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This page shows questions in the Math 5 Reasoning public release module at MSDE. 5th Grade Math
"Math 5 Reasoning"

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

A shopper buys some fruit.

  • The shopper buys a pack of strawberries and 2 pounds of peaches.
  • A pack of strawberries weighs 1.2 pounds and costs $6.55.
  • A pound of peaches costs $3.29.

Which statement explains the shopper’s correct thinking to find the total cost of the fruit?

  1. A.
    The shopper thinks that there is 1 pack of strawberries and 1 pound of peaches, and 6.55+3.29=9.84.
  2. B.
    The shopper thinks that there is 1 pack of strawberries and 2 pounds of peaches, and 6.55+2×3.29=13.13.
  3. C.
    The shopper thinks that there are 1.2 pounds of strawberries and 1 pound of peaches, and 1.2×6.55+3.29=11.15.
  4. D.
    The shopper thinks that there are 1.2 pounds of strawberries and 2 pounds of peaches, and 1.2×6.55+2×3.29=14.44.
i2

Correcti1

Forgot to take the 2 pounds of peaches into accounti3

Forgot to take the 2 pounds of peaches into account and misused the information on the weight of the strawberriesi4

Misused the information on the weight of the strawberries

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

A student performed the division problems shown.

The figure shows the following division problems written by a student. 1,875 divided by 15, equals 125. 3,825 divided by 15, equals 255.

The student claims that when a 4 ‑digit number ending in 5 is divided by 15, the quotient always ends in 5 and there is no remainder.

Determine whether the student’s claim is correct or incorrect. If the claim is correct, explain why it is correct. If the claim is incorrect, give two examples that prove that it is incorrect.

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

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 only one option.

A student found the value of the expression 1014−678.

The student subtracted the whole numbers first and then subtracted the lesser fraction from the greater fraction to find the answer.

Which steps correct the error in the student’s thinking?

  1. A.
    Step 1 : subtract 28 from 78

    Step 2 : subtract 6 from 10

  2. B.
    Step 1 : subtract 78 from 108

    Step 2 : subtract 6 from 10

  3. C.
    Step 1 : regroup the whole number
    Step 2 : subtract 28 from 78

    Step 3 : subtract 6 from 9

  4. D.
    Step 1 : regroup the whole number
    Step 2 : subtract 78 from 108

    Step 3 : subtract 6 from 9

i4

Correcti1 i2 i3

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

A student made the following claim.

“If a quadrilateral has two pairs of congruent sides, then the figure is a parallelogram.”

Which two figures can be used to show that the student’s claim is incorrect?

Select the two correct answers.

  1. A.
    The figure shows a shape with four sides. The top and bottom sides are the same length, and are parallel with each other. The left and right sides are the same length, and are parallel with each other.
  2. B.
    The figure shows a shape with four sides that are the same length. The upper left and lower right sides are parallel with each other. The lower left and upper right sides are parallel with each other.
  3. C.
    The figure shows a shape with four sides. The lower left and upper left sides are the same length. The lower right and upper right sides are the same length. No sides are parallel.
  4. D.
    The figure shows a shape with four sides. The lower left and upper left sides are the same length. The lower right and upper right sides are the same length. No sides are parallel.
  5. E.
    The figure shows a shape with six sides. The top and bottom sides are the same length, and are parallel with each other. The lower left and lower right sides are the same length, and are parallel with each other. The upper left and upper right sides are the same length, and are parallel with each other.

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

An artist is using a squared wooden panel to create a piece of art. The panel is divided in smaller squares as shown.

The figure shows a rectangle, divided into 30 squares, with six vertical columns of squares, and five horizontal rows of squares.

The artist paints 35 of the squares in red, then draws golden circles on 13 of the squares to decorate it.

The artist draws the model shown to represent the fraction of the whole wooden panel that is both painted and decorated.

The figure shows a model, that is like the original rectangle, divided into 30 squares, but now some of the squares are shay did and have diagonal lines drawn in them. Four squares are shay did lightly, and have diagonals drawn from the lower left, to the upper right, corner. Twelve squares are shay did lightly, and have diagonals drawn from the upper left, to the lower right, corner. Six squares are shay did darkly, and have diagonals drawn both from the lower left, to the upper right, corner, and from the upper left, to the lower right, corner. Eight squares are unshaded, and have no diagonals drawn.

Which statement is true about the model the artist drew?

  1. A.
    The model is correct because it represents the equation 35+26=630.
  2. B.
    The model is correct because it represents the equation 35×13=15 and 15 of 30 is 6.
  3. C.
    The model is incorrect because 2 of the 6 columns are shaded and there should be 3 columns with 1 column shaded.
  4. D.
    The model is incorrect because 35×13=15 and 15 of the model can only be represented by shading 1 row of squares.

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

A teacher needs to buy batteries for 32 calculators.

  • There are 20 basic calculators that each require 3 batteries.
  • There are 12 advanced calculators that each require 4 batteries.
  • The batteries are sold in packages of 24.

The teacher thinks that 6 packages of batteries will be needed and that there will be 12 batteries left over after the calculators are filled.

Provide a solution path that shows whether the teacher is correct or incorrect. Explain what each step in the solution path represents in terms of the situation.

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.)