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Write-up


Title
Basketball Performance

 

Problem Statement
Suppose you are a basketball player for your middle school. In the last 13 games you have made the following number of baskets.

game #

# of baskets

1

4

2

7

3

7

4

3

5

8

6

3

7

5

8

3

9

4

10

5

11

7

12

6

13

7


Based on your performance in the first 13 games, how many baskets do you think you will make in game 14? Explain your answer.


Problem setup

This problem requires us to guess how many points can be made in the 14th game based on information gathered from previous games. 

 

Plans to Solve/Investigate the Problem

My initial plans to solve the problem were to try to find a pattern within the number of baskets and to also see if it correlated with the game.  I created a spreadsheet such as the one below.

Game

Points

Change

1

4

 

2

7

3

3

7

0

4

3

4

5

8

5

6

3

5

7

5

2

8

3

2

9

4

1

10

5

1

11

7

2

12

6

1

13

7

1

14

?

 

The values in the “change” column represent the different between the current and previous game.  Values highlighted in red indicate a loss in points.  There was no obvious pattern.  However, I assumed that if the trend repeated, starting from game 11, then the number of points would increase by 2.  Thus, 9 points would be made on game 14.   

 

Investigation/Exploration of the Problem

Since there was no pattern found, I used a graphing calculator to find the line of regression using a scatter plot with the information provided:  games and number of points.  We were able to create an equation in the form of y=mx+b to plug into the calculator using the “STAT” key.  After plugging in all values for games and points, the calculator gave the values of m=.2606 and b=2.8848, x being the game number.  Therefore if we plug in 14 for x, we would get an approximate value for the number of points.     

 

Extensions of the Problem

None.

Author & Contact
Mesha Rainey
Ms. Rainey

Link(s) to resources, references, lesson plans, and/or other materials
None

 

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