This page shows questions in the Geometry Modeling public release module at MSDE. Geometry
"Geometry Modeling"

Holistic Rubric for 4-Point Modeling Constructed Response Items

Sample Top Score Response

The least height for the flagpole will be when the shadow is longest ( $7\text{.}5$ feet or $90$ inches) and the distance between Isabella and the flag is shortest ( $21$ feet or $252$ inches). The following proportion can be solved to arrive at the least height of the flagpole, in inches.

$$\begin{gathered} \frac{62}{90}=\frac{x}{90+252} \\ 62\left(342\right)=90x \end{gathered}$$

$x=235\text{.}6$ inches or $19\text{.}63$ feet.

The greatest height for the flagpole will be when the shadow is shortest ( $7$ feet of $84$ inches) and the distance between Isabella and the flag is longest ( $22$ feet or $264$ inches). The following proportion can be solved to arrive at the greatest height of the flagpole, in inches.

$$\begin{gathered} \frac{62}{84}=\frac{x}{84+264} \\ 62\left(348\right)=84x \end{gathered}$$

$x=256\text{.}9$ inches or $21\text{.}4$ feet.

Points

Sample Characteristics

4 Points

A four-point response provides full and complete evidence of the modeling process used to solve a real-world problem.

The response may:

• identify the problem that needs to be solved.

• determine information that is needed to solve the problem.

• communicate an accurate, organized solution path that is aligned to the problem using appropriate, effective, and essentially precise representations.

• contain minor flaws that do not detract from correct modeling or demonstration of a thorough understanding.

• evaluate or validate a partial or complete solution and show how to improve or refine the solution.

3 Points

A three-point response provides evidence of the modeling process used to solve a real-world problem.

The response may:

• identify most of the problem that needs to be solved.

• determine most of the information that is needed to solve the problem.

• communicate an accurate, organized solution path that is aligned to the problem using appropriate, effective, and precise representations with minor flaws.

• evaluate or validate a partial or complete solution and show how to improve or refine the solution, but the improvement or refinement may include minor flaws.

2 Points

A two-point response provides partial evidence of the modeling process used to solve a real-world problem.

The response may:

• partially identify the problem that needs to be solved.

• determine some of the information that is needed to solve the problem.

• include a partial solution path that may be incomplete.

• contain some errors in identifying the mathematics that is needed to solve the problem.

• evaluate or validate a partial or complete solution and attempt to improve or refine the solution.

1 Point

A one-point response provides limited evidence of the modeling process used to solve a real-world problem.

The response may:

• partially or incorrectly identify the problem that needs to be solved.

• determine a minimal amount of the information that is needed to solve the problem.

• include an incomplete or unorganized solution path.

• contain errors in identifying the mathematics that is needed to solve the problem.

• contain the correct solution, but work is limited or missing.

• evaluate or validate a partial or complete solution but does not show how to improve or refine the solution.

0 Point

NOTE for ETS Editorial:

There is an error in the rubric that was corrected in the paper and online Practice Test keys. The measurement at the end of the third sentence should be "cubic inches" instead of "inches". This rubric will be updated after the Spring 2022 Practice Test is no longer available.

Holistic Rubric for 4-Point Modeling Constructed Response Items

Sample Top Score Response

Part A

The hole must have a diameter that measures approximately $36$ inches and a height that measures approximately $18$ inches. Thus the volume of the hole is approximately $V=\pi {\left(\frac{36}{2}\right)}^2\left(18\right)=5\text{,832}\pi$ cubic inches. The root ball has an approximate volume of $V=\frac{4}{3}\pi {\left(\frac{18}{2}\right)}^3=972\pi$ cubic inches. So approximately $(5\text{,832}−972)\pi ≈15\text{,268}$ cubic inches of soil will be needed. Since $12$ inches $=1$ foot, $1728$ cubic inches $=1$ cubic foot, and $15\text{,}268$ cubic inches $=\frac{15\text{,}268}{1728}$ cubic feet $≈8\text{.}8$ cubic feet.

Part B

The part that will be covered by mulch has the form of a circle of radius $18$ inches. And the area occupied by the tree trunk has radius of $3$ inches. So the total area to be covered by mulch is $({18}^2−3^2)\pi ≈989.6$ square inches. Since $12$ inches $=1$ foot, $144$ square inches $=1$ square foot, and $989\text{.}6$ square inches $=\frac{989.6}{144}$ square feet $≈6\text{.}9$ square feet.

Scoring

Points

Sample Characteristics

4 Points

A four-point response provides full and complete evidence of the modeling process used to solve a real-world problem.

The response may:

• identify the problem that needs to be solved.

• determine information that is needed to solve the problem.

• communicate an accurate, organized solution path that is aligned to the problem using appropriate, effective, and essentially precise representations.

• contain minor flaws that do not detract from correct modeling or demonstration of a thorough understanding.

• evaluate or validate a partial or complete solution and show how to improve or refine the solution.

3 Points

A three-point response provides evidence of the modeling process used to solve a real-world problem.

The response may:

• identify most of the problem that needs to be solved.

• determine most of the information that is needed to solve the problem.

• communicate an accurate, organized solution path that is aligned to the problem using appropriate, effective, and precise representations with minor flaws.

• evaluate or validate a partial or complete solution and show how to improve or refine the solution, but the improvement or refinement may include minor flaws.

2 Points

A two-point response provides partial evidence of the modeling process used to solve a real-world problem.

The response may:

• partially identify the problem that needs to be solved.

• determine some of the information that is needed to solve the problem.

• include a partial solution path that may be incomplete.

• contain some errors in identifying the mathematics that is needed to solve the problem.

• evaluate or validate a partial or complete solution and attempt to improve or refine the solution.

1 Point

A one-point response provides limited evidence of the modeling process used to solve a real-world problem.

The response may:

• partially or incorrectly identify the problem that needs to be solved.

• determine a minimal amount of the information that is needed to solve the problem.

• include an incomplete or unorganized solution path.

• contain errors in identifying the mathematics that is needed to solve the problem.

• contain the correct solution, but work is limited or missing.

• evaluate or validate a partial or complete solution but does not show how to improve or refine the solution.

0 Point