5th Grade Math "Math 5 2024" - Public Release

The following figure is made up of two rectangular prisms with the same width of $5$ centimeters. Other dimensions of the prisms are given in centimeters.

What is the volume, in cubic centimeters , of the figure?

Enter your answer in the space provided.

cubic centimeters

What is the value of $\frac{5}{7} - \frac{1}{3} ?$

Enter your answer as a fraction in the spaces provided.

fraction bar

A number is shown in expanded form.

$3 \times 10 + 6 \times 1 + 8 \times \frac{1}{1, 000}$

What is this number in standard form?

Enter your answer in the space provided.

Tom travels $3 and two thirds$ miles to school every day. Sara travels $\frac{3}{5}$ of Tom’s distance.

How many miles does Sara travel to school?

Correcti2

Subtracted $\frac{3}{5}$ rather than multipliedi3

Multiplied $\frac{2}{3}$ by $\frac{3}{5}$ and then kept the $3$ in fronti4

Divided $3 \frac{2}{3}$ by $\frac{3}{5}$

What is the value of the following expression? $3,235 divided by 20$

Enter the quotient and the remainder in the spaces provided. If there is no remainder, enter $0$ in the space provided for the remainder.

Quotient:

Remainder:

Which two equations are correct?

Select the two correct answers.

Correcti5

Correcti1

Calculated quotient as $\frac{1}{a} \div b = \frac{b}{a}$ i2

Calculated quotient as $\frac{1}{a} \div b = \frac{b}{a}$ i4

Calculated quotient as $\frac{1}{a} \div b = \frac{a}{b}$

Match each of the following expressions to the correct description in the table.

Move each expression into a box.

5 + 7 \times 8

(5 + 7) \times 8

5 \times (7 + 8)

5 \times 7 + 8

$5$ more than the product of $7$ and $8$
$8$ more than the product of $5$ and $7$
$5$ times the sum of $7$ and $8$
$8$ times the sum of $5$ and $7$

A student started a project using a pencil with a length of 7 and one half inches.

After the student completed the project, the pencil had a length of 5 and 7 eighths inches.

How much shorter, in inches, was the pencil after the student completed the project than when the student started the project?

Enter your answer in the space provided. Enter only your answer.

What is the value of the following expression?

$985 times 23$

Select one answer.

A.

$4,925$
B.

$10,345$
C.

$22,655$
D.

$23,555$

Correcti1

Student placed the second partial product starting in the ones place instead of the tens place.i2

Student did not add any of the numbers that were regrouped.i4

Student had an error in multiplying 9 x 3, getting 36, then added the 2 that was regrouped resulting in 3855 in the first partial product.

Monica has $4$ boxes to place in an empty carton.

The mass of each box is $4.5$ kilograms.

The mass of the carton is $500$ grams .

What is the total mass, in grams, of the carton and the $4$ boxes?

Enter your answer in the space provided.

grams

Three ordered pairs are shown.ordered pair 3, 5. Ordered pair 6, 4. Ordered pair 0, 2.

Plot three points on the coordinate plane to show the locations represented by these ordered pairs.

Select the places on the coordinate plane to plot the points.

There are $18$ students in Ms. Avila’s reading class. Ms. Avila will assign an equal number of pages for each student to read aloud from a book that contains a total of $45$ pages.

What is the total number of pages that each student will read aloud?

Select one answer.

A.

$2 fifths$
B.

$2 and 1 half$
C.

$27$
D.

$63$

Correcti1

Divided 18 by 45i3

Subtracted instead of dividingi4

Added instead of dividing

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?

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

Daniel used plastic bricks to build $200$ figures in $5$ hours.

He built $60$ figures during the first hour and $50$ figures during the second hour.

During the first two hours, he used $3$ bricks to build each figure.

During each additional hour, Daniel used $4$ bricks to build each figure.

Which three questions can be answered using the given information?

Select the three correct answers.

Correcti3

Correcti5

Correcti2

May not have recognized that it is necessary to know the number of figures Daniel built during the fifth hour to answer this questioni4

May not have recognized that it is necessary to know how many of those $90$ figures were built during each of the following three hours

A student performed the division problems shown.

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

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.

A teacher is planning a lesson that includes some activities to be completed at a computer.

There are $18$ students in the classroom.

The students will be split up in groups of the same size.

Each group will need to use the computer for $1 half$ hour.

Which additional piece of information is needed to determine how long the computer will need to be in the classroom?

Correcti2

May have thought that the number of activities is needed for the calculationi3

May have not realized that the information is already giveni4

May have not realized that the the size of each group is not given

Kasey will make as many servings of trail mix as possible with these ingredients: walnuts, pretzels, and apricots.

Each serving will have $1 sixth$ cup of walnuts, $1 fourth$ cup of pretzels, and $1 eighth$ cup of apricots.

Kasey has $10$ cups of walnuts, $12$ cups of pretzels, and $9$ cups of apricots with which to make the trail mix.

Determine how many servings Kasey will make.

Determine which ingredient Kasey will completely use, and determine how much of the other ingredients she will have left over.

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

NOTE TO ETS Editorial:

In the scoring rubric there is an incorrect "1/6" in the second-to-last equation. The paper and online PT key documents have the correct equation, "48 x 1/8 = 6". The rubric in this item will be corrected after the Spring 2022 Practice Test is no longer active.

Holistic Rubric for 4-Point Modeling Constructed Response Items
Points	Sample Characteristics
4 Points	A four-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 essentially 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.
3 Points	A three-point response provides evidence of the modeling process used to solve a real-world problem. The response may: identify most of the problem that needs to be solved. determine most of the 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 with minor flaws. evaluate or validate a partial or complete solution and show how to improve or refine the solution, but the improvement or refinement may include minor flaws.
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.

A student found the value of the expression $10 and 1 fourth minus 6 and 7 eighths$

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?

Correcti1 i2 i3

$12 \frac{1}{2} - 4 \frac{7}{10} = ?$

Select one answer.

A rectangular prism has a length of $20$ inches, a width of $10$ inches, and a height of $12$ inches.

What is the volume, in cubic inches, of the rectangular prism?

Enter your answer in the space provided.

cubic inches

The following table shows the corresponding terms in two patterns. Both patterns continue to increase using the same addition rule.

Pattern G	$3$	$7$	$11$	$15$	$19$
Pattern H	$9$	$13$	$17$	$21$	$25$

What is the relationship between corresponding terms in the two patterns?

Select from the lists of choices to complete the statement.

Each term in pattern H is the corresponding term in pattern G.

A package contains $1 third$ pound of deli meat. The meat will be divided evenly among $4$ sandwiches.

How much deli meat, in pounds, will be in each sandwich?

Enter your answer as a fraction in the spaces provided.

fraction bar

Complete each statement with an appropriate comparison symbol.

Drag and drop a symbol into each box to make the comparison true.

<

>

=

$15.374$ $15.347$

$25.502$ $25.52$

$35.716$ $35.671$

$45.280$ $45.28$

The given model can be used to show the solution to a word problem. The shaded counters in the model represent the solution to the word problem.

Which word problem can be modeled by the given model?

Correcti1

Models $12 \times \frac{3}{4}$ i2

Models $16 \times \frac{4}{3}$ i4

Models $12 \times \frac{4}{3}$

The amount of milk needed for each of 5 recipes is shown on the line plot.

What is the total amount of milk needed for the recipes?

Enter your answer in the space provided. Enter only your answer.

A teacher assigned a project to $5$ students. Each student used $3.75$ square feet of paper for the project.

What was the total amount of paper used for the project?

Select one answer.

Correcti1

divided 3.75/5i2

subtracted 5-3.75i3

added 5+3.75

What is the value of 7 divided by 1 fifth?

Enter your answer in the space provided. Enter only your answer.

Which digit in the number $888.888$ has a value that is $10$ times as great as the digit $8$ in the number $456.789 ?$

Select the correct digit.

Which set of statements is true?

Select one answer.

Correcti2

Selected a set in which the 1st and 3rd statements are false.i3

Selected a set in which the 1st (unless the other definition of a trapezoid is used) and 2nd statements are false.i4

Selected a set in which the 2nd and 3rd statements are false.

A contractor measured the length and the width of two rectangular pieces of land.

The two pieces of land are adjacent and share the same width of $17$ yards.

The first piece of land has a length of $32 and 1 third$ yards.

The second piece of land has a length of $25 and 1 fourth$ yards.

Which steps should the contractor use to determine the area, in square yards, of the two pieces of land altogether?

Correcti1 i2 i4

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.

Bernard stacked two gift boxes that are each in the shape of a right rectangular prism. The dimensions of the resulting shape are shown.

What is the total volume, in cubic inches, of the gift boxes?

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

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.

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

The artist paints $3 fifths$ of the squares in red, then draws golden circles on $1 third$ 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.

Which statement is true about the model the artist drew?

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

During a $5$ ‑day paper recycling drive, the students in a classroom collected $12.4$ pounds of paper each day for $4$ days and $8.39$ pounds of paper on the fifth day.

Which steps can be used to find the total number of pounds of paper the students collected for the recycling drive?

Correcti2

Multiplied by the number of days the drive lastedi3

Added before multiplyingi4

Added before multiplying and multiplied by the number of days the drive lasted

This page shows questions in the Math 5 2024 public release module at MSDE. 5th Grade Math "Math 5 2024"

Icon representing a test question. 1. Math 5 2024 Release, Question 1 (5.MD.C.5c) - No Calculator.

Icon representing a test question. 2. Math 5 2024 Release, Question 2 (5.NF.A.1-2) - No Calculator.

Icon representing a test question. 3. Math 5 2024 Release, Question 3 (5.NBT.A.3a) - No Calculator.

Icon representing a test question. 4. Math 5 2024 Release, Question 4 (5.NF.B.6) - No Calculator.

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

Icon representing a test question. 6. Math 5 2024 Release, Question 6 (5.NF.B.7a) - No Calculator.

Icon representing a test question. 7. Math 5 2024 Release, Question 7 (5.OA.A.2) - No Calculator.

Icon representing a test question. 8. Math 5 2024 Release, Question 8 (5.NF.A.2) - No Calculator.

Icon representing a test question. 9. Math 5 2024 Release, Question 9 (5.NBT.B.5) - No Calculator.

Icon representing a test question. 10. Math 5 2024 Release, Question 10 (5.MD.A.1) - No Calculator.

Icon representing a test question. 11. Math 5 2024 Release, Question 11 (5.G.A.1/5.G.A.2) - No Calculator.

Icon representing a test question. 12. Math 5 2024 Release, Question 12 (5.NF.B.3) - No Calculator.

Icon representing a test question. 13. Math 5 2024 Release, Question 13 (5.R.4, 5.MD.A.1, 5.NBT.B.7-1) - Calculator.

Icon representing a test question. 14. Math 5 2024 Release, Question 14 (5.M.1, 5.OA.A.2) - Calculator.

Icon representing a test question. 15. Math 5 2024 Release, Question 15 (5.R.3, 5.NBT.B.6) - Calculator - CR with Annotations.

Icon representing a test question. 16. Math 5 2024 Release, Question 16 (5.M.2, 5.NF.B.4a) - Calculator.

Icon representing a test question. 17. Math 5 2024 Release, Question 17 (5.M.5, 5.NF.B.7c) - Calculator - CR with Annotations.

Icon representing a test question. 18. Math 5 2024 Release, Question 18 (5.R.2, 5.OA.A.1) - Calculator.

Icon representing a test question. 19. Math 5 2024 Release, Question 19 (5.NF.A.1-4) - No Calculator.

Icon representing a test question. 20. Math 5 2024 Release, Question 20 (5.MD.C.5b) - No Calculator.

Icon representing a test question. 21. Math 5 2024 Release, Question 21 (5.OA.B.3) - No Calculator.

Icon representing a test question. 22. Math 5 2024 Release, Question 22 (5.NF.B.7c) - No Calculator.

Icon representing a test question. 23. Math 5 2024 Release, Question 23 (5.NBT.A.3b) - No Calculator.

Icon representing a test question. 24. Math 5 2024 Release, Question 24 (5.NF.B.4a) - No Calculator.

Icon representing a test question. 25. Math 5 2024 Release, Question 25 (5.MD.B.2) - No Calculator.

Icon representing a test question. 26. Math 5 2024 Release, Question 26 (5.NBT.B.7-3) - No Calculator.

Icon representing a test question. 27. Math 5 2024 Release, Question 27 (5.NF.B.7b) - No Calculator.

Icon representing a test question. 28. Math 5 2024 Release, Question 28 (5.NBT.A.1) - No Calculator.

Icon representing a test question. 29. Math 5 2024 Release, Question 29 (5.G.B.3) - No Calculator.

Icon representing a test question. 30. Math 5 2024 Release, Question 30 (5.M.3, 5.NF.B.4b) - Calculator.

Icon representing a test question. 31. Math 5 2024 Release, Question 31 (5.R.3, 5.G.B.4) - Calculator.

Icon representing a test question. 32. Math 5 2024 Release, Question 32 (5.M.4, 5.MD.C.5c) - Calculator - CR with Annotations.

Icon representing a test question. 33. Math 5 2024 Release, Question 33 (5.R.1, 5.NF.B.4a, 5.NF.B.5a) - Calculator.

Icon representing a test question. 34. Math 5 2024 Release, Question 34 (5.R.4, 5.OA.A.1) - Calculator - CR with Annotations.

This page shows questions in the Math 5 2024 public release module at MSDE. 5th Grade Math
"Math 5 2024"