Go to the main content of the page.
Logo, Maryland State Department of Education
MCAP, Maryland Comprehensive Assessment Program

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

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 question with 2 parts, including a question with drop-down menus from which you must select an option to fill in the blank.

A student correctly used division to find the decimal equivalent of 112 using the work shown.

The figure shows a student’s work for a division operation, with a dividend of 1.0000, a divisor of 12, and a quotient of 0.0833,. A 0 is in the ones place of the quotient, above the 1 in the ones place, of the dividend,. A decimal point is to the right of the 0, in the quotient, to correspond to the decimal point to the right of the 1 in the dividend,. A 0 is in the tenths place of the quotient, above the 0 in the tenths place, of the dividend. An 8 is in the hundredths place of the quotient, above the 0 in the hundredths place, of the dividend. The product of that, 8 times the divisor of 12, is entered as 0.96 below 1.00, the first three digits of the dividend,. The difference of 1.00 minus 0.96 is entered as 0.04, and the 0 from the thousandths place of the dividend is dropped down to form 0.040,. A 3 is entered in the thousandths place of the quotient. The product of that, 3 times the divisor of 12, is entered as 0.036, below the 0.040,. The difference of 0.040 minus 0.036 is entered as 0.004, and the 0 from the ten thousandths place of the dividend, is dropped down to form 0.0040,. A 3 is entered in the ten thousandths place of the quotient. The product of that, 3 times the divisor of 12, is entered as 0.0036 below the 0.0040,. The difference of 0.0040 minus 0.0036 is entered as 0.0004.

The student claims that the decimal equivalent of 112 is 0.083 with a repeat bar above the digits 0 8 3

Complete the statement to explain why the student’s claim is incorrect.

Select from the drop-down menus to correctly complete the statement.

The student’s work shows that  
  , which means that the decimal equivalent of 112 is  
  .

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

A hotel wants to buy a pump to fill a hot tub with water. The lines graphed on the coordinate grid represent the rates at which three pumps can fill the hot tub with water.

The figure shows the graph of three lines, k, m, and p, in the x y plane. The x axis is labeled, Time, in minutes, and the numbers 0, through 9, are indicated. The y axis is labeled, Gallons of Water Pumped, and the numbers 0 through 90, in increments of 10, are indicated. Line k moves upward, and to the right, from the coordinates 0, comma, 0, through the coordinates 3, comma, 90. Line m moves upward, and to the right, from the coordinates 0, comma, 0, through the coordinates 9, comma, 90. Line p moves upward, and to the right, from the coordinates 0, comma 0, through the coordinates 9, comma, 45.

The hotel determined that the slowest of the three pumps can fill the hot tub with water in 90 minutes. Using this information, explain how to determine the number of minutes it will take for the fastest of the three pumps to fill the hot tub with water.

Enter your answer and your justification 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 Reasoning Constructed Response Items

Sample Top Score Response

Pump p is the slowest. It pumps 40 gallons in 8 minutes, so the unit rate is 5 gallons per minute.

Pump m is neither the fastest nor the slowest. It pumps 90 gallons in 9 minutes, so the unit rate is 10 gallons per minute.

Pump k is the fastest. It pumps 90 gallons in 3 minutes, so the unit rate is 30 gallons per minute.

Pump k is 6 times as fast as pump p, so it will take 16 of 90 minutes, which is 15 minutes to fill the hot tub with water.

Points

Sample Characteristics

4 Points

A four-point response for reasoning items provides evidence of correct, complete, and appropriate mathematical reasoning.

The response may:

  • be clear and well developed with logical reasoning communicated by the use of precise and appropriate representations, symbols, drawings, or mathematical vocabulary.
  • demonstrate a thorough understanding of the mathematics.
  • contain minor flaws that do not detract from the correct reasoning or demonstration of a thorough understanding.

3 Points

A three-point response for reasoning items provides evidence of essentially correct, essentially complete, and essentially appropriate mathematical reasoning.

The response may:

  • be clear and developed with logical reasoning communicated by the use of essentially precise and appropriate representations, symbols, drawings, or mathematical vocabulary.
  • contain minor flaws that detract from the correct reasoning or demonstration of a thorough understanding.

2 Points

A two-point response for reasoning items provides evidence of partially correct mathematical reasoning.

The response may:

  • display an incomplete reasoning process.
  • contain mathematical flaws.

1 Point

A one-point response for reasoning items provides limited evidence of correct mathematical reasoning.

The response may:

  • demonstrate the beginning of a valid chain of reasoning.
  • reflect a lack of essential understanding of the underlying mathematical concepts.
  • contain the correct solution, but work is limited or missing.
  • contain errors in the fundamental mathematical procedures or reasoning.
  • contain omissions or irregularities that lead to an inadequate 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.

The regular price of $28 for dog food is discounted by 25%. The sales tax is 8% of the discounted price. The steps used to determine the price of the dog food after the discount is applied including sales tax are shown.

  • Step 1: 28(34)(1+0.08)
  • Step 2: 21(1.08)
  • Step 3: 22.68

Which statement is true about the work?

  1. A.
    An error occurred in Step 1 because 34 should have been 0.25.
  2. B.
    An error occurred in Step 1 because (1+0.08) should have been 0.92.
  3. C.
    An error occurred in Step 2 because the product of 28 and 34 is 2834.
  4. D.
    The work is correct and the discounted price of the dog food with sales tax is $22.68.
i4

Correct i1

Attempted to represent the dollar amount of the discount i2

May have associated sales tax with a price decrease instead of an increase i3

May have associated product with sum

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

Two expressions are given.

  • 3.5n+4(514n-1.5)
  • -21(27-76n)

Apply the properties of operations to show why 3.5n+4(514n-1.5) is equivalent to -21(27-76n).

Show your work or explain your reasoning.

Enter 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. (38 files were searched.)

Holistic Rubric for 3-Point Reasoning Constructed Response Items

Sample Top Score Response

3.5 n + 4 ( 5 1 4 n − 1.5 ) = 3.5 n + 4 ( 5 1 4 n ) + 4 ( − 1.5 ) 0 = 3.5 n + 4 ( 21 4 n ) − 6 0 = 3.5 n + 4 ( 21 4 ) n − 6 0 = 3.5 n + 21 n − 6 0 = 24.5 n − 6

− 21 ( 2 7 − 7 6 n ) = ( − 21 ) ( 2 7 ) − 21 ( − 7 6 n ) 0 = ( − 3 ) ( 2 1 ) + 21 ( 7 6 n ) 0 = − 6 + 21 ( 7 6 ) n 0 = − 6 + 7 ( 7 2 ) n 0 = − 6 + 49 2 n = − 6 + 24 1 2 n

The two expressions are equivalent because −6+2412n=2412n−6=24.5n−6.

Points

Sample Characteristics

3 Points

A three-point response for reasoning items provides evidence of correct, complete, and appropriate mathematical reasoning.

The response may:

  • be clear and well developed with logical reasoning communicated by the use of precise and appropriate representations, symbols, drawings, or mathematical vocabulary.
  • contain minor flaws that do not detract from the correct reasoning or demonstration of a thorough understanding.

2 Points

A two-point response for reasoning items provides evidence of partially correct mathematical reasoning.

The response may:

  • display an incomplete reasoning process.
  • contain minor flaws that detract from the correct reasoning or demonstration of a thorough understanding.

1 Point

A one-point response for reasoning items provides limited evidence of correct mathematical reasoning.

The response may:

  • demonstrate the beginning of a valid chain of reasoning.
  • reflect a lack of essential understanding of the underlying mathematical concepts.
  • contain the correct solution, but work is limited or missing.
  • contain errors in the fundamental mathematical procedures or reasoning.
  • contain omissions or irregularities that lead to an inadequate solution.

0 Point

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

This is a question with 2 parts, including a question with drop-down menus from which you must select an option to fill in the blank.

A flat, rectangular garden has a perimeter of 24 meters, and the ratio of the length of the garden to the width is 2 to 1. The steps to determine the length, in meters, of the garden are shown.

At least one mistake was made.

  • Step 1: 2l+2w=24
  • Step 2: 2l+2(2l)=24
  • Step 3: 2l+4l=24
  • Step 4: 6l=24
  • Step 5: l=4

In which step was the first mistake made, and what is the correct length of the garden?

Select from the drop-down menus to correctly complete the statement.

The first mistake was made in  
  and the correct length of the garden is  
  meters.

This is a question with 2 parts, including a question with drop-down menus from which you must select an option to fill in the blank.

Two students both solved the equation −4(x−0.5)=6 incorrectly. The work of each student is shown.

Student A’s Work:

0−4(x−0.5)=6Step1:−4x−2=6000Step2:−4x=8000000Step3:x=−2000000

Student B’s Work:

0−4(x−0.5)=6Step1:−4x+2=6000Step2:−4x=8000000Step3:x=−2000000

In which step of their work did Student A and Student B make their first mistake?

Select from the drop-down menus to correctly complete each statement.

Student A made their first mistake in  
  . Student B made their first mistake in  
  .