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MCAP, Maryland Comprehensive Assessment Program

This page shows questions in the Math 4 Modeling public release module at MSDE. 4th Grade Math
"Math 4 Modeling"

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Expand All Official Practice Test

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

A student drew a quadrilateral with one right angle. The student then divided the quadrilateral into two triangles. The student measured one angle in one of the triangles as shown in the figure.

The figure shows a quadrilateral, with one right angle indicated at the lower left corner, where a vertical left side meets a horizontal bottom side. A diagonal line segment is drawn from that lower left corner, to the upper right corner, to divide the quadrilateral into two triangles. Two new angles are formed by the diagonal line segment, at the lower left corner of the quadrilateral. The angle formed by the diagonal line segment, and the horizontal bottom side of the quadrilateral, is labeled 35 degrees. The angle formed by the diagonal line segment, and the vertical left side of the quadrilateral, is labeled b degrees.

Which solution path could the student use to find the value of b without measuring the angle?

  1. A.
    add 35 to 90
  2. B.
    divide 90 by 35
  3. C.
    multiply 35 by 90
  4. D.
    subtract 35 from 90

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

Last week, a student kept track of how long he practiced soccer each day.

The line plot shows the student’s data.

The figure shows a line plot. The axis is labeled, Time, in hours, and it has 12 evenly spaced tick marks. From left to right, the first tick mark is labeled, 0, the fifth tick mark is labeled, 1, and the ninth tick mark is labeled, 2. The amount of time that the student spent practicing soccer on each of 7 days is indicated with an X graphed at the following positions,: 1 at the first tick mark, 2 at the third tick mark, 1 at the sixth tick mark, 2 at the seventh tick mark, and 1 at the tenth tick mark.

Which three questions can be answered using the information in the line plot?

Select the three correct answers.

  1. A.
    What was the greatest amount of time that the student practiced on any day last week?
  2. B.
    What was the total amount of time the student practiced last week?
  3. C.
    On which day last week did the student practice the longest?
  4. D.
    Did the student practice more last week or the week before?
  5. E.
    How many days last week did the student not practice?
i1

KEYi2

KEYi5

KEYi3

Student thinks marks on line plot go in order.i4

Student thinks you can make an inference about other weeks.

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

The figure shows the dimensions of a rectangular floor. The two openings represent doors. Each door is 3 feet wide.

The figure shows a diagram of a rectangular floor with dimensions labeled 18 feet long, by 14 feet wide. Two openings are labeled as doors. One is toward the top end of the left side, and the other is toward the right end of the bottom side.

A contractor will buy baseboards to place around the entire floor, except for the doors. Each baseboard is 8 feet long and costs $11.

Find the total cost of the baseboards the contractor needs to buy for the room.

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.

There are six different pies left over after a party. Each of the pies has a fractional amount left at the end of the party. The line plot shows the fractions of pies left over.

The figure shows a line plot with five evenly spaced tick marks. From left to right, the tick marks are labeled, 0, one eighth, one fourth, three eighths, and one half. The fraction of each of six pies left over is indicated, with an X graphed at the following positions: two at one eighth, one at three eighths, and three at one half.

Each person who attended the party will receive an equal amount of the leftover pie.

Which piece of information is needed to determine how much pie each person should receive?

  1. A.
    the types of pie that are left over
  2. B.
    the type of pie each person likes most
  3. C.
    the number of slices in each whole pie
  4. D.
    the number of people who attended the party
i4

Correct i1

Did not recognize that this information is unnecessary i2

Did not recognize that this information is unnecessary i3

Did not recognize that this information is unnecessary

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

An athlete needs to exercise 3510 hours each week.

  • The athlete exercised 610 hour on Sunday.
  • The athlete exercised 310 hour on Monday.
  • The athlete exercised 410 hour each on Tuesday, Wednesday, and Thursday.

Create a solution path to find the time that the athlete needs to exercise the rest of the week.

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

The figure represents a rectangular floor. A custodian is installing tiles on the floor. Each tile covers 2 square feet of area.

The figure shows a rectangle that is 74 feet long and 42 feet wide.

Which steps should the custodian take to find the number of tiles needed?

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

First, the custodian should find the value of  
  .
Next, the custodian should  
  .