Math
Released Item 2016
Grade 4
Carl’s Bike Training
VH094716
Prompt
Rubric
Task is worth a total of 6 points.
Carl’s Bike Training – Part A
Score
Description
Student response includes the following 3 elements.
3
•
Modeling component = 1 point
o The student explains or shows the process for finding the
total number of miles Carl rides on Friday.
•
Modeling component = 1 point
o The student explains or shows the process for finding the
total number of miles Carl rides in the three days.
•
Computation component = 1 point
o The student provides a response of 30 miles.
Sample Student Response:
“Carl rides twice as far Friday as he does on Thursday. 7 x 2 =14”
“Carl rides 7+14+9=30 miles in all”
Notes:
•
•
A variety of explanations are possible. As long as the student
explains how to find the total number of miles Carl rides on
Friday and in the three days, credit should be given.
If a computation mistake is made, credit cannot be given for
computation but can be given for a valid explanation.
2
Student response includes 2 of the above elements..
1
Student response includes 1 of the above elements.
0
Student response is incorrect or irrelevant.
Carl’s Bike Traning – Part B
Score
Description
Student response includes the following 3 elements.
•
Modeling component = 1 point
o The student explains or shows the process for finding
the number of additional miles Carl must ride.
•
Modeling component = 1 point
o The student explains or shows the process for finding
the number of additional miles Carl should ride each
day.
•
Computation component = 1 point
o The student provides a response of 2 additional miles
each day.
3
Sample Student Response:
“For Carl to ride 36 miles in the next 3 days, he needs to ride
36-30=6 more miles.”
“For Carl to ride 6 more miles in 3 days, he must ride 6÷3=2 miles
farther each day.”
Notes:
•
•
•
A variety of explanations are valid. As long as the student uses
a valid method to solve the problem, credit should be given.
If a computation mistake is made, credit cannot be given for
computation, but credit should be given for a valid explanation
of how to solve the problem.
If a mistake was made in Part A but carried through Part B
correctly, credit can be given for Part B.
2
Student response includes 2 of the above elements.
1
Student response includes 1 of the above elements.
0
Student response is incorrect or irrelevant.
Anchor Set
A1 – A14
With Annotations
A1
Part A: Score Point 3
Part B: Score Point 3
Annotation
Anchor Paper 1
Part A: Score Point 3
This response receives full credit. It includes each of the three required
elements.
•
The student provides the correct total number of miles Carl rode in
three days (In Thursday, Friday, and Saturday he road his bike 30
miles).
•
The student provides a valid process on how to find the total number of
miles Carl rode on Friday (7 x 2 = 14).
•
The student provides a valid explanation on how to find the total
number of miles for all three days (do 7 x 2 = 14 then add seven 14 +
7 = 21 then add 9 to that for Saturday 21 + 9 = 30).
Part B: Score Point 3
This response receives full credit. It includes each of the three required
elements.
•
The student provides the correct total number of miles Carl will add to
each day (Carl needs to ride two extra miles each day).
•
The student shows a valid process for finding the total number of
additional miles Carl must ride (if we add 2 to each day and there is
three days 2 x 3 = 6, 30 + 6 = 36).
•
The student shows a valid process for finding the number of additional
miles Carl should ride each day (so if we add 2 to each day and there is
three days 2 x 3 = 6).
Note that 6 ÷ 3 = 2 is a basic math fact and other valid, alternative
strategies are acceptable. When calculating the additional miles that Carl will
ride over the next three days (6) the student adds using the starting point
and counting upwards to 36 (30 + 6). Since addition and subtraction have an
inverse relationship, this is a valid strategy, as well as the strategy of
subtracting (36 – 30). The student uses multiplication to show that 2 miles a
day equals 6 miles (2 x 3 = 6), and since multiplication and division also
have an inverse relationship, this is a valid strategy. Finally, multiplying 2 ×
3 shows a clear pattern of three 2’s or 2 miles per day over 3 days.
A2
Part A: Score Point 3
Part B: Score Point 3
Annotation
Anchor Paper 2
Part A: Score Point 3
This response receives full credit. It includes each of the three required
elements.
•
The student provides the correct total number of miles Carl rode in
three days (He rode 30 miles in all).
•
The student provides a valid process on how to find the total number of
miles Carl rode on Friday (You can do 7 x 2 = 14).
•
The student provides a valid explanation on how to find the total
number of miles for all three days (Add it all together. 7 + 14 + 9 =
30).
Part B: Score Point 3
This response receives full credit. It includes each of the three required
elements.
•
The student provides the correct total number of miles Carl will add to
each day (Carl will have to run 2 miles extra each day).
•
The student provides a valid explanation for the total number of
additional miles Carl must ride (2 miles extra each day to get 36. I
added 2 to each number).
•
The student provides a valid explanation for finding the number of
additional miles Carl should ride each day (I added 2 to each number
and got 9, 16, and 11).
Note that 6 ÷ 3 = 2 is a basic math fact and other valid, alternative
strategies are acceptable. Since the student shows in Part A that Carl will ride
a total of 30 miles, it is then simple to use that as a starting point and
visually note (using mental math) that Carl needs to ride an additional 6
miles. In addition, the student shows a clear pattern of adding 2 to each of
the previous three days’ totals, which is a clear equal distribution of 6 miles
over three days. Finally, it shows that the new daily totals add up to 36.
A3
Part A: Score Point 2
Part B: Score Point 3
Annotation
Anchor Paper 3
Part A: Score Point 2
This response receives full credit. It includes two of the three required
elements.
•
The student provides the correct total number of miles Carl rode in
three days (30 miles).
•
The student provides a valid process to find the total number of miles
for all three days (7 + 14 to get 21.then add 21 + 9 to get 30).
There is no explanation or process shown for how the student found number
of miles Carl rode on Friday. The total miles for Friday are included in the
equation (14), but no explanation or process for finding 14 is provided.
Part B: Score Point 3
This response receives partial credit. It includes each of the three required
elements.
•
The student provides the correct total number of miles Carl will add to
each day (If you add 2 more miles each day).
•
The student provides a correct explanation for finding the total number
of additional miles Carl must ride (he needs 6 more miles to get 36. if
you add 2 more miles to each day you will get 36).
•
The student shows a valid process for finding the number of additional
miles Carl should ride each day (9 + 16 + 11 + 36 miles).
It is a valid strategy for students to use the 30 miles from Part A to explain
that Carl needs to ride 6 more miles to reach 36 miles. In addition, the
student clearly shows equal distribution of the 6 miles over three days by
adding 2 to each of the previous days’ distances. Finally, the new distances
are added to show that they add up to 36 total miles.
A4
Part A: Score Point 2
Part B: Score Point 3
Annotation
Anchor Paper 4
Part A: Score Point 2
This response receives partial credit. It includes two of the three required
elements.
•
The student provides the correct total number of miles Carl rode in
three days (30).
•
The student provides a valid operation on how to find the total number
of miles for all three days (14 + 7 + 9 = 30).
There is no explanation or process shown for how the student found number
of miles Carl rode on Friday. The total miles for Friday are included in the
equation (14), but no explanation or process for finding 14 is provided.
Part B: Score Point 3
This response receives full credit. It includes each of the three required
elements.
•
The student provides the correct total number of miles Carl will add to
each day. Two miles is added to each of the day’s mileages in the
equations shown (14 + 2 = 16, 7 + 2 = 9, 9 + 2 = 11).
•
The student provides a valid process for finding the total number of
additional miles Carl must ride (2, 2, 2).
•
The student shows a valid process for finding the number of additional
miles Carl should ride each day by adding 2 to each original total and
finding the new mileage totals of 16, 9, and 11 (14 + 2 = 16, 7 + 2 =
9, 9 + 2 = 11). The pattern of equal distribution of 2’s over three days
clearly addresses this element.
A5
Part A: Score Point 3
Part B: Score Point 1
Annotation
Anchor Paper 5
Part A: Score Point 3
This response receives full credit. It includes each of the three required
elements.
•
The student provides the correct total number of miles Carl rode in
three days (He rode 30 miles).
•
The student provides a valid process on how to find the total number of
miles Carl rode on Friday (2 x 7 = 14).
•
The student provides a valid process for finding the total number of
miles for all three days (7 + 9 + 14 = 30).
Part B: Score Point 1
This response receives partial credit. It includes one of the three required
elements.
•
The student provides a valid process for finding the total number of
additional miles Carl must ride (30 + 6 = 36).
There is no clear process shown for finding the correct total number of
additional miles Carl will add. The student incorrectly attempts to find the
miles Carl should ride by providing a different mileage for each of the three
days (day1, 3; day 2, 1; day 3, 2), so it is unclear what mileage Carl must
ride.
There is no valid process shown for finding the number of additional miles
Carl should ride each day. The student incorrectly distributes the miles to the
days and provides day 1 with 3 miles, day 2 with 1 mile and day 3 with 2
miles (day1, 3; day 2, 1; day 3, 2). The total is 6, but the prompt asks the
student to add the same number of miles to each distance.
A6
Part A: Score Point 3
Part B: Score Point 1
Annotation
Anchor Paper 6
Part A: Score Point 3
This response receives full credit. It includes each of the three required
elements.
•
The student provides the correct total number of miles Carl rode in
three days (30).
•
The student provides a valid process on how to find the total number of
miles Carl rode on Friday (7 x 2 = 14).
•
The student provides a valid process for finding the total number of
miles for all three days (7 + 14 + 9 = 30).
Part B: Score Point 1
This response receives partial credit. It includes one of the three required
elements.
•
The student provides a valid process for finding the total number of
additional miles Carl must ride (30 + 6 = 30).
The student provides an incorrect total number of miles Carl will add to each
day (3 miles a day).
An incorrect process is provided for finding the number of additional miles
Carl should ride each day (6 ÷ 2 = 3).
A7
Part A: Score Point 3
Part B: Score Point 0
Annotation
Anchor Paper 7
Part A: Score Point 3
This response receives full credit. It includes each of the three required
elements.
•
The student provides the correct total number of miles Carl rode in
three days (30 miles).
•
The student provides a valid process for finding the total number of
miles Carl rides on Friday (7 x 2 = 14).
•
The student provides a valid explanation for finding the total number of
miles for all three days (Then I added 9 + 7 = 16 miles. After that I
added 14miles plus 16 miles and that was 30 miles).
Part B: Score Point 0
This response receives no credit. It includes none of the required elements.
The student adds various numbers of miles to each day, indicating no
understanding of the question (add 1 mile to thursday then 2 miles on friday
. . . add 12 miles to saturday).
There is no process or explanation shown for finding the number of additional
miles that Carl must ride.
Additionally, no explanation is provided for finding the number of additional
miles Carl should ride each day. The miles of 1, 2, and 12 are incorrect and
are not evenly distributed miles as required by the prompt.
A8
Part A: Score Point 2
Part B: Score Point 1
Annotation
Anchor Paper 8
Part A: Score Point 2
This response receives partial credit. It includes two of the three required
elements.
•
The student provides a valid process for finding the total number of
miles Carl rides on Friday (7 x 2 = 14).
•
The student provides a valid process for finding the total number of
miles for all three days (7 + 14 + 9).
An incorrect total number of miles (20) is provided due to a calculation error
in the math work to find the total number of miles Carl rides for all three
days (7 + 14 + 9 = 20).
Part B: Score Point 1
This response receives partial credit. It includes one of the three required
elements.
•
The student provides a valid process for finding the total number of
additional miles Carl must ride based on the incorrect solution provided
in Part A (20 + 7 + 7 +2 = 36). The incorrect total number of miles
determined in Part A (20) is used appropriately in Part B to determine
the additional miles needed to reach a total of 36 miles (The number of
miles added was 16 miles).
An incorrect total number of miles added to each day is provided (7 the first
day, 7 the next day and 2 the last day).
No valid explanation or process is provided to find the number of additional
miles Carl should ride each day (7 + 7 + 2). The days are not evenly
distributed as required by the prompt.
A9
Part A: Score Point 2
Part B: Score Point 0
Annotation
Anchor Paper 9
Part A: Score Point 2
This response receives partial credit. It includes two of the three required
elements.
•
The student provides a valid process for finding the total number of
miles Carl rides on Friday (7 x 2 = 14).
•
The student provides a valid process for finding the total number of
miles for all three days (14 + 7 = 26 + 9). The intermediate total of 26
is a computation error, but the student does provide the correct
strategy of adding together 14, 7 and 9 miles.
An incorrect solution of 35 total miles is provided due to a calculation error
when finding the total number of miles Carl rides in the three days.
Part B: Score Point 0
This response receives no credit. It includes none of the required elements.
An incorrect and vague solution of 1 is provided. There is no valid
explanation or process given for finding the total number of additional miles
that Carl must ride or for finding the number of additional miles Carl should
ride each day.
A10
Part A: Score Point 1
Part B: Score Point 1
Annotation
Anchor Paper 10
Part A: Score Point 1
This response receives partial credit. It includes one of the three required
elements.
•
The student provides a valid process for finding the total number of
miles Carl rides on Friday (7 x 2 = 14).
While 23 is the correct solution for the operation given, it is not the correct
total number of miles Carl rides in three days and no credit is given for the
element.
The process for finding the total number of miles Carl rides in three days is
incomplete as Thursday’s miles are not added in (7 x 2 = 14 + 9 = 23).
Part B: Score Point 1
This response receives partial credit. It includes one of the three required
elements.
•
The student provides a valid process for finding the total number of
additional miles Carl must ride based on the incorrect solution provided
in Part A (36 – 23 = 13). A student may look up to the completed work
in Part A.
No attempt is made to provide the correct total number of miles to add to
each day. A total number of miles is given (13), but no miles per day is
provided.
No valid process or explanation for finding the number of additional miles
Carl should ride each day is provided.
A11
Part A: Score Point 1
Part B: Score Point 0
Annotation
Anchor Paper 11
Part A: Score Point 1
This response receives partial credit. It includes one of the three required
elements.
•
The student provides a valid process for finding the total number of
miles Carl rides on Friday (7 x 2).
While 23 is the correct solution for the operation given, it is not the correct
total number of miles Carl rides in three days and no credit is given for the
element.
The process for finding the total number of miles Carl rides in three days in
incomplete as Thursday’s miles are not added in (7 x 2 + 9 = 23).
Part B: Score Point 0
This response receives no credit. It includes none of the required elements.
No valid explanation is provided for the equation given in the response and
no understanding is shown for the elements of the problem.
A12
Part A: Score Point 1
Part B: Score Point 0
Annotation
Anchor Paper 12
Part A: Score Point 1
This response receives partial credit. It includes one of the three required
elements.
•
The student provides a valid explanation for finding the total number of
miles Carl rides on Friday (I multiplied the 7 miles and the 2 miles and
I got 14 miles).
While 23 miles is the correct solution for the explanation given, it is not the
correct total number of miles Carl rides in three days.
The process for finding the total number of miles Carl rides in three days in
incomplete as Thursday’s miles are not added in (add 9 miles to 14 and I got
23 miles).
Part B: Score Point 0
This response receives no credit. It includes none of the required elements.
The student has provided the additional miles of 7, 2 and 5 with no support
as to why these values were chosen. It does not address any elements of the
task.
A13
Part A: Score Point 0
Part B: Score Point 0
Annotation
Anchor Paper 13
Part A: Score Point 0
This response receives no credit. It includes none of the required elements.
No attempt is made to address any rubric elements, providing only an
irrelevant math equation (3 x 3 = 9).
Part B: Score Point 0
This response receives no credit. It includes none of the required elements.
No attempt is made to address any elements of the task. An incorrect math
equation is provided (2 x 9 = 36) that uses the number 36, but it has no
relevance to the rubric elements.
A14
Part A: Score Point 0
Part B: Score Point 0
Annotation
Anchor Paper 14
Part A: Score Point 0
This response receives no credit. It includes none of the required elements.
No attempt is made to address any elements of the task, providing only an
irrelevant math equation (7 x 9 = 63 miles).
Part B: Score Point 0
This response receives no credit. It includes none of the required elements.
No attempt is made to address any elements of the task, providing only an
irrelevant, incorrect math equation (7 ÷ 9 = 36).
Practice Set
P101 - P105
No Annotations Included
P101
P102
P103
P104
P105
Practice Set
Paper
Score
P101
3,3
P102
3,1
P103
3,0
P104
0,0
P105
1,1