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This page shows questions in the Math 3 Reasoning public release module at MSDE. 3rd Grade Math
"Math 3 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 wants to put a border around a notebook that measures 8 inches wide and 10 inches long.

The student thinks that the perimeter of the notebook is 18 inches because eight plus 10 equals 18.

Complete the sentence to explain how to correct the student’s thinking.

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

The student should have  
  then  
  and then added the two products.

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

A teacher is making supply boxes for her students to use when they work in groups.

  • There are 9 supply boxes.
  • Each supply box will have 6 colored markers.
  • The teacher has 15 colored markers to put in the supply boxes.

The teacher thinks that 39 more markers are needed to fill the supply boxes because 6×9=54 and 54 minus 15 equals 39.

Explain why the teacher’s thinking is correct by explaining what the two equations represent in the problem.

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 Reasoning Constructed Response Items

Sample Top Score Response

There are 9 supply boxes and each box will need 6 colored markers, so the equation 6×9=54 means that the teacher needs a total of 54 colored markers to fill the supply boxes.

The teacher needs 54 colored markers and the teacher already had 15 colored markers, so the equation 54−15=39 means that the teacher needs 39 more colored markers to fill the supply boxes.

The teacher’s thinking is correct.

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 point is shown on the number line.

The figure shows a number line with nine evenly spaced tick marks. From left to right, the first tick mark is labeled 0, and the ninth tick mark is labeled 1. A point is graphed on the tick mark labeled 1.

Complete the sentence to compare the numbers represented by the point on the number line.

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

The point on the number line can be used to show that  
  and  
  .

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

A student made 20 necklaces.

  • The student put 5 beads on each necklace.
  • There were 10 beads in each package.

Which statement explains the student’s correct thinking to find the total number of beads the student used to make all the necklaces?

  1. A.
    The student thinks that there are 20 necklaces and there are 10 beads in each package, and 20÷10=2.
  2. B.
    The student thinks that there are 20 necklaces and there are 10 beads in each package, and 20×10=200.
  3. C.
    The student thinks that there are 20 necklaces and there are 5 beads on each necklace, and 20÷5=4.
  4. D.
    The student thinks that there are 20 necklaces and there are 5 beads on each necklace, and 20×5=100.
i4

Correcti1

Confused with the number of beads on each necklace with the number of beads in each package and confused the operationi2

Confused with the number of beads on each necklace with the number of beads in each packagei3

Confused the operation

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

A student has several pennies.

The student organized the pennies into the array shown.

The figure shows an array of 20 pennies arranged in 5 columns and 4 rows.

The student wants to put all the pennies in stacks with the same number of pennies in each stack.

Explain three different ways the student could put the pennies in stacks with the same number of pennies in each stack.

Explain how you used the array of pennies to help you find the different ways to stack the pennies.

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 Reasoning Constructed Response Items

Sample Top Score Response

There are 4 rows of pennies in the array so the student could make 4 stacks of pennies. Since there are 5 pennies in each row, there would be 5 pennies in each stack.

There are 5 columns of pennies in the array, so the student could make 5 stacks of pennies. Since there are 4 pennies in each column, there would be 4 pennies in each stack.

If I divide the array in half between the second and third rows, there would be 10 pennies in the top two rows and 10 pennies in the bottom two, so the student could make 2 stacks of pennies with 10 pennies in each stack.

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 multiple choice question that allows you to select several options.

A student wrote the expression 7+7+7+7+7 to find the value of 7×5.

The student said that when writing a different expression to represent 7×5 , only the numbers 7 and 5 can be used.

Which two expressions could be used to show that the student’s response is incorrect?

Select the two correct answers.

  1. A.
    5×7
  2. B.
    (4+5)×(3+5)
  3. C.
    (4×5)+(3×5)
  4. D.
    (7+3)×(7+2)
  5. E.
    (7×3)+(7×2)
i3

Correcti5

Correcti1

Used the given digitsi2

Reversed multiplication and additioni4

Reversed multiplication and addition