Grade 4

In the 4th grade, instructional time focuses on developing understanding in the following three areas: (1) fluency with multi-digit multiplication and division; (2) fraction equivalence and operations with fractions; and (3) analyzing and classifying geometric figures based on their properties.

Below, you will find examples of the types of question and answer sets students who are operating at a Grade 4 math level in the target language should be able to understand, along with their corresponding NYS Next Generation Learning Standard.

Operations and Algebraic Thinking

Example 1: NGLS Standard NY-4.OA.3a

A group of eighty students goes to a zoo. The price for each student to ride the bus to the zoo is three dollars. The price for each student to get into the zoo is two dollars. What is the total price for all of the students to ride the bus and get into the zoo? A: One hundred sixty dollars, B two hundred forty dollars, C four hundred dollars, D four hundred eighty dollars

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This question is asking the student to solve a multi-step word problem with whole numbers using the four operations. To show mastery of this skill, the student must recognize how to convert this word problem into an equation to solve for the total price. Using the order of operations, (80 students x $3 bus fare) + (80 students x $2 zoo entry), equals $400 total for all of the students to ride the bus and get into the zoo.

Correct Answer: C

Reproduced from: NYS Grade 4 Test Item 32, 2024

Example 2: NGLS Standard NY-4.OA.5

What is the rule for the number pattern shown below? Sixty four, thirty two, sixteen, eight… Answer A subtract eight, B divide by two, C. divide by eight, D multiply by two

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This question is asking the student to analyze a number pattern in order to determine the rule it follows. To show mastery of this skill, the student must identify that the numbers in the pattern provided are being divided by 2.

Correct Answer: B

Reproduced from: NYS Grade 4 Test Item 17, 2023

Number and Operations in Base Ten

Example 1: NGLS Standard NY-4.NBT.2b

Which number sentence correctly compares two numbers? A forty-six thousand three hundred fifteen is less than forty six thousand three hundred fifty. B Twenty nine thousand seventy three equals twenty thousand plus nine thousand plus seven hundred plus three. C ten thousand plus six thousand plus four hundred is greater than sixteen thousand four hundred ten. D eighty six thousand five hundred and two equals eighty thousand plus six thousand plus five hundred plus twenty

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This question is asking the student to read multi-digit whole numbers using number names and compare two multi-digit numbers based on meanings of the digits in each place. To show mastery of this skill, the student must read each number sentence and identify the sentence that is true.

Correct Answer: A

Reproduced from: NYS Grade 4 Test Item 24, 2018

Originally aligned to: CCSS Standard 4.NBT.A.2

Example 2: NGLS Standard NY-4.NBT.6

What is the value of one hundred two divided by six? A. sixteen B. seventeen C. ninety six, D one hundred eight

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This question is asking the student to find a whole-number quotient with a three-digit dividend and one-digit divisor, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. To show mastery of this skill, the student must use one of these strategies to determine that 102 ÷ 6 = 17.

Correct Answer: B

Reproduced from: NYS Grade 4 Test Item 16, 2024

Number and Operations – Fractions

Example 1: NGLS Standard NY-4.NF.1

$The shaded part in the model shown below represents a fraction of the whole model. Description: A model made up of four squares is shown.Two of the four squares are shaded. Which fraction is equivalent to the value represented by the shaded part in the model? A four over two B two over one C one over two D one over four$

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This question is asking the student to recognize that the fraction 2/4 is equivalent to fraction 1/2, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. To show mastery of this skill, the student must recognize that since 2 of the 4 squares shown are shaded, the correct answer is 1/2.

Correct Answer: C

Reproduced from: NYS Grade 4 Test Item 29, 2023

Example 2: NGLS Standard NY-4.NF.2

$Which list of fractions is in order from least to greatest value? A. one half, one fourth, three fourths. B one fourth, one half, three fourths. C. one fourth, three fourths, one half. D. one half, three fourths, one fourth$

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This question is asking the student to compare three fractions with different numerators and different denominators. To show mastery of this skill, the student must be able to organize fractions in the appropriate order and justify measurements of greater than, less than, or equal to.

Correct Answer: B

Reproduced from: NYS Grade 4 Test Item 9, 2021

Originally aligned to: CCSS Standard 4.NF.A.2

Measurement and Data

Example 1: NGLS Standard NY-4.MD.3

The perimeter of a square floor is one hundred twenty feet. What is the length, in feet, of each side of the floor? A twenty B thirty C forty D sixty

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This question is asking the student to apply perimeter formulas for rectangles in real world mathematical problems. To show mastery of this skill, the student must know that a square is composed of 4 sides that are equal in length and use the equation P=4a, to determine that each side of the square floor is 30 feet.

Correct Answer: B

Reproduced from: NYS Grade 4 Test Item 30, 2024

Example 2: NGLS Standard NY-4.MD.7

Ray K M divides straight angle J K L into two parts as shown below. Description: a straight line is shown that begins with point J and ends with point L. In the middle, point K shows a Ray going up to point M. To the right of the ray, which makes angle M K L, is seventy degrees. To the left of the ray, which makes angle J K M has a question mark. Which equation represents how to find the measure, in degrees, of angle J K M? A Ninety minus twenty equals blank. B ninety minus seventy equals blank. C one hundred eighty minus seventy equals blank. D one hundred eighty minus one hundred ten equals blank.

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This question is asking the student to recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. To show mastery of this skill, the student must know that a straight line represents 180 degrees, so the appropriate equation to find unknown angle JKM would be 180 - 70 = ?.

Correct Answer: C

Reproduced from: NYS Grade 4 Test Item 7, 2024

Geometry

Example 1: NGLS Standard NY-4.G.3

A figure with all equal sides is shown below. Description: a hexagon is shown. How many lines of symmetry does the figure have? A one. B two. C five. D six.

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This question is asking the student to recognize vocabulary, including a "line of symmetry." To show mastery of this skill, the student must be able to identify that the polygon shown has 6 equal lines of symmetry.

Correct Answer: D

Reproduced from: NYS Grade 4 Test Item 31, 2024

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