Technology Assessment Management System

Math Boxes, Problem 4See the iTLG.

750 Unit 9 Fractions, Decimals, and Percents

Teaching the Lesson materials

Key ActivitiesStudents tabulate the results from the trivia survey distributed in Lesson 9-1. For each survey question, they write a fraction to express the number of Yes answers as a part of the total number of answers. Then they convert each fraction to a percent.

Key Concepts and Skills• Use a calculator to convert fractions to percents.

[Number and Numeration Goal 5]• Compare fractions with unlike denominators.

[Number and Numeration Goal 6]• Create a table and tally chart.

[Data and Chance Goal 1]• Analyze survey results and make predictions based on collected data.

[Data and Chance Goal 2]

Ongoing Learning & Practice materialsStudents take a 50-facts test. They use a line graph to record individual and class scores.Then students find the median and calculate the mean of the class scores.

Students practice and maintain skills through Math Boxes and Study Link activities.

Ongoing Assessment: Recognizing Student Achievement Use journal page 262.[Operations and Computation Goal 7]

Differentiation Options materials

Students estimate the number of trapezoidsin a collection of pattern blocks and compareestimates.

Students make a side-by-side (double) bargraph of the class survey results.

� Math Journal 2, p. 261� Teaching Master (Math Masters,

p. 292)� Teaching Aid Master (Math Masters,

p. 403)� pattern blocks� large, clear container

See Advance Preparation

ENRICHMENTREADINESS

3

� Math Journal 2, p. 262� Study Link Master (Math Masters,

p. 291)� Teaching Aid Masters (Math Masters,

pp. 410, 414, and 416)� pen or colored pencil

2

� Math Journal 2, p. 261 � Study Links 9 �1 (Math Masters,

p. 280) and 9 �5� Transparency (Math Masters,

p. 290; optional)� calculator� slate

1

Additional InformationAdvance Preparation For the optional Readiness activity in Part 3, gather a large collection ofpattern blocks and place them in a clear container.

Objectives To guide the organization and tabulation of survey

data; and to introduce the use of percents to compare quantities

expressed as fractions with unlike denominators.

� Math Message Follow-UpGo over the answers. 29%, 73%, 71%, 4% Ask volunteers to showwhat they did to rename the fractions as percents. Make sure thatboth methods are presented:

� Using the percent key on a calculator

� Dividing the numerator by the denominator and multiplying by 100

Tell students that in this lesson they will rename the fractionsfrom the Trivia Survey as percents.

� Making a Prediction Based on Individual Survey Data(Math Masters, p. 280)

Have students make some rough guesses about people’s behaviorbased on their survey results. Ask: Do you think it is more likelythat a person will● read a book or go to a movie?● eat breakfast or eat at a fast-food restaurant?● like liver or like Mondays?

Take a vote and record the results on the board.

WHOLE-CLASS

DISCUSSION

WHOLE-CLASS

DISCUSSION

1 Teaching the Lesson

STUDY LINK

9 �1 Trivia Survey

70

Name Date Time

Conduct the survey below. The results will be used in Lesson 9-6.

Find at least five people to answer the following survey questions. You can ask family members, relatives, neighbors, and friends.

BE CAREFUL! You will not ask every person every question. Pay attention to the instructions that go with each question.

Record each answer with a tally mark in the Yes or No column.

Question Yes No

1. Is Monday your favorite day?(Ask everyone younger than 20.)

2. Have you gone to the movies in the last month? (Ask everyone older than 8.)

3. Did you eat breakfast today?(Ask everyone over 25.)

4. Do you keep a map in your car?(Ask everyone who owns a car.)

5. Did you eat at a fast-food restaurant yesterday?(Ask everyone.)

6. Did you read a book during the last month?(Ask everyone over 20.)

7. Are you more than 1 meter tall?(Ask everyone over 20.)

8. Do you like liver?(Ask everyone.)

Answers vary.

Math Masters, p. 280

Study Link Master

Lesson 9�6 751

Getting Started

Math MessageUse your calculator to rename the following fractions as percents to the nearest whole percent:

�1683�, �

5778�, �

4529�, �4

27�

Study Link 9�5 Follow-UpHave partners compare answers. Ask if the percents in the table add up to 100%. yesStudents should note that sometimes because of rounding, percents might not add up to 100%.

Mental Math and ReflexesWrite “easy” fractions on the board. For each fraction, students write the equivalent decimal and percent. Have students share strategies for the problems. Suggestions:

�12� 0.5, 50% �

35� 0.6, 60% �

1290� 0.95, 95%

�14� 0.25, 25% �

34� 0.75, 75% �

2245� 0.96, 96%

�110� 0.1, 10% �

25� 0.40, 40% �

93� 3, 300%

752 Unit 9 Fractions, Decimals, and Percents

261

Trivia Survey ResultsLESSON

9 � 6

Date Time

Class Results for the Trivia Survey

Question Yes No Total % Yes

1. Is Monday your favorite day?

2. Have you gone to themovies in the last month?

3. Did you eat breakfast today?

4. Do you keep a map in your car?

5. Did you eat at a fast-foodrestaurant yesterday?

6. Did you read a book during the last month?

7. Are you more than1 meter tall?

8. Do you like liver?

�TYoetasl

�

Answers vary.

1. The chart below will show the results of the trivia survey for the whole class. Wait for your teacher to explain how to fill in the chart.

2. On the basis of the survey results, is it more likely that a person will

a. read a book or go to a movie?

b. eat breakfast or eat at a fast-food restaurant?

c. like liver or like Mondays?

Math Journal 2, p. 261

Student Page

� Tabulating Survey Results for the Whole Class(Math Journal 2, p. 261; Math Masters, pp. 280 and 290 )

Tell students that they will use the results of all the surveys to check their guesses. The first step is to combine the results from all the surveys. The goal is to create a chart that shows the total number of Yes and No answers to each question for the whole class.

Ask for suggestions on how to do this most efficiently. One possibility is to divide the class into small groups of four or five.For each question on the survey, have the students in each groupfind the total number of Yes answers and the total number of Noanswers for their group. Each group can then report its totals. Youor a student volunteer can add these as they are reported. Finally,record the total number of Yes and the total number of Noanswers to each question on the transparency of Math Masters,page 290.

Students copy the results in the Yes and No columns on page 261in their journals. They add the Yes and No results and record thesums in the Total column. These are the total numbers of peoplewho answered the survey questions.

Next, students record the Yes answers as a fraction of the totalnumber of answers in the �T

Yoetasl� column. If necessary, help them

complete the �TYoetasl� column for the first two rows of the chart. At

this point, the classroom chart might look as follows:

� Analyzing the Survey Results(Math Journal 2, p. 261)

Have students analyze the survey results so far. Ask: Do you think it is more likely that a person will● read a book or go to a movie?● eat breakfast or eat at a fast-food restaurant?● like liver or like Mondays?

WHOLE-CLASS

ACTIVITY

WHOLE-CLASS

ACTIVITYLESSON

9 � 6

Name Date Time

Trivia Survey Data Chart

Class Results for the Trivia Survey

Question Yes No Total % Yes

1. Monday

2. movies

3. breakfast

4. map

5. fast food

6. read

7. meter

8. liver

Yes�Total

Math Masters, p. 290

Teaching Master

Question Yes No Total �TYoetasl

� % Yes

1. Monday 18 45 63 �1683�

2. Movies 57 21 78 �5778�

Lesson 9�6 753

Adjusting the Activity

Some students might argue that you need to simply compare theYes answers.

Example:

Suppose that 45 out of 50 people interviewed read a book and that57 out of 78 people saw a movie last month.● Is it correct to conclude that because more people saw a movie

than read a book, people are more likely to go to the moviesthan to read a book?

● Does the total number of people interviewed need to be takeninto account?

This discussion is crucial to understanding why percents are useful.Students should see that it is difficult to compare quantities that areexpressed as fractions with unlike denominators. Explain that thisis why we rename fractions with unlike denominators as fractionsthat have the same denominator. The denominator 100—used inpercents—is especially useful, because in our base-ten system, it iseasy to rename such fractions as decimals and percents.

Once students understand why it is helpful to rename the fractionof Yes answers as percents, have them use their calculators to fill in the % Yes column. Ask them to round the answers to thenearest whole percent. Students’ completed charts shouldresemble your classroom chart, which might look like this:

Have partners use their completed table to answer Problem 2 atthe bottom of journal page 261.

Have students combine the trivia survey data from all of the fourth-grade classes in the school. Discuss why % Yes estimates based on the combined data are more reliable than estimates based on the data collected by any single classroom.

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

Question Yes No Total �TYoetasl

� % Yes

1. Monday 18 45 63 �1683� 29%

2. Movies 57 21 78 �5778� 73%

754 Unit 9 Fractions, Decimals, and Percents

STUDY LINK

9 � 6 Use Percents to Compare Fractions

291

62 207

Name Date Time

1. The girls’ varsity basketball team won 8 of the 10 games it played. The junior varsity team won 6 of 8 games. Which team has the better record? Explain your reasoning.The varsity team. They won �1

80� � 80% of their games.

The junior varsity team won �68� � �

34� � 75% of their games.

2. Complete the table of shots taken (not including free throws) during a game.Calculate the percent of shots made to the nearest whole percent.

3. The basketball game is tied. Your team has the ball. There is only enoughtime for one more shot. Based only on the information in the table, whichplayer would you choose to take the shot? Why?

Sample answer: I would choose Player 4, who has taken 11 shots and made 82% of her shots. Player 3 has a higherpercent of shots made (100%), but she has only taken 3 shots.

Player Shots Shots Total�SThootatsl S

Mhaodtes

�% of Shots

Made Missed Shots Made

1 5 12 17 �157� 29%

2 5 6 11 �151� 45%

3 3 0 3 �33� 100%

4 9 2 11 �191� 82%

5 4 3 7 �47� 57%

6 11 5 16 �11

16� 69%

7 6 4 10 �160� 60%

8 1 1 2 �12� 50%

4. �13� � �

16� � 5. � �

34� � �

12� 6. � �1

70� � �

15� 7. �

58� � �

14� �

Practice

�36�,or �12�

�14� �190� �38�

Math Masters, p. 291

Study Link Master

�

262

Math Boxes LESSON

9 �6

Date Time

1. If you threw a 6-sided die 54 times, abouthow many times would you expect it toland on a number less than 3? Choosethe best answer.

9 times

12 times

18 times

36 times

2. Name a percent value

a. greater than �14� and less than �

23�.

b. less than �45� and greater than �

58�.

75%

50%

81

60 139136

61 62

3. Store X is selling bathing suits at 20% offthe regular price of $35. Store Y is sellingthe same suits for �

14� off the regular price of

$32. Which store is offering the better buy?

Show how you solved the problem.

Store X: $35 / 10 � $3.50,2 � $3.50 � $7.00, and $35 � $7 � $28. Store Y:$32 / 4 � $8, and $32 � $8 � $24.

Store Y

4. If 1 inch on a map represents 200 miles, then

a. 5 inches represent miles.

b. 8 inches represent miles.

c. inches represent 800 miles.

d. 3�14� inches represent miles.

e. inches represent 350 miles.

6504

1,6001,000

6. a. Which is warmer, �15�C or �3�C?

How many degrees warmer?

b. Which is colder, �15�C or �20�C?

How many degrees colder?

5�C�20�C

12�C�3�C

5. What is the area of the triangle? Include the correct unit.

Number model:

Area � 24 in2

14538 3959

Sample answer:

6"

8"�12� � (8 � 6) � 24

Sample answers:

1�34�

Math Journal 2, p. 262

Student Page

� Taking a 50-Facts Test(Math Masters, pp. 410, 414, and 416)

See Lesson 3-4 for details regarding the administration of a 50-facts test and the recording and graphing of individual and class results.

� Math Boxes 9�6(Math Journal 2, p. 262)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 9-8. The skill in Problem 6previews Unit 10 content.

Ongoing Assessment:Recognizing Student Achievement

Use Math Boxes, Problem 4 to assess students’ ability to interpret a map scale.Students are making adequate progress if they are able to solve Problems4a–4c. Some students may be able to solve Problems 4d and 4e, which involvefractions of inches.

[Operations and Computation Goal 7]

� Study Link 9�6(Math Masters, p. 291)

Home Connection Students use percents to compare quantities expressed as fractions with unlike denominators.

INDEPENDENT

ACTIVITY

Math Boxes

Problem 4 �

INDEPENDENT

ACTIVITY

WHOLE-CLASS

ACTIVITY

2 Ongoing Learning & Practice

� Comparing Estimates for the “Fraction-of” a Collection(Math Masters, p. 292)

To explore the comparison of quantities expressed as fractions with unlike denominators using a concrete model, have studentscompare estimates for the number of red trapezoids in a collection of pattern blocks.

Have students share their strategies for making comparisons.Discuss how finding nearby “easy” fractions or converting to decimalscould help them compare their estimates. Ask why estimates withdifferent denominators cannot be compared directly.

� Graphing Survey Results(Math Journal 2, p. 261; Math Masters, p. 403)

To apply students’ ability to represent data, have themgraph the results of the class survey on centimeter gridpaper (Math Masters, page 403). You might suggest thatstudents use a side-by-side (double) bar graph. For example:

Yes No

1. Monday

2. movies

100%0% 10% 20% 30% 40% 50% 60% 70% 80% 90%

Survey Questions

15–30 Min

PARTNER

ACTIVITYENRICHMENT

5–15 Min

SMALL-GROUP

ACTIVITYREADINESS

3 Differentiation Options LESSON

9 � 6

Name Date Time

“Fraction-of” a Collection

Part One

1. Estimate the total number of pattern blocks in the jar

given to you by your teacher. pattern blocks

2. Estimate the total number of red trapezoids in the jar.

red trapezoids

3. Write your estimates as a fraction.

�

4. Record the estimates made by the members of your group.

Part Two

5. Count the number of pattern blocks in the jar. pattern blocks

6. Count the number of red trapezoids in the jar. red trapezoids

7. Record the counts as a fraction.

�

Part Three

8. Which of your group members’ estimates do you think was closest to the

actual fraction of trapezoids in the jar?

Explain why you think so.

total number of red trapezoids����total number of pattern blocks

total number of red trapezoids����total number of pattern blocks

59Answers vary.

Math Masters, p. 292

Teaching Master

Lesson 9�6 755