Skills:
Solving problems about
outcomes and probabilities
using game spinners
Teaching Taking a Spin
Students compare, contrast, and analyze
three different game spinners.
Tasks
Tier 1
Differentiated Activities for Teaching Key Math Skills: Grades 4-6 © Lee & Miller, Scholastic Teaching Resources
Below Level
Find possible outcomes.
X
Conduct a probability experiment with spinners.
X
Display results in a frequency table.
X
Solve problems about outcomes or probabilities.
X
Design spinners that reflect given probabilities.
Tier 2
On Level
Tier 3
Above Level
X
X
X
X
X
X
Explain solution strategies in writing.
X
Find the probability of two or more independent events.
X
Getting Started
See the tips below for introducing the lesson. Make copies of the student data sheet (page 64) and the
appropriate leveled activity sheet for each group of learners (pages 65–67).
Access prior knowledge by discussing chance and outcomes in familiar games and terms used for
probability, such as likely, unlikely, certain, possible, and impossible.
Tier 1
• Find the Outcomes: Define
outcome. Discuss what
makes an outcome more or
less likely, and what equally
likely outcomes are. Discuss
some impossible outcomes
for these spinners and why
the outcomes are equally
likely for Spinners A and B.
• Do an Experiment: Clarify
the details of the experiment.
Have students work in pairs
or small groups. You might
provide ready-made spinners
like Spinners A and B for
each team. Review using
tally marks. Point out that
the “Frequency” column will
show the total of the tallies
for each sum.
• Summarize the Results:
Talk about outcomes before
students summarize the
results.
Tier 2
• Find the Outcomes: Review
outcomes and what makes
outcomes equally, more, or
less likely. Discuss outcomes
that are impossible and
certain. Help students make
lists or tree diagrams to solve
items 3–4.
• Find the Probability: Define
probability as favorable
outcomes (numerator of
fraction) out of all possible
outcomes (denominator).
• Design a Spinner: You
may have students work
in pairs. They should use
a straightedge to draw the
sections of their spinners.
Encourage them to use a
protractor to draw sectors at
correct degree measures or
guide students to use visual
reasoning to estimate the
sizes of the sectors.
Tier 3
• Find the Probability: Define
probability as favorable outcomes
(numerator of fraction) out of all
possible outcomes (denominator).
Use probability notation, such as:
P(3) = probability of spinning a 3;
P(even number) = probability of
spinning an even number. Review
inequality symbols. In items 5–9,
students find the probability of two
or more independent (mutually
exclusive) events. Explain that one
outcome does not affect another,
such as spinning a spinner and
picking a card.
• Write About It: Discuss why there
are a total of 48 ways to reach all
possible sums. [4 x 3 x 4]
• Design Spinners: You may have
students work in pairs. Encourage
them to use protractors to find
the exact degree measures of the
sectors. Have students compare their
spinners and explain their strategies.
63
Name
Skills:
Date
Take a Spin:
Solving problems about
outcomes and probabilities
using game spinners
Data Sheet
Differentiated Activities for Teaching Key Math Skills: Grades 4-6 © Lee & Miller, Scholastic Teaching Resources
Chauncey Spinnaker does not like to spin his wheels. He
hates to spin out of control. He likes to spin tall tales and he
really likes taking a spin on his skateboard.
Best of all, he loves to make spinners and play games with
them. His nickname at school is Dr. Chance.
Here are three spinners Chauncey made. He will use them
at his school’s annual Math Games Day.
Spinner A
Spinner B
1
2
4
3
1
3
Spinner C
4
4
1
3
2
64
2
Name
Taking a Spin:
Date
Activity Sheet
Spin the Spinners
Differentiated Activities for Teaching Key Math Skills: Grades 4-6 © Lee & Miller, Scholastic Teaching Resources
Each spin of a spinner is an experiment. Each possible result of an experiment is called an
outcome. Solve these problems.
1.
You spin Spinner A. What are all the possible outcomes?
2.
Are all outcomes equally likely for Spinner A? Explain.
3.
If you spin Spinner B, which is not a possible outcome: 1, 2, 3, or 4?
Why?
4.
What are all the possible outcomes when you spin Spinner C?
Are all these outcomes equally likely? Why?
5.
If you win a game when you get the most 3s in 10 spins, would you want to use Spinner A,
Spinner B, or Spinner C? Why? Explain your thinking.
Do an Experiment
Suppose you spin both Spinners A
and B and add the two numbers you
get. List all the possible sums here.
Sum
Tally
Frequency
Now guess which sum you will spin the
most often in 25 spins. Guess:
Write each sum you listed above in the
Sum column of the table to the right.
Using separate paper and materials, make spinners like Spinners A and B. Then spin Spinner A and
Spinner B for a total of 25 times each. Tally the sum you get each time you spin the two spinners.
Fill in the Frequency column with the total for each sum after you finish all 50 spins.
Summarize the Results
On separate paper, summarize. Use these questions as a guide: Which sum did you get most often?
Which sum did you get least often? How did the results of the experiment compare with your guess?
65
Name
Taking a Spin:
Date
Activity Sheet
Spin the Spinners
Differentiated Activities for Teaching Key Math Skills: Grades 4-6 © Lee & Miller, Scholastic Teaching Resources
Each spin of a spinner is an experiment. Each possible result of an experiment is called an
outcome. Solve these problems.
1.
You spin Spinner A. List all the possible outcomes.
Are all outcomes equally likely? Explain.
2.
You spin Spinners A and B and add the two numbers. What are all the possible sums?
Which sum would you expect to get most often in 25 spins? Why?
3.
If you spin all the spinners and add the three numbers you get, what sums are possible?
(Hint: Make a diagram or list.)
4.
Use your diagram or list from item 3. Which sum do you think would come up most often?
Least often? Why?
Find the Probability
5.
You spin Spinner A. What is the probability of spinning a 1?
a 4?
a number less than 4?
6.
You spin Spinner B. What is the probability of spinning an odd number?
an even number?
7.
Use Spinner B. What is the probability of spinning a 5? Why?
8.
Which spinner gives the least probability of spinning a 3? Why?
Design a Spinner
Make the spinner described below in the empty circle.
44 Make 3 sections.
44 Label them R, Y, and G.
44 Make the probability of spinning R = ½.
44 Make the probability of spinning Y = ¼.
44 Make the probability of spinning G = ¼.
44 Draw the pointer.
66
Spinner
Name
Taking a Spin:
Date
Activity Sheet
Find the Probability
Differentiated Activities for Teaching Key Math Skills: Grades 4-6 © Lee & Miller, Scholastic Teaching Resources
Each spin of a spinner is an experiment. Each possible result of an experiment is called an
outcome. Solve these problems.
1.
You spin Spinner A. What is P(3)? What is P(even number)?
2.
You spin Spinner B. What is P(odd number)? What is P(even number)?
3.
For which spinner is P(4) = 0?
4.
You spin Spinner C. What is P(<2)?
5.
You spin Spinners A and B. What is the probability of spinning (1, 3)?
6.
You spin Spinners A and B. What is the probability of spinning (2, odd number)?
7.
You spin Spinners B and C. What is the probability of spinning (1, 1)?
8.
You spin Spinners A and C. What is the probability of spinning (4, 1)?
What is P(<3)?
Of spinning (1, 4)?
9.
You spin Spinners A, B, and C. What is the probability of spinning (1, 1, 1)?
Of spinning (4, 4, 4)?
Write About It
44 What if you spin all 3 spinners and add the 3 numbers you get?
44 What is P(sum of 3)?
44 What is P(sum of 7)?
44 Explain how you determined your answer.
Design Spinners
Use a compass and straightedge to sketch the spinners described. Use a separate page.
Spinner 1 has 4 sections.
The probability of spinning one of the
sections is 3 times that of spinning any
other section.
Spinners 2 and 3 have different numbers
of sections. But for each spinner, the
probability of spinning 1, 2, or 3 = 1/3.
67
Answer Key
Taking a Spin
Differentiated Activities for Teaching Key Math Skills: Grades 4-6 © Lee & Miller, Scholastic Teaching Resources
Tier 1, page 65: Spin the Spinners: 1. 1, 2, 3, and 4; 2. Yes, because
all the sections are the same size 3. 4 because 4 is not one of the
choices included on the spinner. 4. 1, 2, 3, or 4; No because the
sections are different sizes and 4 appears twice 5. B; The section for
3 is a greater part of its spinner than in the other spinners; Do an
Experiment: 2, 3, 4, 5, 6, 7; Answers will vary. Check student tables;
Summarize the Results: Answers will vary.
Tier 2, page 66: Spin the Spinners: 1. 1, 2, 3, 4; Yes, because all the
sections are the same size; 2. 2, 3, 4, 5, 6, 7; The sum that could be
the result of the greatest number of spins is 4 or 5 3. 3, 4, 5, 6, 7,
8, 9, 10, 11 4. Answers will vary; There are 10 ways to get a sum of 7
and 1 way for sums of 3 and 11. Find the Probability: 5. 1 ⁄4; 1 ⁄4; 3 ⁄4
6. 2 ⁄ 3; 1 ⁄ 3 7. 0; 5 is an impossible outcome 8. Spinner C, P(3) = 1 ⁄8;
Design a Spinner: Check student spinners. The spinner should be divided
in half. One half is labeled R and the other half is equally dived into Y and
G sections. The order of sectors doesn’t matter.
Tier 3, page 67: Spin the Spinners: 1. 1 ⁄4; 1 ⁄ 2 2. 2 ⁄ 3; 1 ⁄ 3 3. Spinner B
4. 1 ⁄ 2; 5/8 5. 1 ⁄4 x 1 ⁄ 3 = 1 ⁄12 6. 1 ⁄4 x 2 ⁄ 3 = 2 ⁄12 or 1 ⁄6 7. 1 ⁄ 3 x 1 ⁄ 2 = 1 ⁄6
8. 1 ⁄4 x 1 ⁄ 2 = 1 ⁄8; 1 ⁄4 x 1 ⁄4 = 1 ⁄16 9. 1 ⁄4 x 1 ⁄ 3 x 1 ⁄ 2 = 1 ⁄ 24; 0; Write About It:
1 ⁄48; 10 ⁄48 or 5 ⁄ 2 4. Check student explanations; Design Spinners: Check
student spinners. The Spinner 1 should be divided in half, with one half
subdivided into thirds. Sample answer for Spinners 2 and 3: one spinner
has 3 sections of equal size and sections labeled 1, 2, and 3; the other has
6 sections of equal size with two 1s, two 2s, and two 3s.
80