Table of Contents > Cluster 4 > Open-ended Items > Sample 3

HSPA Math Macro 4b: Using functions to represent mathematical
and real-world situations

Sample Open-ended Item #3

Mike dropped a basketball ball from his bedroom window a height of 20 feet.  Each time the ball bounced, it reached a maximum height of approximately half that of its previous height. Draw a graph to represent the relationship between the number of times the ball bounces and the height reached by the ball. What is the total of the heights the ball reached after the 4th bounce. What do you think this total would have been if the ball had bounced 20 times?

"1" Response | "2" Response | "3" Response | Top

"1" Response

This response scored a "1" because it shows some understanding of the relationship between the bounce and the height attained, but the answers provided are incorrect and not all parts of the question are answered.  

  "1" Response | "2" Response | "3" Response | Top

"2" Response

This response scored a "2" because the chart is correct, but the last question is not answered correctly.

This response scored a "2" because the graph is correct (though it needs to be labeled), and the answer to the first part of the question is correct.  The conclusion about the height of the 20th bounce is theoretically not the correct answer, though it may be a practical reality.

"1" Response | "2" Response | "3" Response | Top

"3" Response

Both these responses scored "3" because they answered all parts of the question correctly, and the graphs are properly constructed.

"1" Response | "2" Response | "3" Response | Top

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