4th Grade Math "Math 4 2024" - Public Release

Which expression has the same value as $1,435 divided by 7$ ?

Select one answer.

Which two expressions are equivalent to $\frac{8}{12}$ ?

Select the two correct answers.

A student will prepare $20$ gift bags. Each bag will have $10$ stickers.

The student already has $50$ stickers and will buy more stickers in packages. Each package has $15$ stickers.

How many packages of stickers does the student need to buy?

Enter your answer in the space provided.

packages

Roberta has a rectangular shelf. The shelf has a length of $40$ inches and a perimeter of $104$ inches.

Which expression best represents the area, in square inches, of the shelf?

Select one answer.

Correct

Round $796,814$ to the nearest ten thousand.

Enter your answer in the space provided.

Which comparison is true?

Select one answer.

Correct i1

May have thought that the numbers are equal if the same digits are in the numbers. i2

May have confused the < and > symbols. i3

May have thought that the placement of the zero does not matter.

There are 5 motorcycles in a parking lot. The number of cars in the parking lot is 8 times as many as the number of motorcycles.

Write an equation that shows how to find the number of cars in the parking lot.

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

Mr. Reis made $5$ batches of cookies. He used $3 fourths$ cup of sugar to make each batch.

What is the total amount of sugar, in cups, Mr. Reis used to make $5$ batches of cookies?

Select one answer.

Correcti1

Multiplied the numerator and the denominator by the whole numberi2

Multiplied the denominator by the whole numberi3

Added the whole number to the numerator and the denominator

Determine whether the dashed line in each shape appears to be a line of symmetry.

Select one box per row.

Samuel had $1 and 7 eighths$ cups of milk. He used $1 and 5 eighths$ cups of milk to make biscuits.

What is the amount of milk, in cups, that Samuel had after he made biscuits?

Enter your answer as a fraction in the spaces provided.

fraction bar

Complete the following area model to represent the product of 26 and 18. Then find the final product.

Move a number into each box.

What is the decimal value of $2 and five hundredths$ ?

Enter your answer in the space provided.

A student drew a quadrilateral with one right angle. The student then divided the quadrilateral into two triangles. The student measured one angle in one of the triangles as shown in the figure.

Which solution path could the student use to find the value of $b$ without measuring the angle?

A student rounded $3872$ to the nearest hundred and to the nearest thousand. The student noticed that the results, $3900$ and $4000,$ were not equal. The student claimed that the two results will never be equal when a number is rounded to the nearest hundred and to the nearest thousand.

Which two numbers could be used to show that the student’s claim is incorrect?

Select the two correct answers.

Correcti1

May not have recognized that the results would be $43,600$ and $44,000$ i3

May not have recognized that the results would be $67,300$ and $67,000$ i4

May not have recognized that the results would be $72,400$ and $72,000$

A train museum has a toy train that goes around the entire museum. The train goes around $10$ times in $2$ hours.

A student calculated the amount of time it takes for the train to go around $1$ time. The work is shown.

The student’s work is incorrect.

Explain any errors in the student’s work.

Explain how to correct the student’s work and find the amount of time it takes for the train to go around the museum $1$ time.

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
Sample Top Score Response The student divided correctly, but $0.20$ hour is not the same as $20$ minutes. $0.20$ hour is $\frac{2}{10}$ of an hour and $20$ minutes is $\frac{1}{3}$ of an hour. Before dividing by $10,$ the student could have changed $2$ hours to $120$ minutes. $120$ minutes $Ã\cdot 10 = 12$ minutes. So it takes $12$ minutes for the train to go around the museum $1$ time.
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.

Last week, a student kept track of how long he practiced soccer each day.

The line plot shows the student’s data.

Which three questions can be answered using the information in the line plot?

Select the three correct answers.

KEYi2

KEYi5

KEYi3

Student thinks marks on line plot go in order.i4

Student thinks you can make an inference about other weeks.

The figure shows the dimensions of a rectangular floor. The two openings represent doors. Each door is $3$ feet wide.

A contractor will buy baseboards to place around the entire floor, except for the doors. Each baseboard is $8$ feet long and costs $$11$

Find the total cost of the baseboards the contractor needs to buy for the room.

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.

A student used these models to compare the fractions $\frac{7}{12}$ and $\frac{6}{8} .$ The student incorrectly claimed that $\frac{7}{12} > \frac{6}{8}$ because more sections are shaded in the model that represents the fraction $\frac{7}{12}$ than in the model that represents the fraction $\frac{6}{8} .$

$The figure shows the expression, seven twelfths, is greater than, six eighths, under two rectangular models of equal size. The model above the fraction seven twelfths, is divided into 12 equal parts, with 7 parts shay did, and 5 parts un shay did. The model above the fraction six eighths, is divided into 8 equal parts, with 6 parts shay did, and 2 parts un shay did.$

Explain why the student’s claim is incorrect.

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

The claim is incorrect because the student only compared the . The student should have compared the number of and the in each model.

The diagram shows angle $A C B .$

Which statement is true about angle $A C B ?$

Correcti2

Misinterpretation of $27$ degreesi3

Misinterpretation of $27$ degreesi4

Misinterpretation of $27$ degrees

What is the value of $\frac{3}{10} + \frac{8}{100}$ ?

Enter your answer as a fraction in the spaces provided.

fraction bar

Which two comparisons are true?

Select the two correct answers.

Correcti5

Correcti2

May have not considered the digits in the hundred thousands placei3

May have thought that the digits in the hundreds and ones place could be interchangedi4

May have not considered the digits in the hundreds place

What is the value of 4 and one fourth minus 1 and 3 fourths?

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

Four problems are given in the table. Identify whether $30 times 40$ could be used to solve each problem.

Select only one box per row.

Problem	Could be solved using $30 times 40$	Could not be solved using $30 times 40$
One box has $30$ pencils. Another box has $40$ pencils. How many pencils are in the boxes in all?
A classroom has $30$ books. The number of pages in the books is $40$ times as many as the number of books. How many pages are in the books?
One elementary school has $30$ teachers. There are $40$ more teachers at a middle school than the elementary school. How many teachers are at the middle school?
There are $30$ employees at a store. The number of hours the employees worked this week is $40$ times as many as the number of employees. How many hours did the employees work this week?

Each model shown represents one whole and each model is partitioned into equal parts.

Complete the statement to explain what the models show.

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

The shaded parts of the models show that the fraction is equivalent to the fraction because .

This line plot shows the weights, in pounds, of different objects in a student’s backpack.

What is the difference, in pounds, between the greatest weight and the least weight?

Enter your answer as a fraction in the spaces provided.

fraction bar

A baker will make $3$ pies. The baker needs $1 fourth$ teaspoon of salt for each pie.

Select parts of one of the models to represent the fraction of a teaspoon of salt the baker needs for $3$ pies.

In the following number pattern, the first term is 3. Use the rule “Add 7” to find the next three terms in the pattern.

Enter your answers in the three spaces provided.

$3,$ $,$ $,$

What is the value of the expression?

$5,217 minus 3,146$

Enter your answer in the space provided.

There are six different pies left over after a party. Each of the pies has a fractional amount left at the end of the party. The line plot shows the fractions of pies left over.

$The figure shows a line plot with five evenly spaced tick marks. From left to right, the tick marks are labeled, 0, one eighth, one fourth, three eighths, and one half. The fraction of each of six pies left over is indicated, with an X graphed at the following positions: two at one eighth, one at three eighths, and three at one half.$

Each person who attended the party will receive an equal amount of the leftover pie.

Which piece of information is needed to determine how much pie each person should receive?

Correct i1

Did not recognize that this information is unnecessary i2

Did not recognize that this information is unnecessary i3

Did not recognize that this information is unnecessary

A teacher with $25$ students needs to prepare $40$ one-page worksheets for each student. Each package of paper has $500$ pages. The teacher thinks that $2$ packages of paper are needed.

Which two steps are part of a solution path to show why the teacher’s thinking is correct?

Select the two correct answers.

An athlete needs to exercise $3 and five tenths$ hours each week.

The athlete exercised $\frac{6}{10}$ hour on Sunday.

The athlete exercised $\frac{3}{10}$ hour on Monday.

The athlete exercised $4 tenths$ hour each on Tuesday, Wednesday, and Thursday.

Create a solution path to find the time that the athlete needs to exercise the rest of the week.

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.

The figure represents a rectangular floor. A custodian is installing tiles on the floor. Each tile covers $2$ square feet of area.

Which steps should the custodian take to find the number of tiles needed?

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

First, the custodian should find the value of .

Next, the custodian should .

A model is shown.

Explain how the model could be used to find the result of $54 times 78.$ Then find the result of $54 times 78.$

Enter your answer and your 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 student added $\frac{3}{10}$ and $\frac{2}{100}$ and got a result of $\frac{5}{100}$ . The student’s work is shown.

Step $1$ (replace $\frac{3}{10}$ with an equivalent fraction): $\frac{3}{10} + \frac{2}{100} = \frac{3}{100} + \frac{2}{100}$

Step $2$ (combine fractions) $: \frac{3}{100} + \frac{2}{100} = \frac{3 + 2}{100}$

Step $3$ (add numerators) $: \frac{3 + 2}{100} = \frac{5}{100}$

Which statement is true about the student’s work and answer?

Correcti1

May have thought that the work and answer are correct.i2

May have thought that the common denominator is found by adding the denominators.i4

May have thought that the common denominators should be added.

Shape	Appears to Be a Line of Symmetry	Does Not Appear to Be a Line of Symmetry

This page shows questions in the Math 4 2024 public release module at MSDE. 4th Grade Math "Math 4 2024"

Icon representing a test question. 1. Math 4 2024 Release, Question 1 (4.NBT.B.6) - No Calculator.

Icon representing a test question. 2. Math 4 2024 Release, Question 2 (4.NF.B.3b) - No Calculator.

Icon representing a test question. 3. Math 4 2024 Release, Question 3 (4.OA.A.3-1) - No Calculator.

Icon representing a test question. 4. Math 4 2024 Release, Question 4 (4.MD.A.3) - No Calculator.

Icon representing a test question. 5. Math 4 2024 Release, Question 5 (4.NBT.A.3) - No Calculator.

Icon representing a test question. 6. Math 4 2024 Release, Question 6 (4.NF.C.7) - No Calculator.

Icon representing a test question. 7. Math 4 2024 Release, Question 7 (4.OA.A.1-2) - No Calculator.

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

Icon representing a test question. 9. Math 4 2024 Release, Question 9 (4.G.A.3) - No Calculator.

Icon representing a test question. 10. Math 4 2024 Release, Question 10 (4.NF.B.3d) - No Calculator.

Icon representing a test question. 11. Math 4 2024 Release, Question 11 (4.NBT.B.5-2) - No Calculator.

Icon representing a test question. 12. Math 4 2024 Release, Question 12 (4.NF.C.6) - No Calculator.

Icon representing a test question. 13. Math 4 2024 Release, Question 13 (4.M.3, 4.MD.C.7) - Calculator.

Icon representing a test question. 14. Math 4 2024 Release, Question 14 (4.R.3, 4.NBT.A.3) - Calculator.

Icon representing a test question. 15. Math 4 2024 Release, Question 15 (4.R.2, 4.NF.C.6, 4.MD.A.2) - Calculator - CR with Annotations.

Icon representing a test question. 16. Math 4 2024 Release, Question 16 (4.M.1, 4.MD.B.4) - Calculator.

Icon representing a test question. 17. Math 4 2024 Release, Question 17 (4.M.4, 4.OA.A.3-2, 4.MD.A.3) - Calculator - CR with Annotations.

Icon representing a test question. 18. Math 4 2024 Release, Question 18 (4.R.1, 4.NF.A.2) - Calculator.

Icon representing a test question. 19. Math 4 2024 Release, Question 19 (4.MD.C.5b) - No Calculator.

Icon representing a test question. 20. Math 4 2024 Release, Question 20 (4.NF.C.5) - No Calculator.

Icon representing a test question. 21. Math 4 2024 Release, Question 21 (4.NBT.A.2) - No Calculator.

Icon representing a test question. 22. Math 4 2024 Release, Question 22 (4.NF.B.3c) - No Calculator.

Icon representing a test question. 23. Math 4 2024 Release, Question 23 (4.OA.A.2) - No Calculator.

Icon representing a test question. 24. Math 4 2024 Release, Question 24 (4.NF.A.1) - No Calculator.

Icon representing a test question. 25. Math 4 2024 Release, Question 25 (4.MD.B.4) - No Calculator.

Icon representing a test question. 26. Math 4 2024 Release, Question 26 (4.NF.B.4a) - No Calculator.

Icon representing a test question. 27. Math 4 2024 Release, Question 27 (4.OA.C.5) - No Calculator.

Icon representing a test question. 28. Math 4 2024 Release, Question 29 (4.NBT.B.4-2) - No Calculator.

Icon representing a test question. 29. Math 4 2024 Release, Question 30 (4.M.2, 4.MD.B.4) - Calculator.

Icon representing a test question. 30. Math 4 2024 Release, Question 31 (4.R.4, 4.OA.A.3-2) - Calculator.

Icon representing a test question. 31. Math 4 2024 Release, Question 32 (4.M.5, 4.NF.B.3d, 4.NF.B.4c) - Calculator - CR with Annotations.

Icon representing a test question. 32. Math 4 2024 Release, Question 33 (4.M.3, 4.MD.A.3) - Calculator.

Icon representing a test question. 33. Math 4 2024 Release, Question 34 (4.R.1, 4.NBT.B.5-1) - Calculator - CR with Annotations.

Icon representing a test question. 34. Math 4 2024 Release, Question 35 (4.R.2, 4.NF.C.5) - Calculator.

This page shows questions in the Math 4 2024 public release module at MSDE. 4th Grade Math
"Math 4 2024"