NY Math Standards (7) | Free Standards Reference

📌 Expressions and Equations (NY-7.EE) 6 standards

NY-7.EE.1

Add, subtract, factor, expand linear expressions

Add, subtract, factor, and expand linear expressions with rational coefficients by applying the properties of operations.

NY-7.EE.2

Understand rewriting expressions reveals relationships

Understand that rewriting an expression in different forms in real-world and mathematical problems can reveal and explain how the quantities are related. e.g., a + 0.05a and 1.05a are equivalent expressions meaning that “increase by 5%” is the same as “multiply by 1.05.”

NY-7.EE.3

Solve multi-step problems with rational numbers

Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. Assess the reasonableness of answers using mental computation and estimation strategies. e.g., If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

NY-7.EE.4 Construct equations/inequalities from real-world quantities 2 sub-parts

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Note: Solving equations that contain variables on both sides is not an expectation in grade 7.

NY-7.EE.4a

Solve word problems with px + q = r equations

Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. e.g., The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Note: This standard is a fluency expectation for grade 7.

NY-7.EE.4b

Solve word problems leading to inequalities

Solve word problems leading to inequalities of the form px + q > r, px + q ≥ r, px + q ≤ r, or px + q < r, where p, q, and r are rational numbers. Graph the solution set of the inequality on the number line and interpret it in the context of the problem. e.g., As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

📌 Geometry (NY-7.G) 6 standards

NY-7.G.1

Solve problems involving scale drawings

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

NY-7.G.2

Draw triangles from given measures

Draw triangles when given measures of angles and/or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Note: Create triangles through the use of freehand drawings, materials, rulers, protractors, and/or technology.

NY-7.G.3

Describe 2D shapes from slicing 3D solids

Describe the two-dimensional shapes that result from slicing three-dimensional solids parallel or perpendicular to the base. Note: Focus of standard is on plane sections resulting from the slicing of right rectangular prisms and right rectangular pyramids.

NY-7.G.4

Apply area/circumference formulas for a circle

Apply the formulas for the area and circumference of a circle to solve problems. Note: Students in grade 7 are not expected to calculate the radius of a circle given its area.

NY-7.G.5

Solve equations for unknown angles

Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Note: Students in grade 7 are limited to solving equations that involve linear expressions on one side of the equation.

NY-7.G.6

Solve area, surface area, and volume problems

Solve real-world and mathematical problems involving area of two-dimensional objects composed of triangles and trapezoids. Solve surface area problems involving right prisms and right pyramids composed of triangles and trapezoids. Find the volume of right triangular prisms, and solve volume problems involving three-dimensional objects composed of right rectangular prisms. Notes: The inclusive definition of a trapezoid will be utilized, which defines a trapezoid as “A quadrilateral with at least one pair of parallel sides.” (This definition includes parallelograms and rectangles.) Right prisms include cubes.

📌 Ratio and Proportional Reasoning (NY-7.RP) 7 standards

NY-7.RP.1

Compute unit rates with fractions

Compute unit rates associated with ratios of fractions. e.g., If a person walks 1/2 mile in each 1/4 hour, compute the rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour with 2 being the unit rate. Note: Problems may include ratios of lengths, areas, and other quantities measured in like or different units, including across measurement systems.

NY-7.RP.2 Recognize and represent proportional relationships 4 sub-parts

Recognize and represent proportional relationships between quantities.

NY-7.RP.2a

Decide if two quantities are proportional

Decide whether two quantities are in a proportional relationship. Note: Strategies include but are not limited to the following: testing for equivalent ratios in a table and/or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

NY-7.RP.2b

Identify constant of proportionality

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

NY-7.RP.2c

Represent proportional relationships by equations

Represent a proportional relationship using an equation. e.g., If total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

NY-7.RP.2d

Explain meaning of a point on a proportional graph

Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

NY-7.RP.3

Solve multistep ratio and percent problems

Use proportional relationships to solve multistep ratio and percent problems. Note: Examples of percent problems include: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.

📌 Statistics and Probability (NY-7.SP) 7 standards

NY-7.SP.1

Construct and interpret box plots

Construct and interpret box-plots, find the interquartile range, and determine if a data point is an outlier. Note: Students in grade 7 are not expected to construct box-plots that include outliers in the data, but students are expected to interpret box-plots that may contain outliers.

NY-7.SP.3

Assess visual overlap of two data distributions

Informally assess the degree of visual overlap of two quantitative data distributions.

NY-7.SP.4

Draw comparative inferences from measures of center/variability

Use measures of center and measures of variability for quantitative data from random samples or populations to draw informal comparative inferences about the populations. Note: Measures of center are mean, median, and mode. The measures of variation include range and the interquartile range.

NY-7.SP.8 Find probabilities of compound events 3 sub-parts

Find probabilities of compound events using organized list, sample space tables, tree diagrams, and simulation.

NY-7.SP.8a

Understand probability as fraction of outcomes

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.

NY-7.SP.8b

Represent sample spaces for compound events

Represent sample spaces for compound events using methods such as organized lists, sample space tables, and tree diagrams. For an event described in everyday language, identify the outcomes in the sample space which compose the event. e.g., “rolling double sixes”.

NY-7.SP.8c

Design a simulation for compound event frequencies

Design and use a simulation to generate frequencies for compound events. e.g., Use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

📌 The Number System (NY-7.NS) 11 standards

NY-7.NS.1 Add and subtract rational numbers 4 sub-parts

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. Represent addition and subtraction on a horizontal or vertical number line.

NY-7.NS.1a

Describe situations where quantities combine to 0

Describe situations in which opposite quantities combine to make 0.

NY-7.NS.1b

Understand addition of rational numbers

Understand addition of rational numbers; p + q is the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

NY-7.NS.1c

Understand subtraction as adding additive inverse

Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

NY-7.NS.1d

Apply properties to add/subtract rational numbers

Apply properties of operations as strategies to add and subtract rational numbers.

NY-7.NS.2 Multiply and divide rational numbers 4 sub-parts

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

NY-7.NS.2a

Understand multiplication extended to rational numbers

Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

NY-7.NS.2b

Understand integer division yields rational numbers

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.

NY-7.NS.2c

Apply properties to multiply/divide rational numbers

Apply properties of operations as strategies to multiply and divide rational numbers.

NY-7.NS.2d

Convert a fraction to a decimal using long division

Convert a fraction to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

NY-7.NS.3

Solve problems with the four operations on rational numbers

Solve real-world and mathematical problems involving the four operations with rational numbers. Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions limited to (a/b)/(c/d) where a, b, c, and d are integers and b, c, and d ≠ 0.