Academic standards list

7th Grade — Mathematics


Academic standards define the expectations for knowledge and skills that students are to learn in a subject by a certain age or at the end of a school grade level. This page contains a list of standards for a specific content area, grade level, and/or course. The list of standards may be structured using categories and sub-categories.

Ratios & Proportional Relationships

Analyze proportional relationships and use them to solve real-world and mathematical problems.
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different
Recognize and represent proportional relationships between quantities.
     There are 4 components within this standard.
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and

The Number System

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a
     There are 4 components within this standard.
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
     There are 4 components within this standard.
Solve real-world and mathematical problems involving the four operations with rational numbers.1

Expressions & Equations

Use properties of operations to generate equivalent expressions.
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
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
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by
     There are 2 components within this standard.


Draw, construct and describe geometrical figures and describe the relationships between them.
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
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
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles,

Statistics & Probability

Use random sampling to draw inferences about a population.
Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a
Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or
Draw informal comparative inferences about two populations.
Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the
Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two
Investigate chance processes and develop, use, and evaluate probability models.
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
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the
     There are 2 components within this standard.
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
     There are 3 components within this standard.
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