Technology Assessment Management System

Mental Math and ReflexesSee the Web site on page 629.See the iTLG.

Additional InformationAdvance Preparation For Part 2, consider copying Math Masters, pages 462, 463, 465, and 466 on cardstock. For the optional Enrichment activity in Part 3, obtain the book Do You Wanna Bet? Your Chance to Find Out About Probability by Jean Cushman (ClarionBooks, 1991).

626 Unit 7 Fractions and Their Uses; Chance and Probability

Teaching the Lesson materials

Key ActivitiesStudents apply basic concepts and vocabulary associated with chance events.

Key Concepts and Skills• Name fractional parts of regions. [Number and Numeration Goal 2]• Use equivalent fractions to design spinners. [Number and Numeration Goal 5] • Use probability language to describe the likelihood of events. [Data and Chance Goal 3]• Conduct experiments and calculate expected probability. [Data and Chance Goal 4]

Key Vocabularyfair (die or spinner) • equal chance • expect • equally (more, less) likely

Ongoing Assessment: Informing Instruction See page 630.

Ongoing Assessment: Recognizing Student Achievement Use Mental Math and Reflexes. [Data and Chance Goal 4]

Ongoing Learning & Practice materialsStudents play Chances Are to practice using probability language and describing the likelihood of an event occurring.

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

Differentiation Options materials

Students review fractionalparts of regions.

Students explore probability activities in DoYou Wanna Bet? YourChance to Find OutAbout Probability.

Students add fair andequal chance to theirMath Word Banks.

� Teaching Master (Math Masters, p. 237)� Differentiation Handbook� straightedge; crayons or markers;

2 six-sided dice per partnership (optional)

See Advance Preparation

ELL SUPPORTENRICHMENTREADINESS

3

� Math Journal 2, p. 212� Student Reference Book, pp. 236 and 237� Study Link Masters (Math Masters,

pp. 234–236)� Game Masters (Math Masters, pp. 462–466)

See Advance Preparation

2

� Math Journal 2, p. 211� Study Link 7�10� Teaching Master (Math Masters, p. 233)� crayons, markers, or colored pencils (red,

green, blue, and at least 3 other colors)� straightedge� 1 large (2") paper clip and 2 pieces of

removable tape per student� slate� data pad or chart paper (optional)� computer with Internet access (optional)

1

Objectives To review basic ideas of probability, including fairness

and expected results; and to guide the application of fractions

to spinners.

Lesson 7�11 627

Getting Started

Math MessageThink of a game you like inwhich the players roll dice. Be prepared to explain how dice are used in the game.

Study Link 7�10Follow-UpHave students compareanswers. Ask volunteers to explain howthey solved Problems 5 and 6. Studentsindicate thumbs-up if they agree with thestrategies used.

Mental Math and Reflexes �Pose probability questions. Have students write the appropriate fractions andbasic probability terms on their slates. Suggestions:

There are 5 red and 5 blue blocks in the bag.

What are the chances of picking a red block? �150�, �

12�, or 50-50 chance

A blue block? �150�, �

12�, 50-50 chance

A green block? �100�, impossible

There are 3 red, 1 blue, and 2 green blocks in the bag.

What are the chances of picking a red block? �36�, �

12�, 50-50 chance

A blue block? �16�, unlikely, or very unlikely

A green block? �26�, �

13�, unlikely

There are 25 red, 25 blue, 20 green, and 30 yellow blocks in the bag.

What are the chances of picking a red or a blue block? �15000�, �

12�, 50-50 chance

A green block? �12000�, �1

20�, �

15�, unlikely

A yellow block? �13000�, �1

30�, unlikely

� Math Message Follow-UpDiscuss the use of dice in games. For example:

� Dice are used to determine how far a player can move.

� Dice are used to determine numbers that are used in a game.

� You cannot know which number will come up on a die. To support English language learners, discuss the meaning of theword die in this mathematical context.

� You should have a fair die—there must be an equal chancefor it to land with any one of its faces up.

Ask students what other devices they have used for the samepurposes as dice. Sample answers: Spinners, coins, number cards

WHOLE-CLASS

DISCUSSION

1 Teaching the Lesson

Ongoing Assessment:Recognizing Student Achievement

Use Mental Math and Reflexes to assess students’ ability to express theprobability of an event as a fraction. Students are making adequate progressif they express the expected probability with a fraction. Some students may write the fraction in simplest form, for example, rename �1

2000� as �

15�.

[Data and Chance Goal 4]

Mental Math

and

Reflexes �

628 Unit 7 Fractions and Their Uses; Chance and Probability

LESSON

7�11

Name Date Time

Spinner Experiments

80 84

1. Use a paper clip and pencil to make a spinner.

a. Spin the paper clip 4 times. Record the number of times it lands on the shaded partand on the white part.

b. Record the number of times the paper cliplands on the shaded part and on the whitepart for the whole class.

2. Make another spinner. Color the circle blue and red so that the paper clip is twice as likely to land on blue as on red.

a. Spin the paper clip 4 times. Record thenumber of times it lands on blue and on red.

b. Record the number of times the paper cliplands on blue and on red for the whole class.

c. What would you expect after spinning the paper clip 300 times?

shaded white

shaded white

blue red

blue red

blue red

200 100

Sample answer:12

6

39

1

2

4

10

8

5

11

7

bluered

Answers vary.

Math Masters, p. 233

Teaching Master

� Spinning a Spinner(Math Masters, p. 233)

Tell students that in this lesson they will use spinners to experiment with situations in which they cannot tell for sure what will happen.

Pass out Math Masters, page 233 and ask each partnership totape it to a flat, level surface. Show them how to make and use a paper-clip spinner. (See margin.)

Discuss what constitutes a fair spinner—one in which the paperclip has an equal chance of landing on any part of the circle. Forexample, placing a spinner on an uneven surface will alter theresults of the spins. Therefore, this would not be a fair spinner.

� Doing Spinner Experiments(Math Masters, p. 233)

Experiment 11. Partners use the first spinner on Math Masters, page 233.

They spin the paper clip four times and record the results inProblem 1a.

2. Students report their results to you. You tally them on chartpaper or on the board.

3. You and the class find the class totals. Students record themin Problem 1b.

Ask students to summarize their results. Encourage language likethe following:

� “The paper clip has the same chance of landing on the shadedpart as on the white part.”

� “If you spin the paper clip many times, it should land on white1 out of 2 times.”

� “Chances are, the paper clip will land on the white part half ofthe time, because each part is half of the circle.”

� “The chance of landing on the shaded part is 50% (or �12�).”

Experiment 2Ask partners to color the second spinner on Math Masters,page 233 blue and red in such a way that the paper clip is twiceas likely to land on blue as on red. Point out that the circle hasbeen divided into 12 equal parts.

Have students share spinner designs. Students should have colored�23� of the circle blue and �

13� red. There are many possible designs.

NOTE Have students work in pencil until they are sure they have a correct solution.

WHOLE-CLASS

ACTIVITY

PARTNER

ACTIVITYMake a mark at the end of the paper clip.

A student uses one hand to hold the penciland the other hand to flick the paper clip.

211

Making SpinnersLESSON

7�11

Date Time

82–86

1. Make a spinner. Color the circle in 6 different colors. Design the spinner so that the paper clip has the same chance of landing on each of the colors.

2. Make another spinner. Color the circle red, blue, and green so that the paper clip has

� a �16� chance of landing on red

and

� a �13� chance of landing on blue.

a. What fraction of the circle did you color

red? blue? green?

b. Suppose you plan to spin the paper clip 24 times. About how many times would you expect it to land on

red? blue? green?

c. Suppose you plan to spin the paper clip 90 times. About how many times would you expect it to land on

red? blue? green? 453015

1284

�26�, or �13� �36�, or �12�

Sample answers:

Purple

Yellow Green

Blue

White Red

121

2

3

4

56

7

8

9

10

11

Green

Green

Green Blue

Blue

Red

121

2

3

4

56

7

8

9

10

11

�16�

Math Journal 2, p. 211

Student Page

Lesson 7�11 629

Repeat the procedure using the blue-and-red spinners:

1. Partners spin four times and record the results in Problem 2a.

2. Students report their results to you. You tally them on chartpaper or on the board.

3. You and the class find the class totals. Students record themin Problem 2b.

Ask students to summarize their results. Encourage language likethe following:

� “The paper clip is more likely to land on blue than on red.”

� “If you spin many times, blue will come up twice as often.”

� “It is hard to know for sure, but if you spin a lot of times, blue will come up about 2 out of 3 spins, or �

23� of the time.”

� “There is a �23� chance of landing on blue.”

Finally, have students complete Problem 2c and discuss theiranswers. Make sure they understand the meaning of the wordexpect in this context. One would expect the paper clip to land on red about 100 times, but this does not mean that it will do so exactly 100 times. In fact, it probably will not land on redexactly 100 times.

When students describe chance events, encourage them to use avariety of words and phrases, such as likely, unlikely, 3 out of 4,three-fourths of the time, 75% chance, the chances are, and you can expect.

� Designing Spinners(Math Journal 2, p. 211)

Have students complete journal page 211 and then share resultsand spinner designs.

Technology Link Alternatively, have students visit http://illuminations.nctm.org/tools/tool_detail.aspx?id=79

to create their own spinners and compare the expected results fora specified number of spins to the actual results.

For Problem 1, students will probably divide the circle into 6 equal parts. Ask how they decided what size to make each part.�16� of 12 � 2, so the circle can be divided into 6 equal parts bystarting at 0 and counting by 2s.

Encourage students to use such phrases as “equally likely,”“equal chance,” and “1 out of 6 chances of landing on red” whenthey discuss their spinner designs.

PARTNER

ACTIVITY

Adjustingthe Activity

As probability terms enter class discussionsin the context of solving problems, write themon chart paper or on the board and reviewtheir meanings.

AUDITORY � KINESTHETIC � TACTILE � VISUAL

ELL

Adjusting the Activity

630 Unit 7 Fractions and Their Uses; Chance and Probability

212

Math Boxes LESSON

7�11

Date Time

4. Write an equivalent fraction, decimal, orwhole number.

Decimal Fraction

a. 0.70

b.�12050

�

c.�99

�

d. 0.2

1.00.25

1. According to a survey of 800 students atMartin Elementary, about �

34� of them chose

pizza as their favorite food. Of those whochose pizza, �

12� liked pepperoni topping the

best. How many students liked pepperoni topping the best?

students300

2. Multiply. Use a paper-and-pencil algorithm.

71 � 38 � 2,698

3. a. Hannah drew a line segment 1�58� inches

long. Then she erased �12� inch.

How long is the line segment now?

inches

b. Joshua drew a line segment �78� inch

long. Then he added another �34� inch.

How long is the line segment now?

inches1�58�

1�18�

18 1959

55–57

162–166 129

61 62

�17000�

6. Complete.

a. 5 ft � yd ft

b. 40 in. � ft in.

c. 80 in. � yd in.

d. 108 in. � ft

e. �13� yd � in.12

9824321

5. Complete the table and write the rule.

Rule: �2.96in out

100.54 97.58

55.91 52.95

72.03 69.0770.4 67.44

59.21 56.25

�120�

Math Journal 2, p. 212

Student Page

In discussing Problems 2b and 2c, give students opportunities touse the language of chance events and to compare the likelihood of the paper clip landing on the various colors. For example:

� “The paper clip is more likely to land on blue than on red, butless likely to land on blue than on green.”

� “The paper clip is 3 times as likely to land on green as on red,and twice as likely to land on blue as on red.”

� “The chance of landing on red is �16�, so �

16� of the circle should

be red.”

� “The chance of landing on red is 1 out of 6, or 1 red for every 6 spins. So I would expect 4 reds if I spin 24 times.”

Ongoing Assessment: Informing InstructionWatch for students who may misunderstand the term expect. For example, inProblem 2b, the paper clip will not necessarily land on red exactly 4 times out ofevery 24 spins, or exactly 8 times on blue.

� Playing Chances Are(Student Reference Book, pp. 236 and 237; Math Masters, pp. 462–466)

Students play Chances Are to practice using basic probabilityterms to describe the likelihood of events.

ELL

Have students use crayons to color code the balls and blocks on the appropriate Event Cards (Math Masters, page 463).

Have students express the probability of the event as a fraction.

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

� Math Boxes 7�11(Math Journal 2, p. 212)

Mixed Practice Math Boxes in this lesson are paired withMath Boxes in Lesson 7-9. The skill in Problem 6 previewsUnit 8 content.

INDEPENDENT

ACTIVITY

PARTNER

ACTIVITY

2 Ongoing Learning & Practice

� Study Link 7�11(Math Masters, pp. 234–236)

Home Connection Students design and describe a spinner. Also, in preparation for Lesson 8-1, students areasked to measure the distance between the appliances intheir kitchens.

� Dividing Circles into Fractional Parts(Math Masters, p. 237)

To explore fractional parts of regions, have students divide circlesinto equal parts and color specified fractions of the regions. Discusshow equivalent fractions can be used to solve the problems.

� Investigating Chance EventsLiterature Link To apply students’ understanding of probability, have them conduct and report results for

experiments found in Do You Wanna Bet? Your Chance toFind Out About Probability by Jean Cushman (Clarion Books, 1991). Suggestions:

� Chapter 7, “Winners and Losers, Roll of the Dice”: Studentstally each “double” in 100 rolls of two dice and compare expected and actual results.

� Chapter 5, “Sampling and Statistics, Left Hand or Right”:Students survey the fourth grade to see if the established ratio of 1 in 10 applies to class data on left-handed students.

� Building a Math Word Bank (Differentiation Handbook)

To provide language support for probability, have students use theWord Bank Template found in the Differentiation Handbook. Askstudents to write the terms fair and equal chance, draw picturesrelated to each term, and write other related words. See theDifferentiation Handbook for more information.

5–15 Min

SMALL-GROUP

ACTIVITYELL SUPPORT

15–30 Min

SMALL-GROUP

ACTIVITYENRICHMENT

5–15 Min

PARTNER

ACTIVITYREADINESS

3 Differentiation Options

INDEPENDENT

ACTIVITY

LESSON

7�11

Name Date Time

Fractions of Circles

Divide each circle into equal parts and color as directed.

1. Divide into 2 equal parts. 2. Divide into 3 equal parts.Color �

12� yellow. Color �

13� red and �

13� blue.

3. Divide into 6 equal parts. 4. Divide into 6 equal parts.Color �

16� green and �

26� orange. Color �

16� green and �

13� orange.

5. Divide into 12 equal parts. 6. Divide into 12 equal parts. Color �

13� red. Color �

13� red in a different way.

red

red

redred

12

6

3

2

4

10

8

1

5

11

7

9

red red

redred

12

6

3

2

4

10

8

1

5

11

7

9

orange

green

12

6

3

2

4

10

8

1

5

11

7

9

oran

georangegreen

12

6

3

2

4

10

8

1

5

11

7

9

oran

ge

red blue

12

6

3

2

4

10

8

1

5

11

7

9

yellow

12

6

3

2

4

10

8

1

5

11

7

9

Sample answers: 44

Math Masters, p. 237

Teaching Master

Lesson 7�11 631

STUDY LINK

7�11 Spinners and Fractions

80 84

Name Date Time

1. Design your own spinner with as many colors as you wish. Use a pencil until you are satisfied with your work, then color your spinner.

2. Describe your spinner.

a. The chances of the paper clip landing on _________ are _________ out of _________.(color)

b. The paper clip has a _________ chance of landing on _________.(color)

c. It is unlikely that the paper clip will land on _________.(color)

d. It is _________ times as likely to land on _________ as on _________.(color) (color)

e. It is more likely to land on _________ than _________.(color) (color)

3. � 87 � 3 4. 6�9�9� �

5. 945 / 9 � 6. 706 � 5 �10529

Answers vary.

16 R3, 16�36�, or 16�

12�

141 R1, or 141�15�

Practice

12

1

2

3

4

5

6

7

8

9

10

11

Math Masters, p. 234

Study Link Master