Grade 7

Expressions, Equations, and Inequalities

In the 7th grade, instructional time focuses on developing understanding in the following three areas: (1) applying concepts of proportional relationships; (2) continued use of operations with rational numbers as well as formulating expressions and working with linear equations; and (3) beginning informal work with drawing inferences based on sample sets.

Below, you will find examples of the types of question and answer sets students who are operating at a Grade 7 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-7.RP.2c

The table shown below represents a proportional relationship between x and y. There are 2 columns labeled X and Y. In the X column, the quantities are 9, 13, 18, 21. In the Y column, the quantities are 2.25, 3.25, 4.25, 5.25. Which equation represents this proportional relationship? A. y = x. B. y = 4x. C. y = one fourth times x. D. y = nine fourths times x.

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This question is asking the student to recognize proportional relationships between quantities. To show mastery of this skill, the student must use the information provided in the table to determine which of the provided equations represents a proportional relationship between x and y.

Correct Answer: C

Reproduced from: NYS Grade 7 Test Item 21, 2024

Example 2: NGLS Standard NY-7.RP.3

A seventh grade class sells gift cards as a fundraiser for the school library. Each gift card sells for $15.00. The library gets 35% of the money earned for each gift card sold. How much money does the library get if the class sells 500 gift cards? A. $1,167.00. B. $1,429.00. C. $2,625.00. D. $4,875.00

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This question is asking the student to analyze proportional relationships and use them to solve real-world problems. To show mastery of this skill, the student must solve the multi-step percent problem by first determining the total amount of money made in the sale (500 gift cards times $15) and then multiplying that number by 35%.

Correct Answer: C

Reproduced from: NYS Grade 7 Test Item 29, 2024

The Number System

Example 1: NGLS Standard NY-7.NS.1c

On average, ocean temperatures around the world range from to negative 2 degrees Celsius to 32 degrees Celsius. What is the difference between the two ocean temperatures? A. negative −34 degrees Celsius. B. 34 degrees Celsius. C. negative 30 degrees Celsius. D. 30 degrees Celsius

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This question is asking the student to apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. To show mastery of this skill, the student must show that the distance between two rational numbers on the number line is the absolute value of their difference.

Correct Answer: B

Reproduced from: NYS Grade 7 Test Item 5, 2024

Example 2: NGLS.Math.Content.NY-7.NS.1d

Negative one point five plus two fifths plus open parentheses negative seven closed parentheses plus two point six. Answer choices A. open parentheses negative five point five plus two point six closed parentheses plus two fifths. B. open parentheses negative eight point five plus two point six closed parentheses plus two fifths. C. open parentheses negative one fifth plus two fifths closed parentheses plus open parentheses negative four point four closed parentheses. D. open parentheses negative one fifth plus two fifths closed parentheses plus open parentheses negative nine point six.

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This question is asking the student to apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. To show mastery of this skill, the student must apply properties of operations as strategies to add the given negative rational numbers together as well as group the decimals.

Correct Answer: B

Reproduced from: NYS Grade 7 Test Item 5, 2023

Expressions, Equations, and Inequalities

Example 1: NGLS Standard NY-7.EE.1

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This question is asking the student to use properties of operations to generate equivalent expressions. To show mastery of this skill, the student must use the distributive property and then add and subtract like variables and constants to determine the appropriate answer.

Correct Answer: B

Reproduced from: NYS Grade 7 Test Item 13, 2024

Example 2: NGLS Standard NY-7.EE.3

An equation is shown below. Two times open parentheses x minus nine closed parentheses equals nine divided by open parentheses negative one third closed parentheses. What value of 𝑥 makes the equation true? A. negative nine point zero. B. negative four point five. C. three point zero. D. seven point five.

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This question is asking the student to solve multi-step mathematical problems posed with positive and negative rational numbers (including whole numbers and fractions), using tools strategically. To show mastery of this skill, the student must apply properties of operations to simplify the given equation and then assess the reasonableness of the provided possibilities using mental computation and estimation strategies.

Correct Answer: B

Reproduced from: NYS Grade 7 Test Item 26, 2021

Originally aligned to: CCSS Standard 7.EE.B.3

Geometry

Example 1: NGLS Standard NY-7.G.1

On a map, two cities are 2 point 8 inches apart. The map has a scale of 1 inch to 25 miles. How far apart, in inches, would the same two cities be on a map that has a scale of 1 inch to 40 miles? A. 1 point 20. B. 1 point 60. C. 1 point 75. D. 1 point 80

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This question is asking the student to Solve problems involving scale drawings of geometric figures, including reproducing a scale drawing at a different scale. To show mastery of this skill, the student must first determine the distance between the 2 cities in miles and then use that information to determine that the same two cities on the new map would be spaced 1.75 inches apart, which is Answer C.

Correct Answer: C

Reproduced from: NYS Grade 7 Test Item 33, 2022

Originally aligned to: CCSS Standard 7.G.A.1

Example 2: NGLS Standard NY-7.G.1

The scale drawing of a field in the shape of a triangle is shown below. The graph shows a 2D coordinate plane with x and y axes ranging from 0 to 10. A triangle is drawn on this plane with vertices at approximately (2,2), (4,7), and (9,2). A box labeled "KEY" contains a horizontal line segment that is the width of one of the grid squares on the drawing and the text "equals two meters," indicating the scale. What is the actual area, in square meters, of this field? A. 8.75. B. 17.5. C. 35. D. 70

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This question is asking the student to solve problems involving scale drawings of geometric figures, including computing actual areas from a scale drawing. To show mastery of this skill, the student must use the given information to determine that the actual area of the triangular field is 70 square meters.

Correct Answer: D

Reproduced from: NYS Grade 7 Test Item 32, 2017

Originally aligned to: CCSS Standard 7.G.A.1

Statistics and Probability

Example 1: NGLS Standard NY-7.SP.3

Two line plots are shown below. The first one represents the average cell phone usage per day, in minutes, of 20 teenagers. The second one represents the average cell phone usage per day, in minutes, of 20 adults.First Dot Plot: TEENAGERS' CELL PHONE USAGE Horizontal axis: Number of Minutes, ranging from 380 to 700, with increments of 20. 460 minutes has one dot. 480 has 2 dots. 500 has 1 dot. 520 has 4 dots 540 has 6 dots. 560 has 1 dot. 580 has 2 dots. 600 has 2 dots. 620 has 1 dot. Second Dot Plot: ADULTS' CELL PHONE USAGE Horizontal axis: Number of Minutes, ranging from 80 to 400, with increments of 40. 120 minutes has 1 dot. 160 has 1 dot. 180 has 1 dot. 200 has 2 dots. 220 has 2 dots. 240 has 5 dots. 260 has 3 dots. 280 has 3 dots. 300 has 1 dot. 360 has 1 dot. Which statement about the two data sets is true? A. The mean of the data for the adults is greater than the mean of the data for the teenagers because the data points for the adults are more spread out. B. The mean of the data for the teenagers is greater than the mean of the data for the adults because the scale for the teenagers has greater numbers than the scale for the adults. C. The range of the data for the teenagers is greater than the range of the data for the adults because the data points for the teenagers are clustered. D. The range of the data for the teenagers is greater than the range of the data for the adults because the scale for the teenagers has greater numbers than the scale for the adults.

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This question is asking the student to draw informal comparative inferences about two populations, in this case: teenagers' vs. adults' cell phone usage. To show mastery of this skill, the student must informally assess the degree of visual overlap of two quantitative data distributions.

Correct Answer: B

Reproduced from: NYS Grade 7 Test Item 35, 2024

Example 2: NGLS Standard NY-7.SP.8a

At a deli, customers buying a sandwich can choose one type of bread, one type of meat, and one type of cheese. The options for each sandwich are listed below.bread: white or wheat. meat: turkey or beef. cheese: American, Swiss, or cheddar. Assuming each choice is equally likely, what is the probability a customer will choose a sandwich with white bread, turkey, and Swiss cheese? A. one out of twelve. B. one out of seven. C. one out of four. D. one out of three

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This question is asking the student to find probabilities of compound events using organized lists. To show mastery of this skill, the student must understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Given the options for each sandwich that are provided, the student must multiply the possibilities (½ x ½ x ⅓) to obtain 1/12.

Correct Answer: A

Reproduced from: NYS Grade 7 Test Item 34, 2023

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