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MCAP, Maryland Comprehensive Assessment Program

This page shows questions in the Math 8 Modeling public release module at MSDE. 8th Grade Math
"Math 8 Modeling"

Select from the list to explore. Read any associated passages and then interact with the questions here.

Expand All Official Practice Test

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

A person purchased 10 items to donate to a school, backpacks that cost $25.75 each and notebooks that cost $4.25 each. The total cost of the items is $150. This situation can be represented by a system of equations with a unique solution.

What does the solution to the system of equations represent in this context?

  1. A.
    the cost of all the backpacks
  2. B.
    the cost of all the notebooks
  3. C.
    the total amount of money spent on the items
  4. D.
    the number of backpacks and notebooks purchased
i4

Correcti1

Student may have thought the solution represents total cost of only one of the itemsi2

Student may have thought the solution represents total cost of only one of the itemsi3

Student may have thought the solution represents total cost the items

This is a fill in the blank question that allows you to enter only numbers.

The figure shows the front side of a store sign and its dimensions, in feet. The store owner will paint the entire front side of the sign.

The figure shows the diagram of a store sign, with four sides. The top and bottom sides are horizontal, and the left side is vertical, so that right angles are formed at the lower left, and upper left, corners. The top side is shorter than the bottom side, so the right side, that connects them, slants downward, and to the right. The top side is 3 feet long, the right side is 5 feet long, and the bottom side is 6 feet long. A vertical line segment is drawn from the right end of the top side, down to the bottom side, where it intersects at a right angle. This creates a right triangle with the right side as a high pot in noose that is 5 feet long.

What is the area, in square feet, of the front side of the sign?

Enter your answer in the space provided.

square feet

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

Student J and Student K are both reading the same book for a class assignment. Student J reads 20 pages of the book each day. Student K starts reading 2 days after Student J starts reading, and Student K reads 30 pages of the book each day.

  • Define one variable and write an equation that represents the information given.
  • Determine the number of days after Student J starts reading when both students will have read the same number of pages of the book. Show your work or explain how you found your answer.

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.)

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.

A grocery store sells pumpkin seeds and sunflower seeds by the pound.

The equation y=6x models the relationship between y, the cost, in dollars, and x, the weight, in pounds, of the pumpkin seeds.

The graph shows the relationship between the cost, in dollars, and the weight, in pounds, of the sunflower seeds.

Sunflower Seeds

The figure shows the graph of a line in the x y plane. The x axis is labeled, Weight, in pounds, and the numbers 0, through 3, are indicated. The y axis is labeled, Cost, in dollars, and the numbers 0, through 9, are indicated. The line moves upward, and to the right, from the coordinates 0, comma, 0, through the coordinates 2, comma, 8.

A customer purchased seeds and paid $12 for the pumpkin seeds and $20 for the sunflower seeds.

Which statement is true?

  1. A.
    The customer purchased 2 more pounds of sunflower seeds than pumpkin seeds.
  2. B.
    The customer purchased 3 more pounds of sunflower seeds than pumpkin seeds.
  3. C.
    The customer purchased 2 more pounds of pumpkin seeds than sunflower seeds.
  4. D.
    The customer purchased 3 more pounds of pumpkin seeds than sunflower seeds.
i2

Correct i1

Confused the difference in unit rates for the difference in the number of pounds the customer purchased i3

Confused the difference in unit rates for the difference in the number of pounds the customer purchased i4

Found the difference between the number of pounds of seeds but, incorrectly concluded that more pumpkin seeds were purchased

This is a question with 2 parts, including a test question that allows you to enter extended text in your response.

A teacher has a cube. Each face of the cube has an area of 136 square foot.

Part A

Let d represent the length, in feet, of each edge of the cube. Write and solve an equation that includes the use of exponents to determine the value of d .

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

Part B

Let v represent the volume, in cubic feet , of the cube. Write and solve an equation that includes the use of exponents to determine the value of v .

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 4-Point Modeling Constructed Response Items

Sample Top Score Response

Part A

d 2 = 1 36

d = 1 36

d = 1 6

Part B

v = d 3

v = ( 1 6 ) 3

v = 1 216

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

A school club ordered medium pizzas and large pizzas for a club meeting. Each medium pizza cost $10 and was shared by 3 students. Each large pizza cost $12 and was shared by 4 students. There are 26 students in the club, and the club spent $80 on the pizzas.

Write a system of equations to model this situation.

Enter your equations in the space provided. Enter only your equations.