Math
Fall Operational 2015
Algebra 1
Item #5
Launching a Rocket
M42063
Prompt
Rubric
Task is worth a total of 3 points.
M42063 Rubric
Score Description
3
Student response includes the following 3 elements.
o correct estimation for the average rate of change
o correct mathematical reasoning used to determine rate of
change
o correct calculations used to derive the estimation for rate
of change
Sample Student Response:
Looking at the graph, I can determine that a  2.5 seconds.
Thus, I know h 2.5  34.25. Using this information and
knowing h (1 )  2 3 meters, I can determine that the average
rate of change from 1 to a as 34.25  23  11.25  7.5
2.5 1
1.5
meters per second. From looking at the graph, I can also
determine that a is where the maximum height will be reached
and I can also determine there is symmetry around a. The
change in height between a and b is less than the change
between 1 and a. Thus, the rate of change will be close to 7.5
(but less than 7.5) and the value will be negative. I can also
estimate that b  3.6 seconds and h ( b )  2 8 meters, thus
34.25  28  6.25  5.68 meters per second. So, a
1.1
2.5  3.6
reasonable estimation for the average rate of change between
a and b seconds is  6 meters per second.
2
Notes:
o An acceptable range for the x-value of h(b) is 3.5 to 3.75
seconds.
o An acceptable range for the y-value of h(b) is 27 to 28.5
meters.
o An acceptable range for the change in x is positive or negative
1.0 to 1.25 seconds.
o An acceptable range for the change in y is positive or negative
5.75 to 7.5 meters.
o An acceptable range for the estimate of the rate of change is 5.0 to -7.5 meters/second.
Student response includes 2 of the 3 elements.
1
Student response includes 1 of the 3 elements.
0
Student response is incorrect or irrelevant.
Anchor Set
A1 – A8
A1
Score Point 3
Annotations
Anchor Paper 1
Score Point 3
The response receives full credit. The student includes all of the three required elements.

The response gives a correct estimation for the average rate of change (an average
estimate rate of change would be -5.6 meters per second).

The response provides mathematical reasoning used to determine rate of change (I
can find the average rate of change by the difference in y (meters) divided by the
difference in x (seconds)).

The response displays correct calculations used to derive the estimation for rate of
change ( 34.25  28  6.25; 2.5  3.6  1.1; 6.25
 5.6 ).
1.1
A2
Score Point 3
Annotations
Anchor Paper 2
Score Point 3
The response receives full credit. The student includes all of the three required elements.

The response gives a correct estimation for the average rate of change (A reasonable
estimate of the average rate of change of the height of the rocket is -5.625 meters
per second).

The response provides mathematical reasoning used to determine rate of change (I
figured out that the rocket’s height changed about -6.75 meters. I estimated the time
between the two heights to be about 1.2 seconds. I divided -6.75 by 1.2). The
student is not required to explain the negative value to receive full credit for element
two, the mathematical reasoning used to determine rate of change.

The response displays correct calculations used to derive the estimation for rate of
change (I divided -6.75 by 1.2 and got -5.625 meters per second).
A3
Score Point 2
Annotations
Anchor Paper 3
Score Point 2
The response receives partial credit. The student provides two of the three required
elements.

The response provides mathematical reasoning used to determine rate of change
(you subtract 34.25 from 23 to find the difference of height, and then divide it by 1.5,
the difference of seconds between the height).

The response displays correct calculations used to derive the estimation for rate of
change (you subtract 34.25 from 23 to find the difference of height, and then divide it
by 1.5, the difference of seconds between the height). Performing this calculation
would result in a negative answer.
The response does not account for the rocket decreasing between h(a) and h(b). This
decrease will make the estimate negative. No credit for element 1.
A4
Score Point 2
Annotations
Anchor Paper 4
Score Point 2
The response receives partial credit. The student provides two of the three required
elements.

The response gives a correct estimation for the average rate of change (Rate of
change =-6.5 meters per second).

The response provides mathematical reasoning used to determine rate of change
(There is about a one second time difference between h(a) and h(b) and there is
about 6.5 meters difference between a and b, but the slope is negative so it is -6.5
meters per second).
The response fails to show calculations to determine the meters per second, therefore no
credit is earned for element three. To earn credit for element three, the rate must show or
explain the division of the difference between the heights over the difference between the
times.
A5
Score Point 1
Annotations
Anchor Paper 5
Score Point 1
The response receives partial credit. The student provides one of the three required
elements.

The response gives a correct estimation for the average rate of change (-6.8 meters
per second).
The response provides no mathematical reasoning and no calculation, therefore no credit is
earned for elements two or three.
A6
Score Point 1
Annotations
Anchor Paper 6
Score Point 1
The response receives partial credit. The student provides one of the three required
elements.

The response provides mathematical reasoning used to determine rate of change (For
every 7meters traveled it takes aprox. 1.1 seconds). While the response does not
show the division step, the explanation does include the relationship between the
change in y and the change in x, which is necessary for credit for the mathematical
reasoning. This can either be explained, as is done in this response, or shown in the
work as the division step.
The response does not account for the rocket decreasing between h(a) and h(b). This
decrease will make the estimate negative. The response fails to show the calculations to
determine the meters per second, therefore no credit is earned for element three.
A7
Score Point 0
Annotations
Anchor Paper 7
Score Point 0
The response receives no credit. The student provides none of the three required elements.
The response calculates the distance from h(a) to h(b) only, without regard to time, making
this only a measure of distance and not a rate of speed. Therefore, no credit is earned.
A8
Score Point 0
Annotations
Anchor Paper 8
Score Point 0
The response receives no credit. The student provides none of the three required elements.
The rate of change is given as a positive value and the minimal work (I rounded the
numbers and then subtracted them) appears to indicate a distance, rather than a rate of
change. No credit.
Practice Set
P101 - P105
P101
P102
P103
P104
P105
Practice Set
Score
Paper
P101
2
P102
1
P103
3
P104
0
P105
2