Grade 8 Math Skills Checklist: What Students Should Know

Explain the difference between rational and irrational numbers.

Recognize that terminating and repeating decimals are rational.

Convert a repeating decimal to an equivalent rational number in appropriate cases.

Use decimal approximations to compare irrational numbers.

Locate irrational numbers approximately on a number line.

Estimate expressions involving irrational values such as square roots and π.

Apply properties of integer exponents to generate equivalent numerical expressions.

Interpret and simplify expressions with positive and negative integer exponents.

Use square-root symbols to represent solutions to equations of the form x² = p.

Use cube-root symbols to represent solutions to equations of the form x³ = p.

Evaluate square roots of small perfect squares and cube roots of small perfect cubes.

Use powers of 10 to estimate very large and very small quantities.

Compare quantities written with powers of 10 and explain how many times larger or smaller one is.

Write numbers in scientific notation.

Multiply and divide numbers written in scientific notation.

Interpret scientific notation produced by calculators or other technology.

Graph proportional relationships and interpret the unit rate as slope.

Compare proportional relationships represented by tables, graphs, equations, or descriptions.

Explain why a nonvertical line has a constant slope using similar-triangle reasoning.

Connect proportional relationships to y = mx and linear relationships to y = mx + b.

Solve linear equations in one variable with rational coefficients.

Use the distributive property and combine like terms when solving equations.

Determine whether a linear equation has one solution, no solution, or infinitely many solutions.

Interpret the solution of a system as the intersection point of two graphs.

Solve simple systems of two linear equations algebraically.

Estimate or verify solutions to systems by graphing.

Solve real-world problems that can be modeled by two linear equations.

Explain that a function assigns exactly one output to each input.

Decide whether a relation represented by ordered pairs, a table, or a graph is a function.

Compare two functions represented in different forms.

Compare rates of change of linear functions.

Compare initial values of linear functions.

Recognize y = mx + b as a linear function.

Distinguish linear functions from nonlinear functions.

Construct a linear function from a situation, table, graph, or two points.

Determine rate of change from a table, graph, equation, or description.

Determine initial value from a table, graph, equation, or description.

Interpret rate of change and initial value in context.

Describe where a graph is increasing, decreasing, or constant.

Describe whether a relationship shown by a graph is linear or nonlinear.

Sketch a graph that matches a verbal description of a functional relationship.

Describe translations, reflections, and rotations of two-dimensional figures.

Recognize that rigid transformations preserve segment lengths and angle measures.

Recognize that rigid transformations preserve parallel lines.

Use a sequence of rotations, reflections, and translations to demonstrate congruence.

Describe the effect of a transformation on coordinates.

Describe dilations on the coordinate plane.

Determine the scale factor of a dilation.

Use transformations and dilations to demonstrate similarity.

Use triangle angle-sum reasoning to find unknown angles.

Use exterior-angle relationships in triangles.

Use angle relationships formed when parallel lines are cut by a transversal.

Use angle-angle reasoning to establish triangle similarity.

Explain the Pythagorean Theorem and its converse at an appropriate Grade 8 level.

Use the Pythagorean Theorem to find missing side lengths in right triangles.

Apply the Pythagorean Theorem in two-dimensional real-world problems.

Apply the Pythagorean Theorem in three-dimensional problems.

Find the distance between two coordinate points using Pythagorean reasoning.

Use the volume formula for cylinders.

Use the volume formula for cones.

Use the volume formula for spheres.

Solve real-world volume problems involving cylinders, cones, and spheres.

Construct a scatter plot for bivariate measurement data.

Describe clustering and outliers in a scatter plot.

Describe positive, negative, or no association.

Distinguish linear from nonlinear patterns of association.

Draw or choose an informal line of fit for data with an approximately linear association.

Judge informally how well a line fits a scatter plot.

Use a linear model to make predictions.

Interpret the slope of a linear model in context.

Interpret the intercept of a linear model in context.

Construct a two-way table for two categorical variables.

Calculate row or column relative frequencies.

Use conditional percentages to compare groups.

Use a two-way table to describe possible association between categorical variables.

Make sense of unfamiliar problems and persevere when a solution is not immediate.

Reason abstractly and quantitatively.

Construct mathematical arguments and evaluate the reasoning of others.

Model real situations with mathematics.

Choose and use mathematical tools strategically.

Communicate with appropriate mathematical precision.

Look for useful mathematical structure.

Look for repeated reasoning and use it to work more efficiently.