Grade 10 Example Mathematics Performance Task 2016
A circus tent is composed of a cylinder with a diameter of 140
feet (ft) topped by a cone of the same diameter, as shown. The
height of the tent at its highest point is 63 ft. The visitors at the
circus stand in the outer area of the base. The base of the tent,
showing the visitor area with shading, is shown from above.
1. How tall is the conical portion of the tent? Write your answer,
and explain how you found it.
2. What is the volume of the tent? Write your answer, and show
your work.
Center for Educational Testing and Evaluation
Grade 10 Example Mathematics Performance Task 2016
3. Without doing the calculations to find the surface area of the
tent, explain how to find its surface area. Either write an
equation, or describe the process in words.
4. The tent holds 1,700 visitors. How many square feet (ft2) of
space does each visitor have in a full tent? Write your answer,
and explain how you found it.
5. The number of tickets, t, that the circus sells is dependent on
the price, p, in dollars. The relationship can be modeled by the
equation t = 1700 – 100p. At what ticket price p will the circus
make the most money?
Center for Educational Testing and Evaluation
Grade 10 Example Mathematics Performance Task 2016
Scoring Guide
Question No. of Partial Explanation
Points Credit?
1
2
Yes
Student earns 1 point for correct
answer, 17.5 ft, or equivalent answer
based on rounding 70tan(14).
Student earns 1 point for describing
use of right triangles and trig
functions given angle and radius of
circle (triangle base).
A student who uses correct trig
function and has mode set for
radians would get an answer of
507.1. If a student gives an answer
in radians, please score the task as
nonscorable (insufficient).
2
3
Yes
Student earns 1 point for showing
work for volume of cone.
Ex: V = (1/3)π(70)2(17.5)
Student earns 1 point for showing
work for volume of cylinder.
Ex: V = π(70)2(63 – 17.5)
Student earns 1 point for correct
answer, 789,814.7 ft3, or equivalent
based on rounding (754600/3)π
(≈790,215.3).
Student can instead earn credit for
work that demonstrates correct
process using heights based on
incorrect answers from Question 1.
Center for Educational Testing and Evaluation
Grade 10 Example Mathematics Performance Task 2016
Question No. of Partial Explanation
Points Credit?
3
1
No
Student earns 1 point for an
explanation or equation about finding
the surface area using the surface
areas of the cylinder and the cone
individually, but excluding the bases.
Example:
I would find the surface areas of the
cone and the cylinder, but I wouldn’t
include any of the circular bases.
Then I would add those areas
together to find the total surface
area.
Students can also earn a point for
writing an equation for the surface
area of the tent and defining the
variables. Example:
s = x + y – 3c where s is the tent’s
surface area, x is the cone’s surface
area, y is the cylinder’s surface area,
and c is the area of the circular base.
4
2
Yes
Student earns 1 point for correct
answer, 6.1 ft2, or equivalent based
on rounding (33/17)π.
5
1
No
Student earns 1 point for explaining
that the shaded region can be found
by subtracting the areas of the
circles, and that the space for each
person can be found by dividing the
found area by the number of people.
Student may also explain answer by
using work, ex: (π(702 - 402)/1700)
Student earns 1 point for correct
answer, $8.50, or an equivalent
(8.50, $8.5, etc). The student need
not include units to receive credit.
Center for Educational Testing and Evaluation