Mathematics
Grade 4
Extended Response Item (Scaffolded)
4.NF.4c; 4.NF.4b; 4.NF.4a; 4.NF.3a
Sylvia knows there are 5 people attending her party, including herself. She wants to be sure she
makes enough punch for everyone. She estimates that each person will drink ¾ cup of punch.
Part A
Write an expression that represents how many cups of punch Sylvia will need to make.
Part B
Find the value of the expression in Part A. How many cups of punch will Sylvia need to make?
Show your work.
Part C
Draw a fraction model to represent your answer from Part B. Explain your answer.
Part D
Sylvia has cups of punch. Based on your answer in Part C, will this be enough punch for her
party? Explain your answer or show your work.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
2
Exemplar Response
Part A
5 3
4
Part B
5  3  15 because 5 is the same as 5 and then multiply the numerators:
4
4
1
5  3  15 and then multiply the denominators: 1  4  4; so the answer is 3 3
4
or 15 .
4
Part C
Each large square is 1 cup, so there are 3 of a cup shaded in each square and
4
there are 5 squares, so if you count the shaded squares, you get 15, so there are
15 cups.
4
Part D
Yes, Sylvia will have enough punch because 4 1 is greater than 3 3 .
2
Or
4
Yes, because 4 1  3 3  4 2  3 3  3 6  3 3  3 .
2
4
4
4
4
4
4
3
Rubric
Score
Designation
Description
4
Thoroughly
Demonstrated
The student correctly completes all elements of the item by
solving word problems involving multiplication of a fraction
by a whole number and using equations and fraction models
to represent the problem (4.NF.4a, b, c) and by
understanding addition and subtraction as joining and
separating parts referring to the same whole (4.NF.3a).
3
Clearly
Demonstrated
The student shows clear understanding of the skills listed
above and correctly answers all parts, but one explanation
or work shown is weak or insufficient.
2
Basically
Demonstrated
The student shows basic understanding of the skills listed
above by correctly answering three parts with at least two
sufficient explanations or work shown.
1
Minimally
Demonstrated
The student shows minimal understanding of the skills listed
by correctly answering two parts with or without sufficient
explanation or work shown.
0
Incorrect or
irrelevant
The response is incorrect or irrelevant to the skill or concept
being measured.
4
Student Response
Score 2
Part A is incorrect.
Part C is correct; however,
there is an insufficient
explanation. Therefore, a
higher score point cannot
be given.
The student demonstrates
a basic understanding of
the mathematical
concepts being measured
by correctly answering
and showing the work for
Part B (5 x ¾ = 3 ¾) and
Part D (Yes, because 4 ½
is more than 3 ¾).
Final Scoring: 2
Part A: Incorrect
Part B: Correct w/work shown
Part C: Correct w/no
explanation
Part D: Correct w/work shown
5
Student Response
Score 1
Student correctly answers
Parts C and D, but without
sufficient explanation.
Part A is incorrect because
the student provides an
equation rather than an
expression. Therefore, a
higher score point cannot
be given.
The student
demonstrates a minimal
understanding of the
mathematical concepts
being measured by
correctly answering and
showing the work for
Part B (3/4 x 5 = 15/4).
Final Scoring: Score 1
Part A: incorrect
Part B: Correct
Part C: Correct w/no explanation
Part D: Correct w/no explanation
6
Mathematics
Grade 6
Extended Response Item
6.NS.7; 6.EE.2; 6.EE.7
Tanya played a computer game in which the score was calculated using the equation where s is the
score, t is the number of points Tanya earned, and c is the number of points her computer opponent
earned. Tanya recorded her scores for one week on the number line shown in the diagram.
The winner is determined by the highest score.
Part A
On Tuesday, Tanya’s computer opponent scored 33 points. How many points did Tanya score? Explain
your answer or show your work.
Part B
On which day were the scores of Tanya and the computer the closest, but not the same? Who won that
day? Explain your answer.
Part C
Explain what Friday’s score means about the number of points Tanya and the computer earned. Justify
your answer using words and a mathematical statement.
Part D
On which day(s) did Tanya win? Using t and c, write a mathematical statement to support your answer.
8
Exemplar Response
Part A
Tanya scored 25 points.
Substitute the values into the equation and solve.
Part B
Their scores were closest on Saturday, and the computer won.
The difference on Saturday is 6 points. Since t – c is negative, c is greater than t. This means the
computer’s score was higher.
Or
To compare scores, use the absolute value of the difference, which is The absolute value of all of
the scores is the smallest on Saturday. Since is negative, c is greater than t. This means the
computer’s score was higher.
Part C
On Friday Tanya and the computer earned the same number of points (or, they tied). This is true
because if then
Part D
Tanya won on Thursday, Monday, and Wednesday. Tanya will win whenever her score is greater
than the computer’s, or whenever t > c.
9
Rubric
Score
Designation
4
Thoroughly
Demonstrated
3
Clearly
Demonstrated
2
Basically
Demonstrated
1
Minimally
Demonstrated
0
Incorrect or
irrelevant
Description
The student successfully completes all elements of the item by
demonstrating an understanding of ordering and absolute value of
rational numbers (6.NS.7), in particular those related to number line
comparisons (6.NS.7a, 6.NS.7c). The student demonstrates the ability to
write, read, and evaluate expressions in which letters stand for numbers
(6.EE.2), and to solve real-world and mathematical problems by solving
equations (6.EE.7).
The student shows clear understanding of the skills listed above, but one
of the explanations is weak or insufficient
Or
All parts of the item are correctly done except for a minor computational
error
Or
The student successfully completes three of the four parts of the item.
The student shows basic understanding of the skills listed above, but
provides insufficient explanations
Or
The student successfully completes two of the four parts of the item.
The student shows minimal understanding of the skills listed above by
completing only one of the four parts of the item
Or
The student had some correct answers, but provided no explanations.
The response is incorrect or irrelevant to the skill or concept being
measured.
10
Student Response
Score 3
Part A has the
correct answer
of 25, with
support.
Part B has the
correct answer,
Saturday, with
explanation.
11
Student Response
Score 3
Part C correctly
explains the
meaning of a
zero on the
graph with a
correct
justification but
is missing a
mathematical
statement.
Part D has the correct answer, with
correct support.
12
Student Response
Score 2
Part A has a correct answer,
with work shown.
Part C correctly
interprets the zero
score on the graph
as a tie, but lacks a
sufficient
justification.
Part B has the
correct answer of
Saturday, indicates
the winner as the
computer but does
not provide a
sufficient
explanation.
Part D has the correct answer of Thursday, Monday, and
Wednesday and gives mathematical statements for each day as
support, but not a general statement.
13
Student Response
Score 1
Part A has a correct answer,
but no explanation or work
shown.
Part B is incorrect.
Part D has the correct answer, but with no support.
Part C correctly
interprets the
meaning of the
zero score on the
graph but the
justification is
insufficient.
14
Mathematics
Analytic Geometry
Extended Response Item
S.CP.7; S.CP.1
The total number of full-time and part-time employees at a store is 50. Each employee works either the
morning shift or the afternoon shift. More information about the employees is given below.
• 15 employees are part-time
• 28 employees are males
• 30 employees work the morning shift
• 6 male employees work part-time
• 12 male employees work the morning shift
The names of each of the 50 employees are written on separate cards. The cards are shuffled and placed into
a container.
Part A
If one card is selected at random from all 50 cards in the container, what is the probability that the employee
is part-time or male? Show your work and explain your answer.
Part B
If one card is selected at random from all 50 cards in the container, what is the probability that the employee
is male or works the afternoon shift? Show your work and explain your answer.
Part C
If one card is selected at random from all 50 cards in the container, what is the probability that the employee
is a female who does not work the morning shift? Show your work and explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
16
Exemplar Response
Part A
37
or 74%.
50
To find this answer, use the general Addition Rule for the union of two events:
The probability that the selected employee is part-time or male is
P(part-time or male) = P(part-time) + P(male) – P(part-time and male)
P(part-time or male)  15  28  6  37
50
50
50
50
Part B
16
or 64%.
25
To find this answer, use the general Addition Rule for the union of two events:
The probability that the employee is male or works afternoons is
P(male or afternoons) = P(males) + P(afternoons) – P(male and afternoons)
28
20
16
32
16
P(male or afternoons) =




50
50
50
50
25
Part C
The probability that the employee is female who does not work mornings is
2
25
or 8%.
To find this answer, we can reason from the given information that there are
22 female employees and 20 employees work afternoons. Since 12 males work
mornings out of the 30 morning employees, 18 females work mornings. That
leaves 4 females who work afternoons.
Or, we can use the general Addition Rule for the union of two events and the
complement:
P(female who doesn’t work mornings) is equal to P(female and afternoons)
P(female and afternoons)=P(not(male or mornings)) = 1 - P(male or mornings)
4
2
 28 30 12 


P(female who doesn’t work mornings) = 1  
  50  25
50
50
50


17
Rubric
Score
4
3
2
1
0
Designation Description
Thoroughly
The student successfully completes all elements of the
Demonstrated item by demonstrating knowledge and application of
the Addition Rule for finding the probability of
compound events, P( A  B)  P( A)  P(B)  P( A  B) ,
and can interpret the probability in terms of the model
(S.CP.7) and describing events as subsets of a sample
space using characteristics of the outcomes, or as
unions, intersections, or complements of other events
(S.CP.1).
Clearly
The student shows clear understanding of the
Demonstrated standards listed above, but one of the explanations or
work shown is insufficient
Or
All parts of the item are correctly done except for a
minor computational error
Or
The student successfully completes two of the three
parts of the item and partially completes the other
part.
Basically
The student shows basic understanding of the
Demonstrated standards listed above, but two of the explanations or
work shown is insufficient
Or
The student successfully completes one of the three
parts of the item and partially completes the other
parts.
Minimally
The student shows minimal understanding of the
Demonstrated standards listed above and completes only one of the
three parts
Or
The student partially completes two of the three parts.
Incorrect or
The response is incorrect or irrelevant to the skill or
irrelevant
concept being measured.
18
Student Response
Score 3
The student demonstrates a
clear understanding of the
mathematical concepts being
measured by successfully
completing two parts of the three
parts of the item. In part A, the
student successfully finds the
correct probability of 37/50 and
converts it to 74%. In part C the
student successfully finds the
correct probability of 4/50 and
converts to 8%. In part B, the
student partially completes the
process, but does not find the
final correct answer.
19
Student Response
Score 2
In parts A and B, the student partially
completes the process, but does not find
the correct final answers.
In part C, the student successfully finds the
probability of 4/50 and successfully
converts to the correct probability of .08
The student demonstrates a
basic understanding of the
mathematical concepts being
measured by successfully
completing one part of the item
and partially completing the
other two parts.
20
Student Response
Score 1
In part A, the student correctly adds the part
time employees and the male employees,
but forgets to subtract out the part time
employees that are male.
In part C, the student correctly identifies the
number of females, and the number of females
who work mornings, but adds the two groups
instead of subtracting.
In part B, the student
correctly adds the male
workers to the afternoon
workers, but forgets to
subtract out the male
workers that work
afternoons.
The student demonstrates
a minimal understanding of
the mathematical concepts
being measured by
partially completing all
three parts.
21