Math Problem-Solving Lesson: Matching Colors Spinner Game
(Adapted from Connected Mathematics’ What Do You Expect? Investigation 1.1, Prentice Hall, 2001)
Link
SOL/POS/Objective: Students will compare theoretical and experimental probability, and they will also use
knowledge of probability to determine whether a game is fair.
SOL 7.14: Probability
SOL 8.11: Probability
Engage
Problem Engagement:
Students can read the directions for the game and read questions 1 and 2 for the launch or The teacher may
want to toss a coin for review and ask: What is the probability of getting a heads? What are the possible
outcomes? Are they equally likely? What is the probability of getting a tail?
The teacher could toss the coin a few times and ask: What would happen if you continue the experiment for
more trials?
The class may need to discuss what it means for a game to be fair.
Active
Inquiry Investigation:
Students will read the directions for the game Match/No-Match and answer questions #1 and 2 which are
predictions. They will then play the game with partners.
Devising a Plan:
Students will experiment to answer questions 3 and 4 and to help answer their predictions from earlier.
Students will investigate the problem by finding the theoretical probably as well as the experimental
probability, listing all possible outcomes.
Carrying Out the Plan:
Students will compute the theoretical and experimental probabilities of spinning a match, in order to help
answer the question: is this game fair? They can use their findings from the Experimental probability or
Theoretical probability or both to answer the question.
Reflection
Reflect:
Students should have explained that this was not a fair game. They will then need to explain how the rules can
be changed to make this a fair game. Answers to this part will vary. The teacher may want to have partners get
together with another pair to form a group and they can discuss their strategies for making the game fair. Or
the teacher can have the class collect the experimental data, discuss the results and summarize: Is it fair? Based
on the experimental probabilities we found for the class data, do you think Match and No-Match are equally
likely?
Next
Tomorrow: Students made lists of possible outcomes in this experiment, but tomorrow they will learn to
make a tree diagram or area model to show all possible outcomes of this experiment.
Matching Colors Spinner Game
Your best friend just came back from vacation and says she learned a game that she just has to
play with you. It is called Match/No-Match and you use a spinner like the one shown here.
Blue
Red
The rules are:
 Two players take turns spinning a spinner.

On each turn, a player spins the pointer of the spinner twice. If both spins land on the
same color (a match), then Player A scores 1 point. If the two spins land on different
colors (a no-match), then Player B scores 2 points.

The player with the most points after 24 spins wins.
1. Do you think this is a fair or unfair game?
__________________________________________________________________
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2. Are both players equally likely to win?
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Experimental Probability

Play the Match/No-Match game with a partner.

For each turn (remember a turn is two spins), record the color pair, for example,
blue-red in the box below. Award points to the appropriate player.

Take a total of 24 turns (12 for each player).
Player A points ________
Player B points________
3. Use your results from the game to determine the experimental probabilities of a match
and a no-match.
P(Match) = _____
P(No-Match) = ______
Theoretical Probability
4. List all the possible outcomes of a turn (2 spins).
5. Use the list of possible outcomes to determine the theoretical probability of a match and
a no-match.
P(Match) = ______
P(No-Match) = ______
6. Are the outcomes equally likely? That is, does each outcome have the same chance of
occurring?
__________________________________________________________________
________________________________________________
Summary
7. How do the experimental and theoretical probabilities compare?
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8. Is Match/No-Match a fair game? If it is fair, explain why. If it is not fair, explain how the rules can be changed to
make the game fair.
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Problem Solving Rubric
Category
Understanding the
Problem –
Researching and
Gathering
Information
Devising the Plan
and Carrying out
the Plan
Problem
Reflection
D–1
C–2
B–3
Lacks
Partially
Explained
understanding of
explained
predictions and
the problem – is
predictions and reasoning behind
unable to move
reasoning behind
his/her
on without a
his/her
predictions, with
complete
predictions,
some missing
explanation and
without key
details.
restatement from
concepts.
the instructor.
Used only one
Brainstormed a
Brainstormed a
strategy, required few strategies but
few strategies,
assistance to
needs assistance
decided on one
evaluate the
to formulate a
strategy that
strategy or is
strategy or a set
would be most
missing key steps of complete steps
effective OR
to solving the
to solve the
brainstormed a
problem.
problem OR
few strategies
Attempted to
strategy and/or
and decided on a
solve the given
steps are
set of steps that
problem without
inconsistent or
were incomplete
working through
incomplete.
or inconsistent.
details OR solved
Solved given
Solved given
a different
problem without
problem
problem than
working through
appropriately
given.
any details.
with some details
covered with
original or
modified plan.
Required
assistance to
evaluate solutions
and could not
suggest strategy
to make game
fair.
Limited
evaluation of
theoretical and
experimental
results. Flawed
explanation for
strategy to make
game fair.
Compared
theoretical and
experimental
results and
suggested an
inappropriate
strategy for
making the game
“fair”.
A–4
Thoroughly
explained
predictions and
reasoning behind
his/her
predictions.
Brainstormed
many strategies,
decided on one
strategy that
would be most
effective OR
brainstormed
many strategies
decided on a set
of steps that
would resolve
the problem
thoroughly.
Solved given
problem
appropriately
with all details
thoroughly
covered with
original or
modified plan.
Compared
theoretical and
experimental
results and
suggested at least
one appropriate
strategy for
making the game
“fair”.
Score