Skip to main content
Tennessee Standards

Tennessee 7th Grade Math Standards

All 23 Tennessee math standards for 7th grade, each explained in plain English. The official wording is one click away under each one.

23 standards

Ratios and Proportional Relationships

3 standards
Analyze proportional relationships and use them to solve real-world and mathematical problems.
7.RP.A.1
Find unit rates from ratios of fractions, like walking 1/3 mile in 1/6 hour being 2 miles per hour, for lengths, areas and other measures.
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 15 minutes, compute the unit rate as the complex fraction (1/2) / (1/4) miles per hour, equivalently 2 miles per hour.
7.RP.A.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.cUse the concept of equality to represent proportional relationships with 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.
Common Core 7.RP.2
7.RP.A.3
Solve multi-step ratio and percent problems with proportions, like tax, tips, discounts, simple interest, commissions, percent change and percent error.
Official wording
Use proportional relationships to solve multi-step ratio and percent problems. Examples: batting averages, recipes, simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error, etc.

The Number System

3 standards
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
7.NS.A.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.aUnderstand 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.bUnderstand 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.cApply properties of operations as strategies to add and subtract rational numbers.
Common Core 7.NS.1
7.NS.A.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 all 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 or eventually repeats.
Common Core 7.NS.2
7.NS.A.3
Solve real-world and math problems using all four operations with positive and negative fractions and decimals, including complex fractions.
Official wording
Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)

Expressions and Equations

4 standards
Use properties of operations to generate equivalent expressions.
7.EE.A.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.
Common Core 7.EE.1
7.EE.A.2
Rewrite an expression in a different form to see a problem in a new way, like seeing a 30% discount as paying 0.7 of the price.
Official wording
Rewrite and connect equivalent expressions in different forms in a contextual problem to provide multiple ways of interpreting the problem and investigating how the quantities in it are related. For example, shoes are on sale at a 25% discount. How is the discounted price P related to the original cost C of the shoes? C – 0.25C = P. In other words, P is 75% of the original cost since C – 0.25C can be written as 0.75C.
Solve real-world and mathematical problems using numerical and algebraic expressions and equations and inequalities.
7.EE.B.3
Solve multi-step problems with positive and negative numbers as whole numbers, fractions or decimals, switching forms as needed and checking with estimates.
Official wording
Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers presented in any form (whole numbers, fractions, and decimals).aApply properties of operations to calculate with numbers in any form; convert between forms as appropriate.bAssess the reasonableness of answers using mental computation and estimation strategies.
7.EE.B.4
Write and fluently solve two-step equations like 3x + 5 = 20 and inequalities like 4x + 6 > 30 from real problems, graphing inequality solutions on a number line.
Official wording
Use variables to represent quantities in a real-world and mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.aSolve real-world and mathematical 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 real-world and mathematical problems leading to inequalities of the form px + q > r, px + q < r, px + q ≥ r, and px + q ≤ r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality on a number line 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

5 standards
Draw, construct, and describe geometrical figures and describe the relationships between them.
7.G.A.1
Use scale drawings of congruent and similar figures to find real lengths and areas, and redraw a scale drawing at a new scale, like a floor plan.
Official wording
Solve problems involving scale drawings of congruent and similar geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
7.G.A.2
Draw triangles from given three angles or three sides, and notice whether those facts make exactly one triangle, several, or none at all.
Official wording
Draw triangles with given conditions: three angle measures or three side measures. Notice when the conditions determine a unique triangle, more than one triangle, or no triangle.
Solve real-world and mathematical problems involving angle measure, area, surface area, and volume.
7.G.B.3
Know and use the formulas for a circle's area and circumference, and explore how the radius, circumference, area and pi relate.
Official wording
Know the formulas for the area and circumference of a circle and use them to solve problems. Explore the relationships between the radius, the circumference, and the area of a circle, and the number π.
7.G.B.4
Set up and solve simple equations for a missing angle in multi-step figures, using what is known about supplementary, complementary, vertical and adjacent pairs.
Official wording
Know and 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.B.5
Solve problems about the area of shapes made of triangles and polygons, and the volume and surface area of solids built from cubes and right prisms.
Official wording
Solve real-world and mathematical problems involving area of two-dimensional figures composed of triangles, quadrilaterals, and polygons, and volume and surface area of three-dimensional objects composed of cubes and right prisms.

Statistics and Probability

8 standards
Use random sampling to draw inferences about a population.
7.SP.A.1
Explain how a sample can tell about a whole population only when it is representative, and why random sampling tends to give fair samples.
Official wording
Explore how 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.A.2
Use data from random samples to estimate something about a population, like the most popular lunch, and run several same-size samples to see how much estimates vary.
Official wording
Collect and 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.B.3
Compare the centers of two data sets with similar spread by eye, like the mean heights of two teams on dot plots or box plots.
Official wording
Informally compare the measures of center (mean, median, mode) of two numerical data distributions with similar variabilities. 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; on a dot plot or box plot, the separation between the two distributions of heights is noticeable.
7.SP.B.4
Use the centers and spreads of random samples to draw rough comparisons between two populations, like whether one book uses longer words than another.
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 7th grade science book are generally longer than the words in a chapter of a 4th grade science book.
Investigate chance processes and develop, use, and evaluate probability models.
7.SP.C.5
Know that the probability of an event is a number from 0 to 1 and explain what it says about how likely the event is.
Official wording
Recognize that the probability of a chance event is a number between 0 and 1 and interpret the likelihood of the event occurring.
7.SP.C.6
Find theoretical probability and estimate it from repeated trials, then compare the two, like expecting about 100 heads in 200 coin flips but rarely exactly 100.
Official wording
Calculate theoretical and experimental probability of simple events.aApproximate 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.bCalculate the theoretical probability of a simple event.cCompare theoretical probabilities to experimental probabilities; explain any possible sources of discrepancy. 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.C.7
Build probability models, with equally likely outcomes or from data of repeated trials, and use them to find chances of events, like a thumbtack landing point up.
Official wording
Develop a probability model and use it to find experimental or theoretical probabilities of events.aUse a uniform probability model, with equal probability assigned to all outcomes, 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, including non-uniform models, by observing frequencies in data generated from a chance process. Use the model to estimate the probabilities of events. 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?
Summarize and describe numerical data sets.
7.SP.D.8
Describe data in context using median or mean, range or interquartile range, its pattern and unusual values, and explain why those measures suit its shape.
Official wording
Summarize a numerical data set in relation to its context.aGive quantitative measures of center (median and/or mean) and variability (range and/or interquartile range), as well as describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.bRelate and understand the choice of measures of center (median and/or mean) and variability (range and/or interquartile range) to the shape of the data distribution and the context in which the data were gathered.

The official Tennessee documents

Tennessee Academic Standards for Mathematics, Tennessee Department of Education, tn.gov/education.

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.