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This page shows questions in the Math 6 Reasoning public release module at MSDE. 6th Grade Math
"Math 6 Reasoning"

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

A machine in a factory makes chairs at a rate of 2 chairs every 10 minutes.

  • How much time does the machine take to make 5 chairs?
  • How many minutes would it take for the factory to fulfill an order for 32 chairs?

Show your work or explain how you determined your answers.

Enter your answers and your work or explanation in the space provided. You may also use the drawing tool to help explain or support your answer.

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Holistic Rubric for 4-Point Reasoning Constructed Response Items

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 numbers -12 and 25 are graphed on the number line.

The figure shows a number line with 21 evenly spaced tick marks. From left to right, the first tick mark is labeled, negative 1, the eleventh tick mark is labeled, 0, and the twenty first tick mark is labeled, 1. A point labeled, negative one half is graphed at the sixth tick mark, which is 5 tick marks to the right of negative 1, and 5 tick marks to the left of 0. A point labeled, two fifths is graphed at the fifteenth tick mark, which is 4 tick marks to the right of 0, and 6 tick marks to the left of 1.

Which statement correctly compares the absolute values of -12 and 25 and gives the correct reasoning for the comparison?

  1. A.
    -12 has the lesser absolute value because -12 is closer to zero than 25 is to zero.
  2. B.
    -12 has the greater absolute value because -12 is closer to zero than 25 is to zero.
  3. C.
    -12 has the lesser absolute value because -12 is further from zero than 25 is from zero.
  4. D.
    -12 has the greater absolute value because -12 is further from zero than 25 is from zero.
i4

Correct - The further the distance from zero on the number line, the greater the absolute value of the number.i1

Incorrect - This statement is incorrect because it incorrectly states that −12 is closer to zero than 25 on the number line, and does not correctly compare their absolute values.i2

Incorrect - This statement is incorrect because even though it correctly states that the absolute value of −12 is greater than the absolute value of 25 , it incorrectly states that it is closer to zero on the number line than 25 UNRECOGNIZED DOT DIRECTIVE .i3

Incorrect - This statement is incorrect because although it correctly states that −12 is further from zero than 25 on the number line, and does not correctly compare their absolute values.

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

The expression 12x+8 is equivalent to the expression a(bx+c), where b and c are constants and have no common factors. A student wrote the answer as 2(6x+4) .

Which statement best explains whether the student’s answer is correct or incorrect?

  1. A.
    The student’s answer is incorrect because the greatest common factor of 12x and 8 is 2x , so the correct expression is 2x(6x+4) .
  2. B.
    The student’s answer is incorrect because the greatest common factor of 12x and 8 is 4x , so the correct expression is 4x(3x+2) .
  3. C.
    The student’s answer is incorrect because the greatest common factor of 12x and 8 is 4 , so the correct expression is 4(3x+2) .
  4. D.
    The student’s answer is incorrect because the greatest common factor of 12x and 8 is 8 , so the correct expression is 8(4x+1) .
i3

Correct. In order to obtain the desired form a(bx+c) the greatest common factor of 4 should be factored out of each term in the expression leaving 4(3x+2) UNRECOGNIZED DOT DIRECTIVE .i1

Incorrect. Factoring out a common factor of 2 does give not get the expression into the desired form with b and c still having a common factor of 2 remaining. 8 i2

Incorrect. Factoring out a common factor of 4x is not possible since there is only one term in the expression that has the variable x i4

Incorrect. Factoring out a common factor of 8 is not possible since it is not a common factor of both terms. The most likely mistake would be that the 8 was subtracted and not divided from the first term of the binomial.

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

An art teacher has a jar containing 34 pound of glitter for use by the students in a class. The glitter is being separated into portions that are each 110 pound of glitter.

The teacher asked, “What is the greatest number of whole portions that can be made?”

One student incorrectly obtains the answer of 43×101=403=1313 , and says 13 portions can be made.

  • Explain the mistake that was made in the calculations.
  • What is the correct answer to the question?

Enter your answers and your work or explanation in the space provided. You may also use the drawing tool to help explain or support your answer.

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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.

The table shows several values of x and y.

x y
1 6
3 8
4 9

A student claims that since each value for y is 5 more than the corresponding value of x , that the ratio of y to x is 5 to 11 for the values in the table.

Which statement best explains whether the student’s claim is correct or incorrect?

  1. A.
    The student’s claim is correct because 6−1=5 , 8−3=5 , and 9−4=5 .
  2. B.
    The student’s claim is incorrect because the ratio of y to x is different for each pair of corresponding x - and y -values.
  3. C.
    The student’s claim is incorrect because the ratio of y to x is 1 to 5 for each pair of corresponding x - and y -values.
  4. D.
    The student’s claim is incorrect because the ratio between the x -values and the y -values of the first two points is 2 to 1 and not 5 to 1 .
i2

Correct - the fractions 16, 38, and 49 are not equal.i1

Incorrect - This response is based on the belief that ratios are based on equal differences.i3

Incorrect - This response is based on an incorrect relationship between the sum of two terms and the product of the input number between them.i4

Incorrect The statement says that the ratio between the x -values and the y -values of the first two points is 2 to 1 , which is incorrect. The difference would be 2 and would not speak to the ratios but would be a necessary step in finding the slope of the linear equation that is modeled.

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

The equation x+5=12 can be solved using one step.

Which statement provides a correct explanation and solution to the equation?

  1. A.
    The number 5 should be added to both sides of the equation, and the solution is x=17 .
  2. B.
    The number 5 should be subtracted from both sides of the equation, and the solution is x=7 .
  3. C.
    The number 5 should be divided from both sides of the equation, and the solution is x=125 .
  4. D.
    The number 5 should be multiplied to both sides of the equation, and the solution is x=60 .
i2

Correct.i1

Incorrect. Adding 5 on both sides of the equation does not isolate the variable x UNRECOGNIZED DOT DIRECTIVE .i3

Incorrect. Dividing both sides of the equation by 5 does not isolate the variable x UNRECOGNIZED DOT DIRECTIVE .i4

Incorrect. Multiplying both sides of the equation by 5 does not isolate the variable x