Common Core State Standards

7th Grade Math Standards

All 24 Common Core math standards for 7th grade, grouped into domains and written in plain English. The official wording is one click away.

24 standards

Ratios & Proportional Relationships RP

3 standards

Analyze proportional relationships and use them to solve real-world and mathematical problems.

7.RP.1

Find a unit rate from a ratio of fractions, like 1/2 mile in 1/4 hour is 2 miles per hour.

Official wording

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.

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, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.bIdentify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.cRepresent proportional relationships by equations. For example, 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.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.

7.RP.3

Solve multi-step percent problems about tax, tips, discounts, simple interest and percent change.

Official wording

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

The Number System NS

3 standards

Apply and extend previous understandings of operations with fractions.

7.NS.1

Add and subtract positive and negative numbers, including fractions and decimals, knowing that subtracting a number is adding its opposite.

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 diagram.aDescribe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.bUnderstand p + q as 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.

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

7.NS.3

Solve word problems that mix all four operations with positive and negative fractions and decimals.

Official wording

Solve real-world and mathematical problems involving the four operations with rational numbers.

Expressions & Equations EE

4 standards

Use properties of operations to generate equivalent expressions.

7.EE.1

Combine, factor and expand linear expressions, like rewriting 3(x + 2) as 3x + 6 or 2x + 5x as 7x.

Official wording

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

7.EE.2

See what a rewritten expression reveals, like a + 0.05a = 1.05a showing that a 5% increase is the same as multiplying by 1.05.

Official wording

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

7.EE.3

Solve multi-step problems with positive and negative whole numbers, fractions and decimals, switching forms as needed and checking answers by estimating.

Official wording

Solve multi-step real-life 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; and assess the reasonableness of answers using mental computation and estimation strategies. For example: 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.

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 specific 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. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?bSolve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: 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 G

6 standards

Draw construct, and describe geometrical figures and describe the relationships between them.

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.

7.G.2

Draw shapes from given measurements, and tell whether three side or angle measures make one triangle, many, or none.

Official wording

Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

7.G.3

Describe the flat shape you get when you slice through a rectangular box or pyramid.

Official wording

Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

7.G.4

Use the formulas for the circumference and area of a circle, and explain how the two are connected.

Official wording

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

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.

7.G.6

Find the area of polygons and the volume and surface area of prisms, including shapes built from several pieces.

Official wording

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Statistics & Probability SP

8 standards

Use random sampling to draw inferences about a population.

7.SP.1

Understand that a random sample can tell you about a whole population, but only if the sample fairly represents it.

Official wording

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

7.SP.2

Use a random sample to estimate something about a population, and take several samples to see how much the estimate might vary.

Official wording

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

Draw informal comparative inferences about two populations.

7.SP.3

Compare two data sets on dot plots by how far apart their centers are, measured in units of their spread.

Official wording

Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

7.SP.4

Use the mean, median and spread of two random samples to decide how two populations compare.

Official wording

Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

Investigate chance processes and develop, use, and evaluate probability models.

7.SP.5

Know that a probability is a number from 0 to 1, where near 0 means unlikely, 1/2 means as likely as not, and near 1 means likely.

Official wording

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

7.SP.6

Estimate a probability from many trials, and predict outcomes from a probability, like rolling a 3 or 6 about 200 times in 600 rolls.

Official wording

Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

7.SP.7

Build a probability model, either with equally likely outcomes or from observed data, and explain when results do not match it.

Official wording

Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.aDevelop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.bDevelop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

7.SP.8

Find the probability of a compound event, like rolling double sixes, by listing outcomes in a table or tree diagram or by running a simulation.

Official wording

Find probabilities of compound events using organized lists, 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, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.cDesign and use a simulation to generate frequencies for compound events. For example, 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?