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New York Standards

New York 7th Grade Math Standards

All 20 New York math standards for 7th grade, each explained in plain English. The official wording is one click away under each one.

20 standards

Ratios and Proportional Relationships

3 standards
Analyze proportional relationships and use them to solve real-world and mathematical problems.
NY-7.RP.1
Find unit rates when the quantities are fractions, like walking 1/2 mile every 1/4 hour meaning 2 miles per hour.
Official wording
Compute unit rates associated with ratios of fractions.
NY-7.RP.2
Decide whether two quantities are proportional, find the constant of proportionality, and write the relationship as an equation like t = pn.
Official wording
Recognize and represent proportional relationships between quantities.aDecide whether two quantities are in a proportional relationship.bIdentify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.cRepresent a proportional relationship using an equation.dExplain 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.
Common Core 7.RP.2
NY-7.RP.3
Use proportions to solve multistep ratio and percent problems, like sales tax, tips, discounts, markups, and percent increase or decrease.
Official wording
Use proportional relationships to solve multistep ratio and percent problems.

The Number System

3 standards
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
NY-7.NS.1
Add and subtract signed numbers on a number line, see that opposites sum to 0, subtract by adding the opposite, and find distance as an absolute difference.
Official wording
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.aDescribe situations in which opposite quantities combine to make 0.bUnderstand 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.cUnderstand 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.dApply properties of operations as strategies to add and subtract rational numbers.
NY-7.NS.2
Multiply and divide positive and negative numbers, including the sign rules, and turn any fraction into a decimal that ends or repeats.
Official wording
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.aUnderstand 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.bUnderstand 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.cApply properties of operations as strategies to multiply and divide rational numbers.dConvert a fraction to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
Common Core 7.NS.2
NY-7.NS.3
Solve real-world and math problems using all four operations with positive and negative rational numbers, including complex fractions like 1/2 over 3/4.
Official wording
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.

Expressions, Equations, and Inequalities

4 standards
Use properties of operations to generate equivalent expressions.
NY-7.EE.1
Combine, factor, and expand linear expressions with fraction, decimal, or negative coefficients, like simplifying 4x - 2 - x + 7 to 3x + 5.
Official wording
Add, subtract, factor, and expand linear expressions with rational coefficients by applying the properties of operations.
NY-7.EE.2
Rewrite an expression in another form to show how quantities relate, like seeing a + 0.05a as 1.05a, meaning a 5% increase.
Official wording
Understand that rewriting an expression in different forms in real-world and mathematical problems can reveal and explain how the quantities are related.
Solve real-life and mathematical problems using numerical and algebraic expressions, equations, and inequalities.
NY-7.EE.3
Solve multistep problems with positive and negative whole numbers, fractions, and decimals, converting between forms as needed and checking answers by estimating.
Official wording
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.
NY-7.EE.4
Write and solve two-step equations like 3x + 5 = 20 and inequalities like 3x + 5 > 20 from word problems, and graph the inequality's solutions.
Official wording
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.aSolve 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.bSolve 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.
Common Core 7.EE.4

Geometry

6 standards
Draw, construct, and describe geometrical figures and describe the relationships between them.
NY-7.G.1
Use scale drawings to find real lengths and areas, and redraw a figure at a different scale.
Official wording
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.
Common Core 7.G.1
NY-7.G.2
Draw triangles from given angles or side lengths and notice when the facts allow exactly one triangle, several triangles, or none at all.
Official wording
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.
NY-7.G.3
Describe the flat shapes made by slicing solid figures parallel or perpendicular to the base, like a rectangle from slicing a box straight down.
Official wording
Describe the two-dimensional shapes that result from slicing three-dimensional solids parallel or perpendicular to the base.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
NY-7.G.4
Use the area and circumference formulas for circles to solve problems, like finding the fence needed around a circular garden with a 5 m radius.
Official wording
Apply the formulas for the area and circumference of a circle to solve problems.
NY-7.G.5
Find an unknown angle by writing an equation from angle facts, like two angles on a straight line adding to 180 degrees.
Official wording
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.
Common Core 7.G.5
NY-7.G.6
Find areas of shapes made of triangles and trapezoids, surface areas of right prisms and pyramids, and volumes of triangular prisms and solids built from boxes.
Official wording
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.

Statistics and Probability

4 standards
Draw informal comparative inferences about two populations.
NY-7.SP.1
Make and read box plots, find the interquartile range, and decide whether a value counts as an outlier.
Official wording
Construct and interpret box-plots, find the interquartile range, and determine if a data point is an outlier.
NY-7.SP.3
Judge informally how much two sets of data overlap when graphed, like comparing dot plots of player heights on two teams.
Official wording
Informally assess the degree of visual overlap of two quantitative data distributions.
NY-7.SP.4
Compare two populations informally using the centers and spreads of data from random samples or whole groups, like the median and range of two classes' scores.
Official wording
Use measures of center and measures of variability for quantitative data from random samples or populations to draw informal comparative inferences about the populations.
Investigate chance processes and develop, use, and evaluate probability models.
NY-7.SP.8
Find probabilities of compound events, like rolling two dice, by listing outcomes in organized lists, tables, or tree diagrams, and by running simulations.
Official wording
Find probabilities of compound events using organized lists, sample space tables, tree diagrams, and simulation.aUnderstand 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.bRepresent 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.cDesign and use a simulation to generate frequencies for compound events.

The official New York documents

New York State Next Generation Mathematics Learning Standards, Copyright 2017, New York State Education Department, used with permission.

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

The plain-English lines are EMStudio's own explanations, shown beside the official wording. They are not part of the standards.