Grade 7 Math Skills Checklist: What Students Should Know

Compute unit rates involving fractions, such as distance per fractional hour or price per fractional amount.

Recognize whether two quantities have a proportional relationship.

Test proportionality using equivalent ratios in a table.

Identify proportionality from a graph that forms a straight line through the origin.

Find the constant of proportionality, or unit rate, from a table.

Find the constant of proportionality from a graph.

Find the constant of proportionality from an equation or real-world description.

Write an equation of the form y = kx for a proportional relationship.

Explain what the points (0, 0) and (1, r) mean on a proportional graph.

Interpret any point (x, y) on a proportional graph in context.

Solve multi-step ratio and proportion problems.

Solve percent problems involving tax, tips, commissions, fees, discounts, markups, and markdowns.

Solve problems involving percent increase and percent decrease.

Solve simple-interest problems.

Solve problems involving percent error.

Use positive and negative numbers to represent opposite directions or values.

Explain when two opposite quantities combine to make zero.

Add rational numbers and interpret the result in context.

Represent rational-number addition on a horizontal or vertical number line.

Understand p + q as moving |q| units from p in the appropriate direction.

Interpret subtraction of rational numbers as adding the opposite.

Use the relationship p − q = p + (−q).

Explain that the distance between two rational numbers is the absolute value of their difference.

Multiply rational numbers and explain the sign of the product.

Divide rational numbers and explain the sign of the quotient.

Apply properties of operations when calculating with rational numbers.

Interpret products and quotients of rational numbers in real-world contexts.

Convert a rational number to a decimal by long division.

Recognize that a rational-number decimal terminates or repeats.

Solve real-world problems using all four operations with positive and negative rational numbers.

Add and subtract linear expressions with rational coefficients.

Expand a linear expression using the distributive property.

Factor a linear expression by removing a common factor.

Use properties of operations to generate equivalent expressions.

Recognize that different equivalent forms can reveal different information.

Rewrite a percent or rate expression in a form that clarifies the problem.

Solve multi-step numerical problems with positive and negative rational numbers.

Convert among fractions, decimals, and percents when a different form is more useful.

Use estimation and mental calculation to assess whether an answer is reasonable.

Use variables to represent quantities in a real-world problem.

Construct a simple equation to represent a real-world situation.

Solve equations of the forms px + q = r and p(x + q) = r.

Compare algebraic and arithmetic approaches to the same problem.

Construct an inequality to represent a real-world condition or constraint.

Solve inequalities of the forms px + q > r, px + q ≥ r, px + q < r, or px + q ≤ r.

Graph an inequality solution set and interpret it in context.

Compute actual lengths from a scale drawing.

Compute actual areas from a scale drawing.

Reproduce a scale drawing at a different scale.

Use a scale factor to compare corresponding lengths.

Draw geometric shapes with given conditions.

Construct triangles from three measurements of sides or angles.

Decide whether given triangle measurements produce a unique triangle, more than one triangle, or no triangle.

Describe two-dimensional figures formed by slicing three-dimensional figures.

Use supplementary angles to find an unknown angle.

Use complementary angles to find an unknown angle.

Use vertical-angle relationships to find unknown angles.

Use adjacent-angle relationships in multi-step problems.

Explain the relationship between a circle's radius, diameter, circumference, and area.

Find the circumference of a circle.

Find the area of a circle.

Solve real-world problems involving circle area and circumference.

Find areas of composite two-dimensional figures.

Find surface areas of three-dimensional figures made from cubes and right prisms.

Find volumes of three-dimensional figures made from cubes and right prisms.

Understand that statistics can use a sample to learn about a population.

Explain why a sample should represent the population.

Understand that random sampling tends to produce representative samples.

Use data from a random sample to draw an inference about a population.

Generate multiple samples of the same size to examine natural sampling variation.

Estimate a population mean or proportion from sample data.

Compare two numerical data distributions visually.

Compare two populations using measures of center.

Compare two populations using measures of variability.

Describe the amount of visual overlap between two distributions.

Express a difference between centers as a multiple of a measure of variability.

Draw an informal comparative inference from two populations.

Understand probability as a number between 0 and 1.

Interpret probabilities near 0, near 1/2, and near 1.

Approximate probability by conducting repeated chance experiments.

Explain why experimental probability may vary in the short run.

Explain why experimental probability tends to approach the theoretical probability over many trials.

Develop a probability model for a simple chance process.

Compare theoretical probability with observed frequencies.

Revise a probability model when observed data do not fit the original assumptions.

Find probabilities of compound events using organized lists.

Find probabilities of compound events using tables.

Find probabilities of compound events using tree diagrams.

Represent compound-event outcomes in a sample space.

Design and use a simulation to estimate the probability of a compound event.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model real situations with mathematics.

Use appropriate tools strategically.

Attend to precision in language, units, notation, and calculation.

Look for and make use of mathematical structure.

Look for and express regularity in repeated reasoning.