Grade 5

In the 5th grade, instructional time focuses on developing skills in the following three areas: (1) fluency with addition and subtraction of fractions as well as a developing a limited understanding of multiplying and dividing with fractions; (2) integrating decimals and operations with decimals to hundredths; and (3) developing an understanding of volume.

Below, you will find examples of the types of question and answer sets students who are operating at a Grade 5 math level in the target language should be able to understand, along with their corresponding NYS Next Generation Learning Standard.

Number and Operations in Base Ten

Example 1: NGLS Standard NY-5.NBT.3b

Which comparison is true? A 0.04 is greater than 0.14. B. 0.83 is greater than 0.92. C. 0.27 is less than 0.36. D. 0.52 is less than 0.49

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This question is asking the student to read, write, and compare decimals to hundredths. To show mastery of this skill, the student must compare two sets of decimals based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Correct Answer: C

Reproduced from: NYS Grade 5 Test Item 16, 2024

Example 2: NGLS Standard NY-5.NBT.7

Carlos walks three point six five kilometers on Saturday and one point four six kilometers on Sunday. How many total kilometers does Carlos walk on Saturday and Sunday? A. two point one nine. B two point two nine C five point zero one, D five point eleven.

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This question is asking the student to perform operations with multi-digit whole numbers and with decimals to hundredths. To show mastery of this skill, the student must add the distances walked each day with decimals to hundredths to determine that Carlos walked 5.11 kilometers total.

Correct Answer: D

Reproduced from: NYS Grade 5 Test Item 1, 2024

Number and Operations – Fractions

Example 1: NGLS Standard NY-5.NF.1

What is the value of the expression shown below? One half plus two thirds minus one fourth. A two firsts B four ninths C eleven twelfths D seventeen twelfths

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This question is asking the student to add and subtract fractions with unlike denominators. To show mastery of this skill, the student must replace given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

Correct Answer: C

Reproduced from: NYS Grade 5 Test Item 32, 2024

Example 2: NGLS Standard NY-5.NF.3

A group of 4 gold miners found 10 ounces of gold. The miners shared the gold equally. How much gold, in ounces, did each miner receive? A one fourth B four tenths C two and two tenths D two and one half

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This question is asking the student to apply and extend previous understandings of multiplication and division to multiply and divide fractions. To show mastery of this skill, the student must solve the word problem involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

Correct Answer: D

Reproduced from: NYS Grade 5 Test Item 7, 2024

Example 3: NGLS Standard NY-5.NF.7c

Steven has three cups of raisins. He shares all the raisins equally among himself and his friends. If each person gets one fourth cup of raisins, how many people, in total, get raisins? A one. B four. C seven. D twelve.

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This question is asking the student to apply and extend previous understandings of division to divide whole numbers by unit fractions. To show mastery of this skill, the student must determine that 3 divided by 1/4 equals 12.

Correct Answer: D

Reproduced from: NYS Grade 5 Test Item 10, 2024

Measurement and Data

Example 1: NGLS Standard NY-5.MD.1

The distance between two houses on a street is four hundred fifty meters. What is the distance measured in kilometers? A forty five. B four point five. C zero point forty five. D zero point zero four five.

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This question is asking the student to convert like measurement units within a given measurement system. To show mastery of this skill, the student must know that there are 1,000 meters in a kilometer, which would mean that 450 meters is the equivalent to 0.45 kilometers.

Correct Answer: C

Reproduced from: NYS Grade 5 Test Item 35, 2024

Example 2: NGLS Standard NY-5.MD.2

Ms. Torres has a box of scraps of wood. She measures the length of each scrap of wood to the nearest half inch. The results are represented on the line plot below. Description: a line plot labeled "Length of scraps of wood" is shown. It is divided into seven sections and the length is in inches. Tick mark five has zero Exes. Tick mark five and a half has one X. Tick mark six has one X. Tick mark six and a half has three Exes. Tick mark seven has two Exes. Tick mark seven and a half has zero Exes. Tick mark eight has one X. What is the approximate length, in inches, of the scraps of wood when they are placed end to end? A Nineteen and a half. B thirty three. C forty five and a half, D fifty three

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This question is asking the student to interpret data on a line plot. To show mastery of this skill, the student must understand how to read the line plot and use this information to add the total number of each length of wood scrap together in order to find the total, approximate length of the wood when placed end to end.

Correct Answer: D

Reproduced from: NYS Grade 5 Test Item 18, 2022

Originally aligned to: CCSS Standard 5.MD.B.2

Example 3: NGLS Standard NY-5.MD.5c

A diagram of a three-dimensional figure is shown below. Description: A polygon is shown that consists of a cube with a rectangular prism on the top right. The left side is eight inches tall. It is ten inches wide and two inches deep. On the right side, it is twelve inches tall. The top of the small rectangular prism is three inches wide. What is the volume, in cubic inches, of the figure? A thirty five B seventy two C one hundred eighty four D two hundred forty

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This question is asking the student to recognize volume as additive in order to solve a real world problem. To show mastery of this skill, the student must understand that the 3-dimensional figure shown is composed of two non-overlapping right rectangular prisms. By determining the volume of each prism individually and adding them together, the student will be able to determine the correct answer.

Correct Answer: C

Reproduced from: NYS Grade 5 Test Item 9, 2024

Geometry

Example 1: NGLS Standard NY-5.G.2

The line graph below shows the number of people in attendance at a baseball game at the beginning of each inning. The line graph shows the number of people per inning. At inning one there were eight hundred. Inning two had approximately one thousand one hundred. Inning three had just over one thousand. Inning four had just under one thousand one hundred, inning five had just under one thousand, inning six had one thousand. Inning seven had around nine hundred, inning eight had just under eight hundred and inning nine had six hundred. At the beginning of what inning were there approximately nine hundred people at the game? A one. B two. C five. D seven.

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This question is asking the student to solve real-world mathematical problems using the first quadrant of the coordinate plane. To show mastery of this skill, the student must interpret the given coordinate values of points in the context of the situation.

Correct Answer: D

Reproduced from: NYS Grade 5 Test Item 17, 2009 (Book 1)

Originally aligned to: Statistics and Probability Standard 4.S04 (2005 Standards)

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