Objectives
To review basic ideas of probability, including fairness
and expected results; and to guide the application of fractions
to spinners.
1
materials
Teaching the Lesson
Key Activities
Students 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 Vocabulary
fair (die or spinner) • equal chance • expect • equally (more, less) likely
Ongoing Assessment: Informing Instruction See page 630.
ⵧ Math Journal 2, p. 211
ⵧ Study Link 7 10
䉬
ⵧ Teaching Master (Math Masters, p. 233)
ⵧ crayons, markers, or colored pencils (red,
green, blue, and at least 3 other colors)
ⵧ straightedge
ⵧ 1 large (2") paper clip and 2 pieces of
removable tape per student
ⵧ slate
ⵧ data pad or chart paper (optional)
ⵧ computer with Internet access (optional)
Ongoing Assessment: Recognizing Student Achievement Use Mental Math
and Reflexes. [Data and Chance Goal 4]
2
materials
Ongoing Learning & Practice
Students 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.
ⵧ Math Journal 2, p. 212
ⵧ Student Reference Book, pp. 236 and 237
ⵧ Study Link Masters (Math Masters,
pp. 234–236)
ⵧ Game Masters (Math Masters, pp. 462–466)
See Advance Preparation
3
materials
Differentiation Options
READINESS
Students review fractional
parts of regions.
ENRICHMENT
Students explore
probability activities in Do
You Wanna Bet? Your
Chance to Find Out
About Probability.
ELL SUPPORT
Students add fair and
equal chance to their
Math Word Banks.
Additional Information
Advance 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 (Clarion
Books, 1991).
626
Unit 7 Fractions and Their Uses; Chance and Probability
ⵧ Teaching Master (Math Masters, p. 237)
ⵧ Differentiation Handbook
ⵧ straightedge; crayons or markers;
2 six-sided dice per partnership (optional)
See Advance Preparation
Technology
Assessment Management System
Mental Math and Reflexes
See the Web site on page 629.
See the iTLG.
Getting Started
Mental Math and Reflexes
夹
Math Message
Pose probability questions. Have students write the appropriate fractions and
basic probability terms on their slates. Suggestions:
There are 5 red and 5 blue blocks in the bag.
Think of a game you like in
which the players roll dice. Be
prepared to explain how dice
are used in the game.
5 1
What are the chances of picking a red block? 10, 2, or 50-50 chance
5 1
A blue block? 10, 2, 50-50 chance
0
A green block? 10, impossible
There are 3 red, 1 blue, and 2 green blocks in the bag.
Study Link 7 10
Follow-Up
䉬
3 1
What are the chances of picking a red block? 6, 2, 50-50 chance
1
A blue block? 6, unlikely, or very unlikely
2 1
A green block? 6, 3, unlikely
There are 25 red, 25 blue, 20 green, and 30 yellow blocks in the bag.
50
Have students compare
answers. Ask volunteers to explain how
they solved Problems 5 and 6. Students
indicate thumbs-up if they agree with the
strategies used.
1
What are the chances of picking a red or a blue block? 100 , 2 , 50-50 chance
20 2 1
A green block? 100 , 10 , 5 , unlikely
30 3
A yellow block? 100 , 10 , unlikely
Ongoing Assessment:
Recognizing Student Achievement
Mental Math
and
Reflexes
夹
Use Mental Math and Reflexes to assess students’ ability to express the
probability of an event as a fraction. Students are making adequate progress
if they express the expected probability with a fraction. Some students may
20
1
write the fraction in simplest form, for example, rename 100 as 5 .
[Data and Chance Goal 4]
1 Teaching the Lesson
䉴 Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
Discuss the use of dice in games. For example:
䉯 Dice are used to determine how far a player can move.
䉯 Dice are used to determine numbers that are used in a game.
䉯 You cannot know which number will come up on a die. To
support English language learners, discuss the meaning of the
word die in this mathematical context.
䉯 You should have a fair die—there must be an equal chance
for it to land with any one of its faces up.
Ask students what other devices they have used for the same
purposes as dice. Sample answers: Spinners, coins, number cards
Lesson 7 11
䉬
627
䉴 Spinning a Spinner
Make a mark
at the end of
the paper clip.
PARTNER
ACTIVITY
(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 to
tape 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 paper
clip has an equal chance of landing on any part of the circle. For
example, placing a spinner on an uneven surface will alter the
results of the spins. Therefore, this would not be a fair spinner.
A student uses one hand to hold the pencil
and the other hand to flick the paper clip.
䉴 Doing Spinner Experiments
WHOLE-CLASS
ACTIVITY
(Math Masters, p. 233)
Experiment 1
1. Partners use the first spinner on Math Masters, page 233.
They spin the paper clip four times and record the results in
Problem 1a.
2. Students report their results to you. You tally them on chart
paper or on the board.
3. You and the class find the class totals. Students record them
in Problem 1b.
Ask students to summarize their results. Encourage language like
the following:
䉯 “The paper clip has the same chance of landing on the shaded
part as on the white part.”
Teaching Master
Name
Date
LESSON
7 11
䉬
1.
䉯 “If you spin the paper clip many times, it should land on white
1 out of 2 times.”
Time
Spinner Experiments
䉯 “Chances are, the paper clip will land on the white part half of
the time, because each part is half of the circle.”
Use a paper clip and pencil to make a spinner.
80 84
a.
Spin the paper clip 4 times. Record the
number of times it lands on the shaded part
and on the white part.
shaded
b.
1
䉯 “The chance of landing on the shaded part is 50% (or 2).”
Record the number of times the paper clip
lands on the shaded part and on the white
part for the whole class.
shaded
2.
Answers vary.
white
Experiment 2
Ask partners to color the second spinner on Math Masters,
page 233 blue and red in such a way that the paper clip is twice
as likely to land on blue as on red. Point out that the circle has
been divided into 12 equal parts.
white
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.
Sample answer:
Spin the paper clip 4 times. Record the
number of times it lands on blue and on red.
blue
12
11
1
red
10
2
red
b.
9
Record the number of times the paper clip
lands on blue and on red for the whole class.
blue
red
3
blue
8
Have students share spinner designs. Students should have colored
2
1
of the circle blue and red. There are many possible designs.
3
3
4
7
5
NOTE Have students work in pencil until they are sure they have a correct solution.
6
c.
What would you expect after spinning the paper clip 300 times?
blue
red
200
100
Math Masters, p. 233
628
Unit 7 Fractions and Their Uses; Chance and Probability
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 chart
paper or on the board.
3. You and the class find the class totals. Students record them
in Problem 2b.
Ask students to summarize their results. Encourage language like
the following:
䉯 “The paper clip is more likely to land on blue than on red.”
䉯 “If you spin many times, blue will come up twice as often.”
䉯 “It is hard to know for sure, but if you spin a lot of times, blue
2
will come up about 2 out of 3 spins, or 3 of the time.”
2
䉯 “There is a 3 chance of landing on blue.”
ELL
Adjusting
the Activity
As probability terms enter class discussions
in the context of solving problems, write them
on chart paper or on the board and review
their meanings.
AUDITORY
䉬
䉬
KINESTHETIC
䉬
TACTILE
VISUAL
Finally, have students complete Problem 2c and discuss their
answers. Make sure they understand the meaning of the word
expect 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 red
exactly 100 times.
When students describe chance events, encourage them to use a
variety 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.
䉴 Designing Spinners
PARTNER
ACTIVITY
(Math Journal 2, p. 211)
Have students complete journal page 211 and then share results
and spinner designs.
Student Page
Date
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 for
a specified number of spins to the actual results.
Time
LESSON
7 11
䉬
Making Spinners
1. Make a spinner. Color the circle in 6 different
12
11
colors. Design the spinner so that the paper
clip has the same chance of landing on each
of the colors.
10
Sample answers:
Purple
Red
3
4
5
7
6
12
2. Make another spinner. Color the circle red,
Encourage students to use such phrases as “equally likely,”
“equal chance,” and “1 out of 6 chances of landing on red” when
they discuss their spinner designs.
Green
White
8
82–86
2
Blue
Yellow
9
For Problem 1, students will probably divide the circle into
6 equal parts. Ask how they decided what size to make each part.
1
of 12 2, so the circle can be divided into 6 equal parts by
6
starting at 0 and counting by 2s.
1
11
1
blue, and green so that the paper clip has
1
䉬 a 6 chance of landing on red
10
Green
Red
2
and
1
䉬 a 3 chance of landing on blue.
Green
9
red?
1
6
2
blue? 6
, or
1
3
3
green? 6
, or
1
2
Blue
Green
8
a. What fraction of the circle did you color
3
Blue
4
5
7
6
b. Suppose you plan to spin the paper clip 24 times.
About how many times would you expect it to land on
red?
4
blue?
8
green?
12
c. Suppose you plan to spin the paper clip 90 times.
About how many times would you expect it to land on
red?
15
blue?
30
green?
45
211
Math Journal 2, p. 211
Lesson 7 11
䉬
629
In discussing Problems 2b and 2c, give students opportunities to
use the language of chance events and to compare the likelihood
of the paper clip landing on the various colors. For example:
䉯 “The paper clip is more likely to land on blue than on red, but
less likely to land on blue than on green.”
䉯 “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.”
1
1
䉯 “The chance of landing on red is 6, so 6 of the circle should
be red.”
䉯 “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 Instruction
Watch for students who may misunderstand the term expect. For example, in
Problem 2b, the paper clip will not necessarily land on red exactly 4 times out of
every 24 spins, or exactly 8 times on blue.
2 Ongoing Learning & Practice
䉴 Playing Chances Are
PARTNER
ACTIVITY
(Student Reference Book, pp. 236 and 237;
Math Masters, pp. 462–466)
Students play Chances Are to practice using basic probability
terms to describe the likelihood of events.
Student Page
Date
Time
LESSON
7 11
1. According to a survey of 800 students at
3
Martin Elementary, about 4 of them chose
pizza as their favorite food. Of those who
1
chose pizza, 2 liked pepperoni topping the
best. How many students liked pepperoni
topping the best?
300
2. Multiply. Use a paper-and-pencil algorithm.
71 ⴱ 38 2,698
A U D I T O R Y
3. a. Hannah drew a line segment
1
long. Then she erased 2 inch.
inches
4. Write an equivalent fraction, decimal, or
whole number.
Decimal
inches
a. 0.70
b.
How long is the line segment now?
5
18
c.
inches
0.25
1.0
d. 0.2
Fraction
70
100
2.96
Rule:
in
100.54
97.58
55.91
52.95
72.03
69.07
67.44
59.21
56.25
2
10
1 yd 2
3 ft 4
2 yd 8
80 in. 9 ft
108 in. 1
12
yd in.
3
b. 40 in. c.
e.
162–166
ft
in.
in.
129
212
Math Journal 2, p. 212
630
T A C T I L E
䉬
V I S U A L
INDEPENDENT
ACTIVITY
9
9
6. Complete.
d.
70.4
䉴 Math Boxes 7 11
61 62
a. 5 ft out
䉬
(Math Journal 2, p. 212)
25
100
55–57
5. Complete the table and write the rule.
K I N E S T H E T I C
䉬
How long is the line segment now?
7
b. Joshua drew a line segment 8 inch
3
long. Then he added another 4 inch.
䉬
18 19
59
1
18
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.
students
5
18
ELL
Adjusting the Activity
Math Boxes
䉬
Unit 7 Fractions and Their Uses; Chance and Probability
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 7-9. The skill in Problem 6 previews
Unit 8 content.
Study Link Master
䉴 Study Link 7 11
䉬
Name
INDEPENDENT
ACTIVITY
Date
STUDY LINK
Spinners and Fractions
7 11
䉬
(Math Masters, pp. 234–236)
Time
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.
1.
80 84
12
Home Connection Students design and describe a
spinner. Also, in preparation for Lesson 8-1, students are
asked to measure the distance between the appliances in
their kitchens.
11
1
10
2
3
9
4
8
7
5
6
Describe your spinner.
2.
3 Differentiation Options
READINESS
䉴 Dividing Circles into
PARTNER
ACTIVITY
Answers vary.
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)
5–15 Min
Practice
Fractional Parts
29
3.
(Math Masters, p. 237)
945 / 9 5.
87 3
4.
105
6.
16 R3, 1636, or 1612
1
706 5 141 R1, or 141 5
6冄9
苶9
苶
Math Masters, p. 234
To explore fractional parts of regions, have students divide circles
into equal parts and color specified fractions of the regions. Discuss
how equivalent fractions can be used to solve the problems.
ENRICHMENT
䉴 Investigating Chance Events
SMALL-GROUP
ACTIVITY
15–30 Min
Literature Link To apply students’ understanding of
probability, have them conduct and report results for
experiments found in Do You Wanna Bet? Your Chance to
Find Out About Probability by Jean Cushman (Clarion
Books, 1991). Suggestions:
䉯 Chapter 7, “Winners and Losers, Roll of the Dice”: Students
tally each “double” in 100 rolls of two dice and compare
expected and actual results.
Teaching Master
Name
Date
LESSON
Time
Fractions of Circles
7 11
䉬
Divide each circle into equal parts and color as directed.
Sample answers:
1.
12
9
w
6
5
red
red
12
7
6.
9
r
3
4
8
7
6
12
10
2
5
5
3
11
red
6
Divide into 12 equal parts.
1
Color red in a different way.
1
ed
4
1
red
6
3
10
3
ge
8
or
an
4
Divide into 12 equal parts.
1
Color red.
11
green
9
2
red
9
3
red
8
4
red
5.
orange
7
2
nge
ora
3
1
ora
10
2
ge
n
8
3
12
11
green
9
5
6
Divide into 6 equal parts.
1
1
Color green and orange.
1
10
(Differentiation Handbook)
To provide language support for probability, have students use the
Word Bank Template found in the Differentiation Handbook. Ask
students to write the terms fair and equal chance, draw pictures
related to each term, and write other related words. See the
Differentiation Handbook for more information.
4.
6
3
4
7
Divide into 6 equal parts.
1
2
Color green and orange.
11
2
8
5
12
1
red blue
9
4
6
3
12
10
3
6
5–15 Min
3
11
llo
䉴 Building a Math Word Bank
3.
Divide into 3 equal parts.
1
1
Color red and blue.
1
2
7
SMALL-GROUP
ACTIVITY
2.
2
11
10
8
ELL SUPPORT
44
Divide into 2 equal parts.
1
Color yellow.
ye
䉯 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.
7
6
5
Math Masters, p. 237
Lesson 7 11
䉬
631