6th Grade Math "Math 6 2024" - Public Release

Yards of Fabric	Number of Skirts
3	2
6	4
9	6

What is the value of $63,798 divided by 49?$

A.

$132$
B.

$1,302$
C.

$1,320$
D.

$1,506$

Correcti1

Incorrect - Left out placeholder $0$ i3

Incorrect - Left out placeholder, then padded answer to fill “missing” units digit in quotienti4

Incorrect - Obtained $24$ rather than $14$ when subtracting $63 - 49$ and rounded answer.

What is the value of the following expression?

$\frac{9^{2} + 5 \cdot 2 - 1^{3}}{2^{4} - 6}$

Enter your answer in the space provided.

Which point represents the value of $the absolute value of 3$ on the number line?

Move the point to the correct location.

All numbers that do not exceed $15$ will be graphed on a number line. Describe the graph of the numbers.

Select from the lists of choices to complete the sentences.

The graph will be a ray that starts at and points to the . The graph include the endpoint of the ray.

What is the value of $25.761 minus 17.49$

A.

$8.271$
B.

$8.371$
C.

$8.712$
D.

$24.012$

Correcti2

Incorrect - Aligns decimal portions as $.761 - .049$ i3

Incorrect - Forgets to reduce $7$ in minuend by $1$ when borrowing to subtract $9$ from $6 .$ i4

Incorrect - Aligns numbers by right-hand digit, rather than on decimal.

Melvin and Roberto played football on two different teams last season.

Melvin’s team won $w$ games.

Roberto’s team won $3$ fewer games than Melvin’s team.

Create an expression that can be used to represent the number of games Roberto’s team won last season.

Move a number, variable, or symbol into each box.

3

w

-

+

\cdot

\div

A jar contains some marbles that are either white or red. The ratio of the number of white marbles to the number of red marbles is $2 to 3$ .

What might be the total amount of white and red marbles in the jar?

Select all that apply.

An artist is creating several pieces of pottery.

He has $10 and four fifths$ pounds of clay.

He will use $7 tenths$ of a pound to create each piece of pottery.

What is the greatest number of pieces of pottery the artist can make with this clay?

Correcti1

Divided correctly but transposed the digits using the remainder as the whole number, the divisor as the numerator and the quotient as the denominatori2

Converted $10 \frac{4}{5}$ to $\frac{19}{5} (5 + 10 + 4)$ i3

Rounded both figures up to 11 and 1 and used their sum

An expression is shown.

$56 plus 91$

Use the greatest common factor of the two numbers in the expression to rewrite the expression as a number multiplied by the sum of two numbers that have no common factor.

Enter your answer in the spaces provided.

$56 + 91 =$ $($ $+$ $)$

Which expressions are equivalent to $4 x plus 16$

Select all that apply.

Correct - $2 x + 2 x + 8 + 8 = 4 x + 16$ i4

Correct - $4 (x + 4) = 4 x + 16$ i2

Incorrect - $2 x (2 + 8) = 4 x + 16 x,$ not $4 x + 16$ i3

Incorrect - $4 x + 4 x + 4 x + 4 x = 4 (x \times 4),$ not $4 (x + 4),$ which equals $4 x + 16$ i5

Incorrect - $4 x (1 + 4) = 4 x + 16 x,$ not $4 x + 16$

Describe how the numbers $negative 7 and 1 half$ and $negative 7$ would be positioned relative to each other on a horizontal number line.

Select from the lists of choices to complete the statement.

The number

negative 7 and one half

would be positioned to the of

negative 7

on a horizontal number line because .

Point $A$ is located at $the coordinates 6 comma 3$ in the coordinate plane. Point $B$ is located $5$ units below Point $A .$

Select the quadrant in the coordinate plane that contains point $B .$

Three distributions are displayed as histograms in the following table. What is the best description of the shape of each distribution?

Select one cell per row.

What is the value of $43.7 times 0.25$

A.

$1.0925$
B.

$4.395$
C.

$10.925$
D.

$43.95$

Correcti1

Incorrect - Misplaced decimal pointi2

Incorrect - Added instead of multiplied, but correctly (for multiplication) used $3$ decimal placesi4

Incorrect - Added instead of multiplied

Which value from the set $open brace, three fourths, 1, three halves, 3 and three fourths, close brace$ is a solution to the equation $x + \frac{3}{2} = 2 \frac{1}{4}$ ?

Correct - This is the only value that makes the equation true.i2

Incorrect - This number does not make the equation true.i3

Incorrect-This number does not make the equation true.i4

Incorrect - This number does not make the equation true.

Kevin has a rectangular prism that was made up of identical cubes, with no gaps between any cubes. The following figure shows the prism and one of the cubes.

What was the total number of the cubes used to make up the prism?

Enter your answer in the space provided.

cubes

A baker made $8$ pounds of cookie dough. The baker used the dough to make several batches of cookies. The graph shows the amount of cookie dough that is needed to make different numbers of batches of cookies.

Use the information from the model to complete the statements.

Enter your answers in the spaces provided.

The number of batches of cookies the baker can make from each pound of cookie dough is .

The total number of batches of cookies the baker can make from the $8$ pounds of cookie dough made is .

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.

Drawing Box

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.

A worker has $25$ feet of ribbon to make bows. Each bow uses $2$ feet of ribbon. The worker divides $25$ by $2$ and gets $12.5$ as an answer.

What does the worker’s answer mean in this context?

Correct. In this context, $x$ represents the number of bows and $y$ represents the amount of ribbon left over.i2

Incorrect. This option is the result of switching the representations of $x$ and $y .$ i3

Incorrect. This option is the result of having $x$ represent the amount of ribbon needed and having $y$ represent the number of bows.i4

Incorrect. This option is the result of having $y$ represent the amount of ribbon needed.

The numbers $negative 1 half$ and $2 fifths$ are graphed on the number line.

Which statement correctly compares the absolute values of $negative 1 half$ and $2 fifths$ and gives the correct reasoning for the comparison?

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 $â \frac{1}{2}$ is closer to zero than $\frac{2}{5}$ 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 $â \frac{1}{2}$ is greater than the absolute value of $\frac{2}{5}$ , it incorrectly states that it is closer to zero on the number line than $\frac{2}{5}$ UNRECOGNIZED DOT DIRECTIVE .i3

Incorrect - This statement is incorrect because although it correctly states that $â \frac{1}{2}$ is further from zero than $\frac{2}{5}$ on the number line, and does not correctly compare their absolute values.

At a store, $40 percent$ of all the refrigerators are silver. There are $50$ silver refrigerators at the store.

How many refrigerators are at the store?

Enter your answer in the space provided.

refrigerators

Laura uses $3$ yards of fabric to make $2$ skirts. She uses the same amount of fabric to make each skirt.

At this rate, what is the total amount of fabric, in yards, she needs to make $6$ skirts?

Select one answer.

A.

$4$
B.

$6$
C.

$7$
D.

$9$

The diagram shows the net of a wooden chest in the shape of a rectangular prism. All dimensions are in feet.

A painter will apply stain to all the faces of the wooden chest. The calculations that the painter used to find the surface area, in square feet , of the wooden chest are shown. $\begin{matrix} 2 \frac{1}{2} \times 3 \frac{1}{2} = (2 \times 3) + (\frac{1}{2} \times \frac{1}{2}) = 6 \frac{1}{4} \times 2 = 12 \frac{1}{2} \end{matrix}$ $\begin{matrix} 2 \frac{1}{2} \times 4 \frac{1}{2} = (2 \times 4) + (\frac{1}{2} \times \frac{1}{2}) = 8 \frac{1}{4} \times 2 = 16 \frac{1}{2} \end{matrix}$ $\begin{matrix} 3 \frac{1}{2} \times 4 \frac{1}{2} = (3 \times 4) + (\frac{1}{2} \times \frac{1}{2}) = 12 \frac{1}{4} \times 2 = 24 \frac{1}{2} \end{matrix}$

The total surface area is $12 \frac{1}{2} + 16 \frac{1}{2} + 24 \frac{1}{2} = 53 \frac{1}{2}$ square feet.

What mistake was made in the calculation of the surface area of the wooden chest?

Find the correct surface area of the wooden chest.

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.

Drawing Box

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.

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

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

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

An art teacher has a jar containing $3 fourths$ pound of glitter for use by the students in a class. The glitter is being separated into portions that are each $1 tenth$ 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 $\frac{4}{3} \times \frac{10}{1} = \frac{40}{3} = 13 \frac{1}{3}$ , 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.

Drawing Box

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.

Students in a science class measured rain by writing down the depth of water in a bucket that collected the rain. The bucket was empty before the rain began to fall at a steady rate over a 6-hour period during school. After 3 hours, the water had a depth of 18 millimeters.

At what average unit rate, in millimeters per hour, did the bucket fill after rain started to fall at a steady rate?

Enter only your answer in the space provided.

The following histogram summarizes the recorded number of push-ups that a group of fitness instructors completed in a certain time period. Each interval contains possible values at the left endpoint up to but not including the right endpoint.

What is the total number of fitness instructors represented in the histogram who completed $57$ or more push-ups?

Enter your answer in the space provided.

Yvonne’s age, in years, is represented by y. Rebekah’s age is one year less than three times Yvonne’s age.

Which expression represents Rebekah’s age, in years?

Select one answer.

A.

$3 y minus 1$
B.

$1 minus 3 y$
C.

$3 open parenthesis y minus 1 closed parenthesis$
D.

$3 open parenthesis 1 minus y closed parenthesis$

To determine the correct expression, the student could have represented three times Yvonne’s age as 3y. Subtracting 1 from 3y would represent 1 less than three times Yvonne’s age. Rebekah’s age would then be represented as 3y – 1.i2

Reversed the order of the termsi3

Reversed the order of operationsi4

Reversed the order of the terms and the order of the operations

Point $K$ is located at $the coordinates 1 comma 2$ on the following coordinate plane. A square that has a perimeter of $20$ units will be drawn so that $K$ is one vertex of the square.

Which three ordered pairs could represent the location of another vertex of the square?

Select the three correct answers.

Correcti2

Correcti5

Correcti3

Added 3 to the x-coordinate and 2 to the y-coordinatei4

Incorrectly determined the length of a side to be 4

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?

Correct - the fractions $\frac{1}{6},$ $\frac{3}{8},$ and $\frac{4}{9}$ 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.

Many frames are being made to hold a number of paintings that all have a width of $18$ inches. The wood being used to make the frames is $2$ inches wide.

If the height of one of the paintings was $24$ inches, what is the total length, in inches, of $2$ -inch wood that would be needed to make the frame? Show your work and your calculations.

What is the number of square inches of wood that a frame would have if the painting had a height of $36$ inches?

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

Drawing Box

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

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

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 $x$

A machine at a company makes toy cars at a constant rate. The company received an order for toy cars that exceeded the number of toy cars that the company had in stock.

Which three pieces of information are needed to determine the amount of time it will take the machine to make enough additional toy cars to fill the order?

Select the three pieces of information that are needed.

Correct. The rate of production is a necessary piece of information.i3

Correct. The target number is a necessary piece of information.i5

Correct. The initial number is a necessary piece of information.i1

Incorrect. It is not necessary to know the cost.i4

Incorrect. It is not necessary to know the number of people running the machine.

A game designer used $9$ ounces of clay to make $24$ identical pieces for a game.

How many ounces of clay were used for each piece?

Enter your answer as a fraction in the spaces provided.

fraction bar

	Symmetric	Skewed to the Left	Skewed to the Right

This page shows questions in the Math 6 2024 public release module at MSDE. 6th Grade Math "Math 6 2024"

Icon representing a test question. 1. Math 6 2024 Release, Question 1 (6.NS.B.2) - No Calculator.

Icon representing a test question. 2. Math 6 2024 Release, Question 2 (6.EE.A.1-2) - No Calculator.

Icon representing a test question. 3. Math 6 2024 Release, Question 3 (6.NS.C.7c-1) - No Calculator.

Icon representing a test question. 4. Math 6 2024 Release, Question 4 (6.EE.B.8) - No Calculator.

Icon representing a test question. 5. Math 6 2024 Release, Question 5 (6.NS.B.3-2) - No Calculator.

Icon representing a test question. 6. Math 6 2024 Release, Question 6 (6.EE.B.6) - No Calculator.

Icon representing a test question. 7. Math 6 2024 Release, Question 7 (6.RP.A.1) - No Calculator.

Icon representing a test question. 8. Math 6 2024 Release, Question 8 (6.NS.A.1) - No Calculator.

Icon representing a test question. 9. Math 6 2024 Release, Question 9 (6.NS.B.4-2) - No Calculator.

Icon representing a test question. 10. Math 6 2024 Release, Question 10 (6.EE.A.4) - No Calculator.

Icon representing a test question. 11. Math 6 2024 Release, Question 11 (6.NS.C.6c-1) - No Calculator.

Icon representing a test question. 12. Math 6 2024 Release, Question 12 (6.NS.C.8) - No Calculator.

Icon representing a test question. 13. Math 6 2024 Release, Question 13 (6.SP.A.2) - No Calculator.

Icon representing a test question. 14. Math 6 2024 Release, Question 14 (6.NS.B.3-3) - No Calculator.

Icon representing a test question. 15. Math 6 2024 Release, Question 15 (6.EE.B.5-2) - Calculator.

Icon representing a test question. 16. Math 6 2024 Release, Question 16 (6.G.A.2-1) - Calculator.

Icon representing a test question. 17. Math 6 2024 Release, Question 17 (6.M.4, 6.EE.C.9) - Calculator.

Icon representing a test question. 18. Math 6 2024 Release, Question 18 (6.R.1a, 6.RP.A.3b) - Calculator - CR with Annotations.

Icon representing a test question. 19. Math 6 2024 Release, Question 19 (6.M.5, 6.EE.C.9) - Calculator.

Icon representing a test question. 20. Math 6 2024 Release, Question 20 (6.R.2c, 6.NS.C.7d) - Calculator.

Icon representing a test question. 21. Math 6 2024 Release, Question 21 (6.RP.A.3c-2) - Calculator.

Icon representing a test question. 22. Math 6 2024 Release, Question 22 (6.RP.A.3b) - Calculator.

Icon representing a test question. 23. Math 6 2024 Release, Question 24 (6.M.1, 6.G.A.2-2, 6.G.A.4) - Calculator - CR with Annotations.

Icon representing a test question. 24. Math 6 2024 Release, Question 25 (6.R.3a, 6.EE.A.3) - Calculator.

Icon representing a test question. 25. Math 6 2024 Release, Question 26 (6.R.2b, 6.NS.A.1) - Calculator - CR with Annotations.

Icon representing a test question. 26. Math 6 2024 Release, Question 27 (6.M.4, 6.RP.A.3b) - Calculator.

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Icon representing a test question. 28. Math 6 2024 Release, Question 29 (6.EE.A.2a) - Calculator.

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Icon representing a test question. 30. Math 6 2024 Release, Question 31 (6.R.1a, 6.RP.A.3a) - Calculator.

Icon representing a test question. 31. Math 6 2024 Release, Question 32 (6.M.1, 6.EE.B.6) - Calculator - CR with Annotations.

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Icon representing a test question. 34. Math 6 2024 Release, Question 35 (6.EE.B.7) - Calculator.

This page shows questions in the Math 6 2024 public release module at MSDE. 6th Grade Math
"Math 6 2024"