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This page shows questions in the Math 4 Reasoning public release module at MSDE. 4th Grade Math
"Math 4 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 multiple choice question that allows you to select only one option, and, a test question that allows you to enter extended text in your response.

Pre-recorded audio

Part A

A pair of fraction models is given.

Image Two circular fraction models. Both the left and right fraction models show a circle divided into 8 parts, with six parts shaded.

Which explanation is a correct reasoning for the sum of the shaded parts?

  1. A.
    Each model shows six eighths shaded, so the sum is twenty-six eighths.
  2. B.
    Each model shows six eighths shaded, so the sum is two and six eighths.
  3. C.
    Each model is divided into 8 parts. There are 12 total parts shaded, so the sum is twelve eighths.
  4. D.
    Each model is divided into 8 parts. There are 12 total parts shaded, so the sum is one and two eighths.

Part B

Each shape is equal in size and is divided into 5 equal parts.

Image Five pentagons, each divided into five equal sections.
  • Explain one possible way to shade the three shapes to represent a total of seven fifths In your explanation, at least one part of each shape must be shaded. Explain why your shading is correct.
  • One shape is removed. Explain how to decompose seven fifths into the sum of two fractions. Give an example in the form ofbox over box plus box over box equals seven fifths, and explain how the two remaining shapes would be shaded.

Enter your explanations in the space provided.

Copyright 2023, New Meridian Corporation. Reprinted with permission. All rights reserved. The printing, copying, redistribution, or retransmission of this content without express written permission is prohibited.

This is a question with 4 parts, including a question with drop-down menus from which you must select an option to fill in the blank, and, a test question that allows you to enter extended text in your response.

Pre-recorded audio

Part A

Describe how to show the sum three eighths plus two eighths on the number line shown.

0 1 Image An image is shown, but there is no alternative text.

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

Divide the segment of the number line between 0 and 1 into  
  equal parts. Starting at 0, shade the first  
  part(s). Then shade the next  
  parts to show the sum three eighths plus two eighths.

Part B

The number line shown can be used to model the expression seven tenths minus three tenths

0 1 Image An image is shown, but there is no alternative text.
  • To model the expression, how many parts should the segment of the number line between 0 and 1 be divided into? Explain your answer.
  • Describe each of the remaining steps needed to model the expression.
  • What is the value of the expression?

Enter your answers, your explanation, and your description in the space provided. You may use the drawing box to add a drawing to help explain your answer.

Copyright 2023, New Meridian Corporation. Reprinted with permission. All rights reserved. The printing, copying, redistribution, or retransmission of this content without express written permission is prohibited.

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

Pre-recorded audio

Figure K is covered with square tiles each measuring 1 square foot. There are no gaps or overlaps in the tiles. Figure M is a square with side lengths of 4 feet.

Figure K Figure M 4 feet = 1 square foot Image Figure K is a rectangle divided into three rows with seven columns in each row. Key, each cell equals 1 square foot. Figure M is a square with side length 4 feet.

Part A

Joan said the area of Figure K is found by adding 3 + 7 + 3 + 7, so the area is 20 square feet. Joan made a mistake in her reasoning.

Explain the mistake Joan made. Find the correct area for Figure K.

Enter your explanation and your answer in the space provided.

Part B

Figures K and M are pushed together to form a larger figure. There are no gaps or overlaps of the two figures. To find the area of the larger figure, Andy multiplied the area of Figure K by the area of Figure M. Andy is incorrect in his reasoning.

  • Explain the steps Andy should take to find the area of the larger figure.
  • What is the area, in square feet, of the larger figure?
  • Show your work or explain your answers.

Enter your explanation, your answer, and your work or explanation in the space provided.

Copyright 2023, New Meridian Corporation. Reprinted with permission. All rights reserved. The printing, copying, redistribution, or retransmission of this content without express written permission is prohibited.