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This page shows questions in the Math 5 Modeling public release module at MSDE. 5th Grade Math
"Math 5 Modeling"

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Expand All Official Practice Test

This is a multiple choice question that allows you to select several options.

Daniel used plastic bricks to build 200 figures in 5 hours.

  • He built 60 figures during the first hour and 50 figures during the second hour.
  • During the first two hours, he used 3 bricks to build each figure.
  • During each additional hour, Daniel used 4 bricks to build each figure.

Which three questions can be answered using the given information?

Select the three correct answers.

  1. A.
    How many figures did Daniel build using 4 bricks?
  2. B.
    How many bricks did Daniel use during the fifth hour?
  3. C.
    How many bricks did Daniel use during the second hour?
  4. D.
    During which hour did Daniel build the greatest number of figures?
  5. E.
    What is the total number of bricks Daniel used to build all the figures?
i1

Correcti3

Correcti5

Correcti2

May not have recognized that it is necessary to know the number of figures Daniel built during the fifth hour to answer this questioni4

May not have recognized that it is necessary to know how many of those 90 figures were built during each of the following three hours

This is a multiple choice question that allows you to select only one option.

A teacher is planning a lesson that includes some activities to be completed at a computer.

  • There are 18 students in the classroom.
  • The students will be split up in groups of the same size.
  • Each group will need to use the computer for 12 hour.

Which additional piece of information is needed to determine how long the computer will need to be in the classroom?

  1. A.
    the number of students in each group
  2. B.
    the number of activities that must be completed at the computer
  3. C.
    the number of times the computer will be available in the classroom
  4. D.
    no more information is needed to find how much time each group will have
i1

Correcti2

May have thought that the number of activities is needed for the calculationi3

May have not realized that the information is already giveni4

May have not realized that the the size of each group is not given

This is a test question that allows you to enter extended text in your response.

Kasey will make as many servings of trail mix as possible with these ingredients: walnuts, pretzels, and apricots.

  • Each serving will have 16 cup of walnuts, 14 cup of pretzels, and 18 cup of apricots.
  • Kasey has 10 cups of walnuts, 12 cups of pretzels, and 9 cups of apricots with which to make the trail mix.
  • Determine how many servings Kasey will make.
  • Determine which ingredient Kasey will completely use, and determine how much of the other ingredients she will have left over.
  • Show your work or explain how you determined your answers.

Enter your answers and your work or explanation in the space provided. You may also use the drawing tool to help explain or support your answer.

Drawing Box

There is no alt-text. (37 files were searched.)

NOTE TO ETS Editorial:

In the scoring rubric there is an incorrect "1/6" in the second-to-last equation. The paper and online PT key documents have the correct equation, "48 x 1/8 = 6". The rubric in this item will be corrected after the Spring 2022 Practice Test is no longer active.

Holistic Rubric for 4-Point Modeling Constructed Response Items

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

A zero-point response is completely incorrect, incoherent or irrelevant.

This is a multiple choice question that allows you to select only one option.

A contractor measured the length and the width of two rectangular pieces of land.

  • The two pieces of land are adjacent and share the same width of 17 yards.
  • The first piece of land has a length of 3213 yards.
  • The second piece of land has a length of 2514 yards.

Which steps should the contractor use to determine the area, in square yards, of the two pieces of land altogether?

  1. A.
    Add 3213 and 2514 and then add the result by 17.
  2. B.
    Multiply 3213 and 2514 and then add the result by 17.
  3. C.
    Add 3213 and 2514 and then multiply the result by 17.
  4. D.
    Multiply 3213 and 2514 and then multiply the result by 17.
i3

Correcti1 i2 i4

This is a test question that allows you to enter extended text in your response.

Bernard stacked two gift boxes that are each in the shape of a right rectangular prism. The dimensions of the resulting shape are shown.

The figure shows a three dimensional shape, that resembles a rectangular prism, that has had a section removed from its upper right corner, in the shape of a smaller rectangular prism. The length of the whole shape is 24 inches. The height of the left face, with no missing section, is 12 inches, and the height of the lower right face, below the missing section, is 6 inches. The width of the bottom face, with no missing section, is 20 inches, and the width of the top face, to the left of the missing section, is 8 inches.

What is the total volume, in cubic inches, of the gift boxes?

Enter your answer and your work or explanation in the space provided. You may also use the drawing tool to help explain or support your answer.

Drawing Box

There is no alt-text. (37 files were searched.)

Holistic Rubric for 3-Point Modeling Constructed Response Items

Points

Sample Characteristics

3 Points

A three-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 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.

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

A zero-point response is completely incorrect, incoherent or irrelevant.

This is a multiple choice question that allows you to select only one option.

During a 5 ‑day paper recycling drive, the students in a classroom collected 12.4 pounds of paper each day for 4 days and 8.39 pounds of paper on the fifth day.

Which steps can be used to find the total number of pounds of paper the students collected for the recycling drive?

  1. A.
    Multiply 12.4 by 4, then add 8.39.
  2. B.
    Multiply 12.4 by 5, then add 8.39.
  3. C.
    Add 12.4 and 8.39, then multiply the result by 4.
  4. D.
    Add 12.4 and 8.39, then multiply the result by 5.
i1

Correcti2

Multiplied by the number of days the drive lastedi3

Added before multiplyingi4

Added before multiplying and multiplied by the number of days the drive lasted