Grades 6-8, Claim 2
Task Model 1
DOK Levels
2, 3
Target A:
Apply
mathematics
to solve wellposed
problems in
pure
mathematics
and arising in
everyday life,
society, and
the workplace.
Task Expectations:
Mathematical information is presented in a table or graph or extracted from a context.
Student is asked to solve well-posed problems in pure mathematics and arising in everyday life,
society, and the workplace.
Example Item 1 (Grade 6):
Primary Target 2A (Content Domain RP), Secondary Target 1A (CCSS 6.RP.3), Tertiary Target 2C)
A landscape designer is planning
the layout of trees in a park.
There are two types of trees:
elm and pine.
There should be at least 16
total trees but no more than 30.
The ratio of elm trees to pine
trees will be 3:2.
Drag trees anywhere to the model
to show a possible number of each
type of tree.
Rubric: (1 point) Student correctly places 16 to 30 trees in the response area with a 3 elm to 2 pine ratio
(e.g., 12 elm, 8 pine; 15 elm, 10 pine).
Response Type: Drag and Drop
Grades 6-8, Claim 2
Task Model 1
Example Item 2 (Grade 6):
Primary Target 2A (Content Domain G), Secondary Target 1H (CCSS 6.G.2), Tertiary Target 2B
DOK Levels
2, 3
Target A:
Apply
mathematics
to solve wellposed
problems in
pure
mathematics
and arising in
everyday life,
society, and
the workplace.
Cube-shaped boxes will be loaded into the cargo hold of a truck.
The edges of each box measure 2.5 feet.
The cargo hold of the truck is in the shape of a rectangular prism.
The dimensions of the cargo hold are 7.5 feet by 15.0 feet by 7.5 feet.
What is the volume, in cubic feet, of the cargo hold of the truck? Enter your answer in the first response
box.
How many boxes will it take to completely fill the cargo hold of the truck? Enter your answer in the second
response box.
Rubric: (2 points) The student correctly determines the volume and the number of 2.5 x 2.5 x 2.5 boxes
the truck can hold (e.g., 843.75, 54). Two response boxes are needed.
(1 point) The student correctly answers either the volume or the number of boxes, but not both.
Response Type: Equation/Numeric
Grades 6-8, Claim 2
Task Model 1
DOK Levels
2, 3
Target A:
Apply
mathematics
to solve wellposed
problems in
pure
mathematics
and arising in
everyday life,
society, and
the workplace.
Example Item 3 (Grade 6):
Primary Target 2A (Content Domain RP), Secondary Target 1A (6.RP.3c), Tertiary Standard 2C
Katie and Becca each bought a new book for $50.
Katie sold her book to the used bookstore for 25% less than the original price.
Becca sold her book to the used bookstore for 40% less than the original price.
Enter how much more money, in dollars, Katie received for her book than Becca received for her book.
Rubric: (1 point) The student computes the correct difference (e.g., 7.50).
Response Type: Equation/Numeric
Example Item 4 (Grade 6):
Primary Target 2A (Content Domain RP), Secondary Target 1A (CCSS 6.RP.3), Tertiary Target 2D
It takes Shaun 90 minutes to complete a 15 mile race. The
route, with four checkpoints (labeled A, B, C, and D), is
shown.
Assume Shaun runs at a constant rate during the race.
Complete the table to show Shaun’s time, in minutes, and
distance, in miles, at each checkpoint.
Checkpoint
Number of
minutes
Number of
miles
A
B
C
6
7.5
D
Finish
60
90
15
Rubric: (2 points) The student correctly determines all four missing values.
(1 point) The student correctly determines both minutes (e.g., 16.5, 45) or both miles (e.g., 1, 10) or three
out of four values correct.
Response Type: Fill-in Table
Grades 6-8, Claim 2
Task Model 1
Example Item 5 (Grade 6):
Primary Target 2A (Content Domain NS), Secondary Target 1C (CCSS 6.NS.3), Tertiary Target 2C
DOK Levels
2, 3
Target A:
Apply
mathematics
to solve wellposed
problems in
pure
mathematics
and arising in
everyday life,
society, and
the workplace.
Carlos has 2.4 meters of wire. He needs
1.7 meters for one project and 0.8 meter for
another project.
Shade the model to represent the total
amount of wire Carlos needs. Each row in the
model represents 1.0 meter. Does Carlos
have enough wire?
If so, answer how much wire he will
have left over.
If not, answer how much more he
needs.
Rubric: (2 points) The student shades 25 sections of the model and places 0.1 in the bottom box.
(1 point) The student completes only one of the tasks correctly.
Response Type: Hot Spot, Drag and Drop
Grades 6-8, Claim 2
Task Model 1
Example Item 6 (Grade 7):
Primary Target 2A (Content Domain NS), Secondary Target 1B (CCSS 7.NS.A), Tertiary Target 2C
DOK Levels
2, 3
Target A:
Apply
mathematics
to solve wellposed
problems in
pure
mathematics
and arising in
everyday life,
society, and
the workplace.
This table shows the total change in Sara's account balance for each month listed. For example, the account
change of +$38 means that Sara's balance increased by $38 during the month of January.
Month
January
February
March
April
Account Change
+$38
–$30
–$19
+$49
Determine whether each statement about Sara’s bank account balance is true based on the table. Select
True or False for each statement.
Statement
True
False
Sara has less money in her account at the end of
February than at the end of any other month.
Sara’s account balance is the same at the end of April as
it is at the end of January.
Sara has more money in her account at the end of April
than she had at the beginning of January.
Rubric: (1 point) The student identifies all three statements correctly as true or false (e.g., FTT).
Response Type: Matching Tables
Grades 6-8, Claim 2
Task Model 1
Example Item 7 (Grade 7):
Primary Target 2A (Content Domain RP), Secondary Target 1A (CCSS 7.RP.2b), Tertiary Target 2D
DOK Levels
2, 3
Target A:
Apply
mathematics
to solve wellposed
problems in
pure
mathematics
and arising in
everyday life,
society, and
the workplace.
Tim makes 80 gallons of paint by mixing 48 gallons of green paint with
32 gallons of blue paint.
What part of every gallon is from green paint?
The model represents 1 gallon of mixed paint.
Select the bars to show how much of the gallon is from green paint.
Rubric: (1 point) The student clicks on the model up to 0.6 gallon.
Respone Type: Hot Spot
Example Item 8 (Grade 7):
Primary Target 2A (Content Domain EE), Secondary Target 1D (CCSS 7.EE.4)
The marching band has 85 members. There are 15 more girls than boys in the band. How many boys are
members of the marching band?
Rubric: (1 point) The student is able to correctly determine the number of boys (e.g., 35).
Response Type: Equation/Numeric
Grades 6-8, Claim 2
Task Model 1
DOK Levels
2, 3
Target A:
Apply
mathematics
to solve wellposed
problems in
pure
mathematics
and arising in
everyday life,
society, and
the workplace.
Example Item 9 (Grade 7):
Primary Target 2A (Content Domain RP), Secondary Target 1A (CCSS 7.RP.3), Tertiary Target 2D
Luke buys a television that is on sale for 25% off the original price. The original price is $120 more than the
sale price. What is the original price of the television?
Rubric: (1 point) The student enters the correct full price (e.g., 480).
Response Type: Equation/Numeric
Example Item 10 (Grade 7):
Primary Target 2A (Content Domain RP), Secondary Target 1A (CCSS 7.RP.1), Tertiary Target 2C
A bottle is
full. It contains
gallon of water.
There are 16 cups in one gallon.
Enter the total number of cups it takes to completely fill the whole bottle.
Rubric: (1 point) The student gives the volume of the bottle in cups (e.g., 3 ).
Response Type: Equation/Numeric
Example Item 11 (Grade 8):
Primary Target 2A (Content Domain G), Secondary Target 1H (CCSS 8.G.7), Tertiary Target 1D
Two sides of a right triangle have lengths √
side.
units and √ units. There are two possible lengths for the third
Enter the longest possible side length, in units, of this triangle.
Rubric: (1 point) The student correctly enters the longest side of the triangle (e.g., 4).
Response Type: Equation/Numeric
Grades 6-8, Claim 2
Task Model 1
Example Item 12 (Grade 8):
Primary Target 2A (Content Domain EE), Secondary Target 1C (CCSS 8.EE.5), Tertiary Target 2D
DOK Levels
2, 3
Target A:
Apply
mathematics
to solve wellposed
problems in
pure
mathematics
and arising in
everyday life,
society, and
the workplace.
Justin’s car can travel
miles using
gallons of
gas.
Kim’s car can travel
using
gallons of gas.
At these rates, how far, in miles, can each car travel
using 1 gallon of gas?
Drag each person’s car to the number line to show
the number of miles.
Rubric: (2 points) The student places both cars at the correct point (e.g., Justin’s car at the 25-mile mark
and Kim’s car at the 31 mile mark).
(1 point) The student places only one car at the correct point.
Response Type: Drag and Drop
Grades 6-8, Claim 2
Task Model 2
DOK Levels
1, 2
Target B:
Select and use
appropriate
tools
strategically.
Task Expectations:
Mathematical information is presented in a table or graph or extracted from a context.
The student is asked to solve a problem that requires strategic use of tools or formulas.
Example Item 1 (Grade 6):
Primary Target 2B (Content Domain RP), Secondary Target 1A (CCSS 6.RP.3a)
Nate waters the garden every 3 days and weeds it
every 4 days.
He does both on April 2nd.
What is the next date that he will both water and
weed his garden?
Select that date on the calendar.
Rubric: (1 point) The student selects the correct date (e.g., April 14).
Response Type: Hot Spot
Grades 6-8, Claim 2
Task Model 2
Example Item 2 (Grade 7):
Primary Target 2B (Content Domain RP), Secondary Target 1A (CCSS 7.RP.1)
DOK Levels
1, 2
Target B:
Select and use
appropriate
tools
strategically.
John needs to paint one wall in his house. The wall is
shaped like a rectangle with a triangular top, as
shown. He knows that each 1-quart container of
paint covers an area of 24 square feet. John uses a
meter stick to measure the dimensions of the wall.
[1 meter is approximately 39 inches]
Select the fewest number of 1-quart containers of
paint John can use to paint the wall. You may use the
meter sticks to measure the dimensions of the wall.
Rubric: (1 point) The student selects 4 paint cans.
Response Type: Hot Spot
Grades 6-8, Claim 2
Task Model 2
Example Item 3 (Grade 8):
Primary Target 2B (Content Domain EE), Secondary Target 1D (CCSS 8.EE.8b)
DOK Levels
1, 2
Target B:
Select and use
appropriate
tools
strategically.
Line a is shown on the graph. Use the Add Arrow tool to
construct line b on the graph so that:
Line a and line b represent a system of linear
equations with a solution of (7, -2).
The slope of line b is greater than -1 and less
than 0.
The y-intercept of line b is positive.
Interaction: The double arrow Add Arrow tool is available, as well as the Add Point tool.
Rubric: (1 point) The student is able to construct a line that meets the requirments (e.g., see below).
Response Type: Graphing
Grades 6-8, Claim 2
Task Model 2
Example Item 4 (Grade 8):
Primary Target 2B (Content Domain G), Secondary Target 1F (CCSS 8.F.4)
DOK Levels
1, 2
Target B:
Select and use
appropriate
tools
strategically.
A cylindrical tank has a height of 10 feet and a radius of 4 feet. Jane fills this tank with water at a rate of 8
cubic feet per minute. Using this rate, determine the number of minutes it will take Jane to completely fill
the tank without overflowing.
Enter your answer, rounded to the nearst minute, in the response box.
Rubric: (1 point) The student enters the correct number of minutes (e.g., 63).
Response Type: Equation/Numeric
Grades 6-8, Claim 2
Task Model 3
DOK Level 2
Target C:
Interpret
results in the
context of a
situation.
Task Expectations:
Mathematical information is presented in a table or graph or extracted from a context.
The student is asked to solve a problem that may require the integration of concepts and skills from
multiple domains.
Example Item 1 (Grade 6):
Primary Target 2C (Content Domain RP), Secondary Target 1A (CCSS 6.RP.3b)
A factory makes 2,200 bottles every 5.5 hours. The factory makes bottles for 8 hours each work day.
Enter a whole number to represent the fewest number of work days the factory will need to make 28,000
bottles.
Rubric: (1 point) The student solves for the least number of days (e.g., 9).
Response Type: Equation/Numeric
Grades 6-8, Claim 2
Task Model 3
Example Item 2 (Grade 7):
Primary Target 2C (Content Domain EE), Secondary Target 1D (CCSS 7.EE.4b)
DOK Level 2
David wants to buy 2 pineapples and some bananas and spend no more than $10.00.
Target C:
Interpret
results in the
context of a
situation.
The price of 1 pineapple is $2.99.
The price of bananas is $0.67 per pound.
Use the Connect Line or Add Arrow tool to draw a graph that represents all possible values for the number of
pounds of bananas, b, David can buy.
Interaction: The student is given both the Connect Line and Add Arrow tools to draw an inequality.
Rubric: (1 point) The student is able to correctly graph the inequality defined by the problem
(e.g., see below).
Response Type: Graphing
Grades 6-8, Claim 2
Task Model 4
DOK Levels
2, 3
Target D:
Identify
important
quantities in a
practical
situation and
map their
relationships
(e.g., using
diagrams,
two-way
tables, graphs,
flowcharts, or
formulas).
Task Expectations:
Mathematical information is presented in a table or graph or extracted from a context.
The student is asked to solve a problem that may require the integration of concepts and skills from
multiple domains.
Example Item 1 (Grade 6):
Primary Target 2D (Content Domain G), Secondary Target 1H (CCSS 6.G.2)
Brady started to fill the box shown with some unit cubes.
Including the cubes that are already in the box, what is the
total number of unit cubes needed to completely fill the box?
Rubric: (1 point) The student enters the number of unit cubes (e.g., 210).
Response Type: Equation/Numeric
Example Item 2 (Grade 6):
Primary Target 2D (Content Domain NS), Secondary Target 1C (CCSS 6.NS.1)
Bill wants to run a total of 4000 meters in 5 days. The table shows how far he
runs each day for 4 days.
Each lap is 400 meters.
Enter the number of laps Bill should run on Friday so his total for the 5 days
is exactly 4000 meters.
Rubric: (1 point) The student enters the correct number in the box
7
(e.g., 2 ).
8
Response Type: Equation/Numeric
Day of Week
Monday
Tuesday
Wednesday
Thursday
Laps Run
1
1
4
3
1
4
5
1
8
1
2
2
Grades 6-8, Claim 2
Task Model 4
Example Item 3 (Grade 7):
Primary Target 2D (Content Domain G), Secondary Target 1F (CCSS 7.G.4)
DOK Levels
2, 3
Two circles touch a rectangle and each other as shown in this diagram.
Target D:
Identify
important
quantities in a
practical
situation and
map their
relationships
(e.g., using
diagrams,
two-way
tables, graphs,
flowcharts, or
formulas).
r
r
The area of the rectangle is 50 square inches. Enter the radius (r), in inches, of each circle.
Rubric: (1 point) The student is able to determine the radius (e.g., 2.5).
Response Type: Equation/Numeric
Grades 6-8, Claim 2
Task Model 4
Example Item 4 (Grade 7):
Primary Target 2D (Content Domain EE), Secondary Target 1D (CCSS 7.EE.3)
DOK Levels
2, 3
Target D:
Identify
important
quantities in a
practical
situation and
map their
relationships
(e.g., using
diagrams,
two-way
tables, graphs,
flowcharts, or
formulas).
Kayla asked 10 students in her class
whether they owned a dog or cat or both.
Drag one number into each box to complete
the table, given this information:
40% of the students own a dog.
30% of the students own a cat.
10% of the students own both a dog
and a cat.
Rubric: (1 point) The student places the correct numbers in the boxes (See below).
Response Type: Drag and Drop
Grades 6-8, Claim 2
Task Model 4
DOK Levels
2, 3
Target D:
Identify
important
quantities in a
practical
situation and
map their
relationships
(e.g., using
diagrams,
two-way
tables, graphs,
flowcharts, or
formulas).
Example Item 5 (Grade 7):
Primary Target 2D (Content Domain EE), Secondary Target 1D (CCSS 7.EE.3)
(Source: Adapted from Illustrative Mathematics, Grade 7.EE)
The students in Mr. Sanchez's class are converting distances measured in miles (m) to kilometers (k). Abby
and Renato use the following methods to convert miles to kilometers.
Abby takes the number of miles, doubles it, then subtracts 20% of the result.
Renato first divides the number of miles by 5, then multiplies the result by 8.
Which equation correctly shows why both their methods produce the same result?
A.
B.
C.
D.
( )
( )
Rubric: (1 point) The student selects the correct equation (e.g., B).
Response Type: Multiple Choice, single correct response
Grades 6-8, Claim 2
Task Model 4
Example Item 6 (Grade 8):
Primary Target 2D (Content Domain F), Secondary Target 1E (CCSS 8.F.2)
DOK Levels
2, 3
The table shows some values from a linear function.
Target D:
Identify
important
quantities in a
practical
situation and
map their
relationships
(e.g., using
diagrams,
two-way
tables, graphs,
flowcharts, or
formulas).
x
y
-1
-5
1
-1
3
3
Use the Add Arrow tool to create a graph of a different function
that has the same rate of change as the one shown by the table of
values.
Rubric: (1 point) The student draws a line with the correct slope and does not pass through the points
shown in the function table [e.g., slope of 2, passes through any y-intercept except (0, -3)].
Response Type: Graphing
Example Item 7 (Grade 8):
Primary Target 2D (Content Domain G), Secondary Target 1I (CCSS 8.G.9)
A sphere and a cone have the same volume. Each has a radius of 3 inches. What is the height of the cone?
A.
B.
C.
D.
4 inches
6 inches
9 inches
12 inches
Rubric: (1 point) The student selects the correct height (e.g., D).
Response Type: Multiple Choice, single correct response