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This page shows questions in the Math 7 Modeling public release module at MSDE. 7th Grade Math
"Math 7 Modeling"

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Expand All Official Practice Test

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

A student will buy packs of AA batteries, packs of AAA batteries, and 1 pack of C batteries.

  • The student will buy the same number of packs of AA and AAA batteries.
  • Each pack of AA batteries costs $10.
  • Each pack of AAA batteries costs $5.
  • The pack of C batteries costs $18.
  • The student will spend a total of $108.

Which equations can be used to determine x, the number of packs of each of AA batteries and AAA batteries the student will buy?

Select all that apply.

  1. A.
    15x=90
  2. B.
    23x=98
  3. C.
    33x=108
  4. D.
    10+(5+18)x=108
  5. E.
    (10+5)x+18=108
  6. F.
    (10+5+18)x=108
i1

Correcti5

Correcti2

Combined the unit prices of AAA and C batteriesi3

Combined the unit prices for each type batteryi4

Combined the unit prices of AAA and C batteriesi6

Combined the unit prices for each type of battery

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

The floor of a room is going to be covered with ceramic tiles.

  • The length of the room is 12 feet.
  • The width of the room is 23 of the length of the room.
  • The ceramic tiles are squares with 112 inches per side.

Which expression represents the number of ceramic tiles that will be needed?

  1. A.
    (12×12)(12×23×12)÷(32×32)
  2. B.
    (12×12)(12×23×12)×(32×32)
  3. C.
    12(12×23)÷(32×32)
  4. D.
    12(12×23)×(32×32)
i1

Correcti2

Multiplied by the area of a tilei3

Did not convert the room dimensions to inchesi4

Did not convert the room dimensions to inches and multiplied by the area of a tile

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

A farmer’s horses drink from a rectangular water tank with dimensions shown.

The figure shows a three dimensional shape, that resembles a rectangular prism, that has a section removed from one corner. The section that has been removed is in the shape of a smaller rectangular prism. The height of the whole shape is 2 and one half feet. The length of the shape at the face that has not had a section removed, is 5 and three fifths feet, while the length of the shape at the opposite face, where a section has been removed, is 2 and four fifths feet. The width of the shape at the face that has not had a section removed is 4 and four fifths feet, while the width of the shape on the face where the section has been removed, is 2 and two fifths feet.

When the farmer refills the tank, it takes the horses 4 days to drink all the water. The farmer wants to build a new, larger tank and plans to increase each measurement of the tank by 25%.

  • By what percentage will the amount of water the farmer can put in the tank increase when the larger tank is built?
  • How many days will it take the horses to drink all the water in the larger tank?

Explain how you found your answers.

Enter your answers and your 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. (38 files were searched.)

NOTE to ETS Editorial:

There is an error in the scoring rubric which has been corrected in the online and paper PT answer keys. The volume of the smaller rectangular prism is given as 15 4/5, but should be 16 4/5. The rubric in this item will be updated after the Spring 2022 Practice Test is no longer available.

Holistic Rubric for 3-Point Modeling Constructed Response Items

Sample Top Score Response

The current tank is represented by the L-shaped figure, formed by two connected rectangular prisms. The amount of water, in cubic feet, the current tank can hold is the combined volume of both prisms. The volume of the large rectangular prism is 245445212=14524552=14512111=1685=3335.

The volume of the smaller rectangular prism is (225)(212)(535−245)=(125)(52)(485−245)=6(245)=6(145)=845=1645.

The current tank can hold 3335+1645=4975=5025 cubic feet of water.

For the new tank, each dimension of both rectangular prisms will be increased by 25% which can be represented by multiplying each current dimension by 1.25 or 54 as follows:

For the large rectangular prism, (145×54)(245×54)(52×54)=(72)(6)(258)=21(258)=5258=6558.

For the small rectangular prism, (125×54)(52×54)(145×54)=3(258)(72)=321316.

The new tank will be able to hold 6558+321316=651016+321316=972316=98716 cubic feet of water.

The percentage of increase from the amount of water contained in the current tank to the amount that will be contained in the new larger tank is (98716−5025)÷5025. Simplifying, (98.4375−50.4)÷50.4=48.0376÷50.4=0.953125, so the amount of water will increase by about 95%. The number of days it will take for the horses to drink water from the new tank is 4(1.95)=7.8 or approximately 8 days.

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 several options.

Each day, a salesperson earns $25 plus 5% of their total sales for the day. The salesperson’s goal is to earn more than $50 on Thursday.

Which statements are true?

Select all that apply.

  1. A.
    The salesperson would reach the goal if their total sales on Thursday are $60.
  2. B.
    The salesperson would reach the goal if their total sales on Thursday are $700.
  3. C.
    The salesperson would reach the goal if their total sales on Thursday are exactly $500.
  4. D.
    The salesperson can use the inequality 25+5x>50 to determine x, the total dollar amount of sales needed to exceed the goal.
  5. E.
    The salesperson can use the inequality 25+0.05x>50 to determine x, the total dollar amount of sales needed to exceed the goal.
i2

Correcti5

Correcti1

May have disregarded the percentage and added the total sales to 25i3

Chose a situation which results in earning of exactly $50i4

Represented the percent as a whole number instead of the decimal 0.05

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

A worker will create a circular concrete patio around a square planter. The shaded region in the figure shown represents the patio and the unshaded region represents the planter.

The figure shows a square inscribed in the center of a circle. The square is unshaded while the rest of the circle around it is shaded.
  • The side length of the square planter is 4 feet.
  • The cost of the concrete is $0.90 per square foot.

The worker needs to calculate the cost of the concrete needed for the patio based on r, the radius, in feet, of the patio.

Write an expression that represents the total cost, in dollars, of the concrete the gardener needs to create the patio in terms of r.

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

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

A game has two players. On each turn, a player spins two spinners to determine how far to move a game piece.

  • Each spinner is divided into 4 equal sections.
  • A different integer from 1 to 4 is written on each section of one spinner.
  • A different integer from -1 to 2 is written on each section of the other spinner.
  • The player finds the sum of the integers shown and moves the game piece that number of spaces.
  • The first player to land on or pass the “Win” space wins the game.

The figure shows the position of each player’s game pieces. Player A needs to move 6 spaces or more to win and Player B needs to move 3 spaces or more to win.

The figure shows a rectangle divided into 7 square-shaped sections of equal size. From left to right, the first section is labeled, A, the fourth section is labeled, B, and the seventh section is labeled, win. The second, third, fifth, and sixth sections are blank.
  • If Player A has the next turn, what is the probability that Player A wins the game? Show or explain how you determined your answer.
  • If Player B has the next turn, what is the probability that Player B wins the game? Show or explain how you determined your answer.

Enter your answer and your 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. (38 files were searched.)

Holistic Rubric for 4-Point Modeling Constructed Response Items

Sample Top Score Response

The 16 possible outcomes for this situation are represented in the table.

First Spinner Second Spinner Sum
1 - 1 0
1 0 1
1 1 2
1 2 3
2 − 1 1
2 0 2
2 1 3
2 2 4
3 − 1 2
3 0 3
3 1 4
3 2 5
4 − 1 3
4 0 4
4 1 5
4 2 6

Player A needs to move at least 6 spaces to win the game. Of the 16 possible outcomes, 1 will result in a win. The probability that Player A will win is 1 16 .

Player B needs to move at least 3 spaces to win the game. Of the 16 possible outcomes, 10 will result in a win. The probability that Player B will win is 10 16 or 5 8 . UNRECOGNIZED DOT DIRECTIVE .row

Points `

Sample Characteristics UNRECOGNIZED DOT DIRECTIVE .row

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.
UNRECOGNIZED DOT DIRECTIVE .row

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.
UNRECOGNIZED DOT DIRECTIVE .row

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.
UNRECOGNIZED DOT DIRECTIVE .row

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.
UNRECOGNIZED DOT DIRECTIVE .row

0 Point ` A zero-point response is completely incorrect, incoherent or irrelevant. UNRECOGNIZED DOT DIRECTIVE .end-table