Grade 6

Expressions, Equations, and Inequalities

In the 6th grade, instructional time focuses on developing skills in the following five areas: (1) multiplication and division involving ratio and rate; (2) more advanced division of fractions as well as understanding of positive and negative rational numbers; (3) writing, interpreting, and using expressions and equations; (4) further exploration of area, surface area, and volume; and (5) an introduction to the basics of probabilities and statistical thinking.

Below, you will find examples of the types of question and answer sets students who are operating at a Grade 6 math level in the target language should be able to understand, along with their corresponding NYS Next Generation Learning Standard.

Ratios and Proportional Relationships

Example 1: NGLS Standard NY-6.RP.1

Claire has six large envelopes and eleven small envelopes. What is the ratio of large envelopes to the total number of envelopes? A five to eleven. B six to eleven. C six to seventeen. D eleven to seventeen

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This question is checking the student's understanding of ratio concepts and ratio reasoning to solve problems. To show mastery of this skill, the student must use ratio language to describe a ratio relationship between the two quantities, by relating the number of large envelopes to the total number of envelopes.

Correct Answer: C

Reproduced from: NYS Grade 6 Test Item 5, 2022

Originally aligned to: CCSS Standard 6.RP.A.1

Example 2: NGLS Standards NY-6.RP.3b & NY-6.RP.3d

The ratio of number of yards to number of miles is three thousand five hundred twenty to two. How many yards are in five miles? A one thousand seven hundred sixty. B five thousand two hundred eighty. C seven thousand forty. D eight thousand eight hundred

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This question is asking the student to use ratio reasoning to convert measurement units and solve a real-world mathematical problem. To show mastery of this skill, the student must multiply the given quantity of yards by 2.5 in order to reach the appropriate ratio of yards to 5 miles.

Correct Answer: D

Reproduced from: NYS Grade 6 Test Item 34, 2023

The Number System

Example 1: NGLS Standard NY-6.NS.1

Ben purchases one and one quarter pounds of nuts and puts them into bags. Each bag holds one eighth pound of nuts. He uses all the nuts to fill each bag completely. How many bags does Ben fill with nuts? A five thirty seconds. B one and one eighth. C two. D ten.

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This question is asking the student to solve word problems involving division of fractions by fractions. To show mastery of this skill, the student must divide 1 1/4 pounds by 1/8 in order to solve for the correct answer.

Correct Answer: D

Reproduced from: NYS Grade 6 Test Item 15, 2024

Example 2: NGLS Standard NY-6.NS.6a

Which expression represents the opposite of the number negative two and a half ? A. Negative open parentheses two and a half closed parentheses. B Negative open parentheses negative two and a half closed parentheses. C Negative two open parentheses one half closed parentheses. D Two times open parentheses negative one half closed parentheses

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This question is asking the student to recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line. To show mastery of this skill, the student must know that a negative times a negative equals a positive.

Correct Answer: B

Reproduced from: NYS Grade 6 Test Item 18, 2024

Expressions, Equations, and Inequalities

Example 1: NGLS Standard NY-6.EE.3

Which expression is equivalent to four open parentheses three M plus one closed parentheses? A seven M plus one. B seven M plus five. C. Twelve M plus one. D Twelve M plus four

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This question is asking the student to apply the properties of operations to generate equivalent expressions. To show mastery of this skill, the student must apply the distributive property to the expression 4(3m + 1) to produce the equivalent expression 12m + 4.

Correct Answer: D

Reproduced from: NYS Grade 6 Test Item 35, 2023

Example 2: NGLS Standard NY-6.EE.5

Which value of M makes the inequality true? Three M minus four is less than eleven. Answer choices A four. B five. C six. D seven

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This question is asking the student to reason about and solve one-variable equations and inequalities. To show mastery of this skill, the student must use substitution to determine which of the answer choices would make the inequality true.

Correct Answer: A

Reproduced from: NYS Grade 6 Test Item 1, 2022

Originally aligned to: CCSS Standard 6.EE.B.5

Example 3: NGLS Standard NY-6.EE.9

Joe walks on a treadmill at a constant rate. The equation below describes the relationship between T, the time he walks in hours, and D, the distance he walks in miles. D equals four T. Which graph represents the relationship between the amount of time Joe walks and the distance he walks? Each line graph shows the relationship between distance in miles (y-axis) and time in hours (x-axis). A. shows a line graph with a highlighted point at (1,4) and (2,8). B shows a line graph with a highlighted point at (4,1) and (8,2). C shows a line graph with a highlighted point at (4,4) and (8,8). D shows a line graph with a highlighted point at (4, 4) and (4,8)

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This question is asking the student to analyze the relationship between dependent and independent variables using graphs, and relate these to a given equation. To show mastery of this skill, the student must identify t as the independent variable and d as the dependent variable. They must then use this information to identify which graph represents the relationship between the amount of time, t, Joe walks and the distance, d, he walks.

Correct Answer: A

Reproduced from: NYS Grade 6 Test Item 12, 2021

Originally aligned to: CCSS Standard 6.EE.C.9

Geometry

Example 1: NGLS Standard NY-6.G.1

The grid shown below is in the shape of a rectangle. It is 8 units high by 6 units wide. A line is drawn diagonally across the grid, dividing it in half. One of the two triangles created is shaded. What is the area, in square units, of the shaded part of the rectangle? A, fourteen. B twenty four. C twenty eight. D forty eight

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This question is asking the student to solve a mathematical problem involving area. To show mastery of this skill, the student must first find the area of the entire rectangle and then understand that by dividing that number in half, they will be able to find the area of the shaded triangle.

Correct Answer: B

Reproduced from: NYS Grade 6 Test Item 3, 2019

Originally aligned to: CCSS Standard 6.G.A.1

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

Jose builds a skateboard ramp in the shape of a right triangular prism. The net below shows the dimensions of each part of the ramp. The net consists of two triangles and three rectangles. One triangle is shown at the top left, with a base of 6 ft and a height of 2.5 ft. The hypotenuse of this triangle is 6.5 ft. Below this triangle, a rectangle is attached, which is the base of the prism. This rectangle has a length of 6 ft and a width of 4 ft. To the right of the base rectangle, another rectangle is attached, representing one of the side faces. This rectangle has a length of 6.5 ft and a width of 4 ft. Below the base rectangle, another triangle is shown, identical to the top one, with a base of 6 ft, a height of 2.5 ft, and a hypotenuse of 6.5 ft. There is also a hidden rectangle that would connect the 2.5 ft side of the triangles to the 4 ft height of the prism, with dimensions 2.5 ft by 4 ft. What is the surface area, in square feet, of the ramp? A. 90 B, 75. C. 51. D. 44

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This question is asking the student to solve a real-world problem involving surface area. To show mastery of this skill, the student must use the find the surface area of the non-overlapping rectangles and triangles represented in the image and then add them together to find the total surface area of the ramp.

Correct Answer: B

Reproduced from: NYS Grade 6 Test Item 32, 2024

Statistics and Probability

Example 1: NGLS Standard NY-6.SP.5c

The list below shows the heights, in meters, of five different buildings. 180, 170, 120, 180, 160 What is the median height, in meters, of the buildings? A. 162 B. 165 C. 170 D. 180

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This question is asking the student to summarize quantitative data sets in relation to their context. To show mastery of this skill, the student must understand the the "median" is the middle value in a set of data, and use this knowledge to determine the middle height of the listed buildings.

Correct Answer: C

Reproduced from: NYS Grade 6 Test Item 11, 2010 (Book 1)

Originally aligned to: Statistics and Probability Standard 6.S05 (2005 Standards)

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