HCPSS Worthwhile Math Task
Fun Spinner
Common Core Standard
S.CP.B.8 Apply the general Multiplication Rule in a uniform probability model, P(A and B) =
P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
MP1:
MP2:
MP3:
MP5:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Use appropriate tools strategically.
Common Core Geometry, Unit 5
The Task
You’ve been hired to create a spinner for the latest game, Take a Chance! The spinner must only
contain red and black sections and each section has one number. The game company needs you
to design a spinner to satisfy the following probabilities:
1.
2.
3.
4.
5.
P(Red and Even Number) = 1/4
P(Black and Odd Number) = 1/4
P(Black|Odd Number) = 3/5
P(Red|Even Number) = 3/7
P(Multiple of 5 and Red) = 1/6
Produce a prototype of the spinner. Use mathematics to explain how you arrived at your answer.
Facilitator Notes
1. Form groups of two or three.
2. Allow students to read the task.
3. Provide paper, compasses, protractors, colored pencils, markers, rulers, and calculators.
(Look for evidence of MP5.)
4. Circulate the room while students are working. If students need starting suggestions: start
with statements 3, 4 to determine number of sections or use statements 1, 4 to determine
how many even numbers, or statements 2, 3, to determine how many odd numbers, etc.
(Look for evidence of MP1 and MP2.)
5. When groups are finished, have them trade spinners to check each other’s answers. (Look
for evidence of MP3.)
6. Allow groups to share their spinners with the class and show or explain how they created
their spinners. (Look for evidence of MP3.)
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Follow-Up Questions
1. Prove your answer is correct using the general multiplication rule.
2. How many degrees are in each sector?
Solutions
In order for the spinner to be correct, the following probabilities, in addition to the givens, must
be true: P(Even) = 7/12
P(Odd) = 5/12
P(Red) = 5/12
P(Black) = 7/12
Student Sample A:
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Student Sample B:
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Follow Up Questions:
1. P(Red and Even) = P(Even)P(Red|Even)
P(Black and Odd) = P(Odd)P(Black|Odd)
2. 30º if you have 12 sections
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.