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Open – Ended Template

 

Pat Miller

Joanna McIntyre

Karen Wallace

Patricia Douglass

 

Grade Level: 3-5

Content Area:

Probability and Prediction

 

PA standard addressed: 2.7.5D                  

 

NCTM Standard Addressed: Data Analysis and

Probability – Understand and apply basic concepts of probability

 

Problem Name: The Spinner Game

 

 

Problem and Directions:

 

Jill and Sam were playing a game against the computer.  The computer gets the expected probability.  They used the spinner pictured below:

 

 

 

Part A:

On the chart below, write in fraction form the expected probability for each number on the spinner.

 

Number on

Spinner

 

1

 

    2

 

   3

 

   4

 

    5

 

Probability of

Spinning this

number

 

 

 

 

 

 

 

Part B:

The results of Jill’s spins were: 1,5,2,4,3,3,2,3.

The results of Sam’s spins were: 1,3,1,5,5,3,4,3.

Complete the chart below to show in fraction form the results of each child’s spins.

 

 

Number on

Spinner

 

1

 

2

 

3

 

4

 

5

 

Jill’s

Results

 

 

 

 

 

 

Sam’s

Results

 

 

 

 

 

 

 

 

Part C:

Did Jill or Sam come closer to the computer’s results?  Explain your answer.

 

 

 

 

 

Solution

 

Part A:

Number on

Spinner

 

   1

 

     2

 

    3

 

    4

 

    5

 

Probability of

Spinner

 

 1/8

 

 3/8

 

 2/8

 

 1/8

 

 1/8

 

Part B:

 

Number on

Spinner

 

1

 

2

 

3

 

4

 

5

Jill’s

Results

 

1/8

 

2/8

 

3/8

 

1/8

 

1/8

Sam’s Results

 

2/8

 

0/8

 

3/8

 

1/8

 

2/8

 

 

Part C:

Jill came closer to the computer’s result.  She matched the computer’s results for 3 numbers – 1,4, and 5.  Sam matched the computer’s results for only 1 number – 4

 

OR

 

Jill came closer to the computer’s result.  She matched the computer’s result for 1, she was 1 off for 2, 1 off for 3, matched for 4 and matched for 5 for a total of 2 off.

 

Sam was 1 off for 1, off 3 for 2, was 1 off for 3, matched 4, and was 1 off for 5 for a total of 6 off.

 

Scoring the Rubric

Part A

 

 

        1 point

All correct possibilities written in fraction form

 

Part B

 

 

2 points  

All entries correct and written in fraction form

 

1 point

At least 8 entries correct and written in fraction form

 

Part C

 

 

3 points

The explanation demonstrates why Jill won and all parts are correct.

Must include some discussion of probability.

Translating errors from Parts A and Part B, if                                                                                 used correctly in the explanation, can still receive full credit.

                            

2 points

Jill is declared winner. Explanation is attempted but incomplete. For example, no comparison between Jill and Sam is made.

Translating errors from Parts A and B, if used correctly in explanation can still receive full credit.

1 point

Jill is declared winner. Faulty or no explanation.

 

 

Rubric

 

5 - Advanced Understanding, Excellent

 

·       Attains all 6 points

 

4 - Satisfactory Understanding

 

·       Attains 5 points

 

3  - Almost Satisfactory Understanding

 

·       Attains 4 points

 

2 - Partial Understanding

 

·       Attains 3 points

 

1 - Minimal Understanding

 

·       Attains 1 or 2 points

 

0 - Incorrect

 

·       Attains 0 points

 

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