, SMP2, SMP3, SMP4, SMP5, SMP6

Content Standards

Getting Started

5.NBT.7

Mental Math and Reflexes

Math Message

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

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.

1 50% _ 2

40% _ 5 2

%_ 33_ 3 3 1

20% _ 5

1

1

25% _ 4

80% _ 5

1

4

37.5% _ 8 3

87.5% _ 8 7

68% _ 25 17

Study Link 5 10 Follow-Up 

Briefly review answers for Problems 1 and 2. Ask volunteers to share their data sets for Problem 3.

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)

Student Page Date LESSON

5 11 

Time

Making Circle Graphs: Concrete Recipe

Concrete is an artificial stone. It is made by first mixing cement and sand with gravel or other broken stone. Then enough water is mixed in to cause the cement to set. After drying (or curing), the result is a hard piece of concrete. The cement, sand, and gravel are commonly mixed using this recipe.

Recipe for Dry Mix for Concrete Material Cement Sand Gravel

Fractional Part of Mix

Percent Part of Mix

1 ᎏᎏ 6 1 ᎏᎏ 3

33 ᎏᎏ%

1 ᎏᎏ 2

2 3 1 3

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.

16 ᎏᎏ%

50%

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.

Recipe for Dry Mix for Concrete cement

sand gravel

Math Journal 1, p. 157

350

Unit 5

Fractions, Decimals, and Percents

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.

Student Page 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 Instruction Watch for students who have difficulty devising a method for constructing the circle graph. Demonstrate the following.

2. Place the center of the Percent Circle over the center of the circle on the 1 2 _ board and make tick marks on the chalk circle at the 0 and _ 6 (16 3 %) points. 3. Remove the Percent Circle and draw a line segment from the center of the 1 circle through the tick marks. This _ 6 section represents the proportion of cement in the mix. 1 4. Now place the Percent Circle 0% line along the line segment drawn at the _ 6 1 1 _ _ mark. Then mark the 3 (33 3 %) measure. Draw a line segment from the center 1 of the chalk circle to the tick mark to get the _ section. This represents the proportion of sand in the mix.

LESSON

5 11 

Time

Making Circle Graphs: Snack Survey

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.

Votes Snack

Other

8 4 10 2 1

Total

25

Cookies Granola Bar Candy Bar Fruit

Sample answers:

Number

Fraction

ᎏ8ᎏ 25 ᎏ4ᎏ 25 10 ᎏ ᎏ 25 ᎏ2ᎏ 25 ᎏ1ᎏ 25 25 ᎏ ᎏ 25

Percent

32% 16% 40% 8% 4% About 100%

Favorite-Snack Survey Results fruit

other

1. Use a board compass to draw a 12-inch diameter circle. Mark the center with a dot.

Date

cookies candy bar granola bar

3

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

Math Journal 1, p. 158

6. Label the graph and add a title.

▶ Constructing a Circle Graph

PARTNER ACTIVITY

for the Snack-Survey Data

PROBLEM PR PRO P RO R OB BLE BL LE L LEM EM E M SO S SOLVING OL O LV VING VIN IN ING

(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: Recognizing Student Achievement

Exit Slip

Use 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]

Lesson 5 11 

351

Game Master Name

Date

Time

1 2 4 3

Fraction Of Set Cards

▶ Playing Fraction Of

PARTNER ACTIVITY

(Math Masters, pp. 464–466, and 469; Student Reference Book, p. 313) 3 counters 20 counters 15 counters

4 counters 21 counters 30 counters

5 counters 12 counters 20 counters

6 counters 28 counters 40 counters

8 counters 27 counters 20 counters

10 counters 32 counters 24 counters

12 counters 30 counters 25 counters

15 counters 36 counters 20 counters

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 18 counters 36 counters 10 counters

20 counters 4 counters 3 counters

21 counters 30 counters 24 counters

25 counters 6 counters 40 counters

28 counters 35 counters 30 counters

30 counters 32 counters 15 counters

36 counters 20 counters 24 counters

40 counters 18 counters 25 counters

▶ 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).

Math Masters, p. 469

Adjusting the Activity To 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. AUDITORY



KINESTHETIC



TACTILE



Denominator

Numerator 1

2

3

4

5

6

7 0.⎯⎯⎯⎯ 142857 0.⎯⎯⎯⎯ 285714 0.⎯⎯⎯⎯ 428571 0.⎯⎯⎯⎯ 571428 0.⎯⎯⎯⎯ 714285 0.⎯⎯⎯⎯ 857142 8

0.125

0.25

0.375

0.5

0.625

0.75

7

8

0.875

1.0

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

VISUAL

Student Page Games

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

2

Skill

Multiplication of fractions and whole numbers

Object of the game To score more points by solving “fraction of ” problems. Directions 1. Shuffle each deck separately. Place both decks number-side down on the table. 2. Players take turns. On your turn, draw 1 card from each deck. Use the cards to create a “fraction of ” problem on your gameboard.

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

♦ The Set Card offers 3 possible choices. Choose a set that will result in a “fraction of ” problem with a wholenumber solution.

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

Player 1 draws

1 10

28 counters 35 counters 30 counters

and

.

1 ᎏᎏ 10

of 28 will not result in a whole-number solution.

1 ᎏᎏ 10

of 35 will not result in a whole-number solution. 1 ᎏᎏ of 35 counters is 3.5 counters. 10

1 ᎏᎏ 10

of 30 will result in a whole-number solution. 1 ᎏᎏ of 30 counters is 3 counters. 10

1 ᎏᎏ 10

of 28 counters is 2.8 counters.

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

Student Reference Book, p. 313

352

Unit 5

Fractions, Decimals, and Percents

9

10

1.⎯⎯⎯⎯ 142857 1.⎯⎯⎯⎯ 285714 1.⎯⎯⎯⎯ 428571

1.0

1.125

1.25

Student Page

▶ Math Boxes 5 11 

INDEPENDENT ACTIVITY

(Math Journal 1, p. 159)

Date

Time

LESSON

Math Boxes

5 11 

1.

Write a 5-digit number with

2.

5 in the tens place, 5 in the thousandths place, and 0 in all the other places.

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.

5

0

0

.

Use the division rule to find equivalent fractions in simplest form. 25 a. ᎏᎏ 100

0

5

Write this number in words.

Fifty and five thousandths

1 ᎏᎏ 4

⫽

8 b. ᎏᎏ 24

⫽

1 ᎏᎏ 3

27 c. ᎏᎏ 36

⫽

3 ᎏᎏ 4

16 d. ᎏᎏ 24

⫽

2 ᎏᎏ 3

28

Title:

30

soccer basketball 25% swimming 40% 15%

20 10

5%

O

th er

0 cy cl in g

er

INDEPENDENT ACTIVITY

Favorite Sports

40

Bi

5th-Grade Students

Favorite Warm Weather Sports 50

im m in g Ba sk et ba ll

Sports

oth



66 67

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

Sw

▶ Study Link 5 11

3.

So cc er

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.

122 125

(Math Masters, p. 150)

4.

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.

Marcus had $5 to spend on lunch. He bought a hot dog for $1.75 and some French fries for $0.69. How much money did he have left to spend on dessert?

5.

bicycling 15%

Cheryl has a babysitting business. In five months, she made the following amounts: $28, $42, $59, $42, $64

$2.56

Find the range.

b.

Find the mode.

c. 34–36

$36 $42 Find the median. $42 Find the mean. $47

a.

d.

119–121

Math Journal 1, p. 159

3 Differentiation Options READINESS

▶ Measuring Circle Graphs

INDEPENDENT ACTIVITY 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.)

Study Link Master Name

Date

STUDY LINK

▶ Calculating Percents:

SMALL-GROUP ACTIVITY 15–30 Min

On the Square

What’s in a Landfill?

5 11 

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:

Think of it this way: For every 100 boxes of garbage hauled to the dump, expect that about 50 boxes could be filled with paper, 6 with metal, 1 with glass, and so on.

Paper . . . . . . . . . . . . . . . . 50% Food and yard waste . . . . 13% Plastic . . . . . . . . . . . . . . . 10% Metal . . . . . . . . . . . . . . . . . 6%

To 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.

126

Glass . . . . . . . . . . . . . . . . . 1% Other waste . . . . . . . . . . . 20% 1.

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

Landfill Contents 95%

0%

5%

90%

other waste

85%

glass

paper

15% 1/6

80%

75%

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:

10%

1/1 1/8 0

ENRICHMENT

Time

3/4

1/4

metal 70%

plastic food and yard waste

20%

1/5

1/3

2/3

65%

25% 30%

35% 1/2

60% 55%

50%

40% 45%

Practice

2.

23冄苶3 苶9 苶1 苶

17

3.

17冄苶3 苶9 苶1 苶

23

4.

43冄苶3 苶8 苶7 苶

9

5.

37冄苶2 苶5 苶9 苶

7

Math Masters, p. 150

Lesson 5 11 

353

Teaching Aid Master Name

Date

Time

Measuring Circle-Graph Sections Use your Percent Circle to find the percent of each piece (sector) within the whole circle. 1.

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.

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.

%

%

%

%

%

%

%

%

3.

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.

4.

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.

Math Masters, p. 428

354

Unit 5

Fractions, Decimals, and Percents