Newer Type II and Type III tasks for Grades 6-8
Includes 1 Example of an Algebra 1/ Math 1 Task
Example 1: Proportional Reasoning (Gr 7 Type II-3 points)
Part A
Each row of the table identifies a line containing a pair of points. Indicate whether each line represents a
proportional relationship between x and y.
You may use the graphing tool by selecting two points. The line containing the two points will be
automatically drawn.
Be sure to indicate whether each line represents a proportional relationship or not by selecting the
appropriate box in the table.
Part B
For the lines in Part A that do not represent a proportional relationship, explain why they do not.
For each line in Part A that does not represent a proportional relationship, describe how you would
change the coordinate of one of the two given points on the line to create a proportional relationship.
Example 2: Proportions of Instruments ( Gr 6 Type II-4points)
Mr. Ruiz is starting a marching band at his school. He does his research and finds the following data
about other local marching bands.
Part A
Type your answer in the box. Backspace to erase.
Mr. Ruiz realizes that there are __________ brass instrument players(s) per percussion player.
Part B
Mr. Ruiz has 210 students who are interested in joining the marching band. He decides to have 80% of
the band be made up of percussion and brass instruments. Use the unit rate you found in Part A to
determine how many students should play brass instruments.
Show or explain all your steps.
---------------------------------Example 3: Fraction Model (Gr 6 Type III-6 points)
Scientists are sending a rover to the moon. Their plan is to study a rectangular area of the moon using
the map shown. On the grid 1cm represents 1 km.
Part A
The rover will land at (3.5, 1) explore up to (3.5, 4) and then over to (2,4) Plot these points on the map.
Part B
What are the coordinates of the fourth vertex of the rectangle that the scientists plan to explore?
( __________ , __________ )
Part C
What is the horizontal length of the rectangle? ___________ kilometers
What is the vertical length of the rectangle? ____________ kilometers
Part D
Find the area of the moon exploration area in square meters. Show your work.
-------------------------------------------------Example 4: Brett’s Race (Alg I, Math I Type III-3 points)
Brett is on the high school track team and his coach surprises the team by having an Olympic track
champion attend a practice. To make the race more interesting, the Olympian will not start until Brett
reaches the 20 meter mark. Brett’s average time in the 100-meter race is 12 seconds, while the
Olympian’s average time is 10 seconds. Assume that Brett and the Olympian run at a constant speed
throughout the race.
Part A
Based on their average running times, write an equation for each person that describes the relationship
between their distance from the starting line, in meters, and time, in seconds.
Part B
Based on your equations in Part A, who will win the race and by how much? Justify your answer.
Solution/Scoring Rubric: Example 1: Proportional Reasoning
Task is worth 3 points. Task can be scored as 0, 1, 2, or 3.
Part A: This part is machine-scored and worth 1 point for a correct indication of whether each line
represents a proportional relationship or not.
Part B: This part is worth 2 points for reasoning.
Reasoning point 1: The student indicates that lines 1 and 4 do not represent a proportional relationship
because in both lines, the x and y values of the two given points are in different ratios. Or, the student
provides another valid response, such as, the lines do not contain the origin.
Reasoning point 2:
For line 1 to become a proportional relationship, either:
• the second point can be changed so that its y-coordinate is 3 times its x-coordinate (NOTE: Solutions
include, but are not limited to: (0, 0); (2, 6); (3, 9); and (1/3, 1)) OR
• the first point can be changed so that its y-coordinate is 32 of its x-coordinate (NOTE: Solutions
include, but are not limited to: (0, 0); (4, 6); (6, 9); and (1, 1.5)).
For line 4 to become a proportional relationship, the only option is to change the first point, because it is
on the y-axis.
• The first point can be changed so that its y-coordinate is 45 of its x-coordinate. (NOTE: Solutions
include, but are not limited to: (0, 0); (10, 8); (15, 12); and (5/4, 1).
Task score: The task score is the sum of the points awarded in each part.
Note: If a student only identifies one of the two lines that are not in a proportional relationship, they may
receive 1 point for correct reasoning shown in Part B.
----------------------------------Solution/Scoring Rubric: Example 2: Proportions of Instruments
Task is worth 4 points. Task can be scored as 0, 1, 2, 3, or 4.
Part A
• 1 computation point for stating 3
Part B: 3 points.
• 1 point reasoning, explains or shows how to use the 80%
• 1 point reasoning, explains or shows how to use the 3:1 ratio
• 1 point computation, provides answer of 126
---------------------------------Solution/Scoring Rubric: Example 3: Fraction Model
Task is worth 6 points. Task can be scored as 0, 1, 2, 3, 4, 5, or 6. Scoring consists of 4 points for
modeling and 2 points for computation.
Part A, machine---­‐scored
1 modeling point for creating a model with three correctly plotted points.
Part B, machine---­‐scored
1 modeling point for writing the point of the fourth coordinate point.
Part C, machine-scored
1 computational point for finding that the horizontal length is 1.5 kilometers.
1 computational point for finding that the vertical length is 3 kilometers.
Part D, hand scored
1 modeling point for creating a solution path that addresses unit conversion.
1 modeling point for creating a solution path to determine the area in square meters.
For example, Part A.
Part B. (2, 1)
Part C. 1.5 kilometers and 3 kilometers
Part D.
I converted 3 kilometers to 3,000 meters and1.5 kilometers to 1,500 meters. Then, I multiplied 3,000 by
1,500 to find that the moon exploration area is 4,500,000 square meters.
OR students may solve Part D in this manner:
I multiplied 3 kilometers by 1.5 kilometers to get 4.5 square kilometers. One square kilometer is 1,000
meters multiplied by 1,000 meters, which is 1,000,000 square meters. That means that 4.5 square
kilometers is 4,500,000 square meters.
Solution/Scoring Rubric: Example 4: Brett’s Race
Task is worth 3 points. Task can be scored as 0, 1, 2, or 3.
Task has 2 parts.
Scoring for Part A – Formulating the Model – 1 point
Student produces two equations to determine the distance in meters from the starting line, of each person
as a function of the time x, in seconds since the Olympian starts running.
For example, Brett’s distance y, as related to time, x:
!
!""
𝑦= 8!𝑥+20. Or y = !" x + 20
The Olympian’s distance y, as related to time, x: 𝑦= 10𝑥.
NOTE: All variables should be defined. The student may choose to define x as time in seconds since
Brett starts running.
Scoring for Part B
Student earns 1 calculation point for stating the correct winner and the correct margin of victory.
Students earn 1 modeling point for providing an accurate justification using the equations in Part A.
Sample Student Response 1:
• For Brett, 𝑦 = 100 when
!
100= 8!𝑥+20
!
80= 8!𝑥
𝑥 = 9.6
• For the Olympian 𝑦 = 100 when
100 = 10𝑥
𝑥 =10.
• So, Brett wins the race by 10 – 9.6 = 0.4 seconds.
Sample Student Response 2:
• When Brett finishes the race at 9.6 seconds, the Olympian is only 10(9.6) = 96 meters from the start.
Therefore, Brett was 4 meters ahead of the Olympian when he finished the race.
Note:
• If Part A contains incorrect equations, but Part B is correct based on one or two incorrect equations in
Part A, the student is still awarded 1 or 2 points of the 3 possible points.
Task score: The task score is the sum of the points awarded in each component.