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

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.

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.

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.

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.

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

Icon representing a test question. 1. Math 4 2024 Release, Question 14 (4.R.3, 4.NBT.A.3) - Calculator.

Icon representing a test question. 2. 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. 3. Math 4 2024 Release, Question 18 (4.R.1, 4.NF.A.2) - Calculator.

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

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

Icon representing a test question. 6. Math 4 2024 Release, Question 35 (4.R.2, 4.NF.C.5) - Calculator.

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