Grade 8 Math Practice

Analyze a function whose graph is a straight line, and interpret its slope and y-intercept in the context of the problem.

Construct a function that models a linear relationship between two quantities, including interpreting the meaning of the slope and intercept.

Understand that a function is a rule that assigns to each input exactly one output.

Understand that solutions to a system of two linear equations correspond to points of intersection of their graphs, and graph linear equations.

Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear.

Solve linear equations with one variable, including equations with variables on both sides and those requiring the distributive property.

Recognize when linear equations in one variable have no solution or infinitely many solutions.

Solve linear equations with rational coefficients, including those involving fractions and decimals.

Distinguish between linear and non-linear functions based on their equations, graphs, and tables.

Solve systems of two linear equations algebraically using the elimination (or addition) method.

Graph systems of two linear equations and estimate or find the exact solutions.

Solve systems of two linear equations algebraically using the substitution method.

Solve systems of two linear equations that have no solution or infinitely many solutions.

Understand that solutions to a system of two linear equations correspond to points of intersection of their graphs.

Understand the concept of slope as the rate of change between two points on a line.

Write linear equations in the form y = mx + b given the slope and y-intercept, or from a graph or table.

This topic covers understanding and applying the properties of integer exponents to generate equivalent numerical expressions, and performing operations with numbers expressed in scientific notation.

This topic focuses on extending arithmetic operations (addition, subtraction, multiplication, and division) to include all rational numbers, including fractions and decimals, with an emphasis on fluency and understanding the properties of operations.

Analyze and interpret patterns in bivariate data, including identifying trends and making predictions.

Understand the concept of probability and calculate the probability of simple events occurring.

Understand the concept of square roots and cube roots, and be able to find them for perfect squares and cubes.

Explore the properties of irrational numbers, including approximating their values and comparing them to rational numbers.

Students will identify and analyze angle relationships (alternate interior, corresponding, consecutive interior) formed when a transversal intersects parallel lines.

Students will understand that two-dimensional figures are congruent if one can be transformed into the other by a sequence of translations, rotations, and reflections.

Students will understand and apply the converse of the Pythagorean theorem to determine if a triangle is a right triangle.

Students will use the Pythagorean theorem to solve problems involving distances between points on a coordinate plane and in various real-world contexts.

Students will understand that two-dimensional figures are similar if one can be transformed into the other by a sequence of rotations, reflections, translations, and dilations.

Students will understand and apply the Pythagorean theorem to find the length of an unknown side in a right triangle and to solve real-world and mathematical problems.

Students will understand and perform dilations on a coordinate plane, analyzing how the scale factor affects the size and position of the image.

Students will understand and perform translations, rotations, and reflections on a coordinate plane, analyzing the effect of each transformation on the coordinates of points.

Students will derive and apply formulas for the volumes of cylinders, cones, and spheres, and solve problems involving these volumes.

Students will understand the relationship between the volume of a cone and a cylinder with the same base radius and height.

Students will understand the relationship between the volume of a sphere and a cylinder that circumscribes it.

Understand that straight lines are not a good fit for data that clearly shows a curved pattern, and analyze patterns in bivariate data that are categorical by creating, analyzing, and interpreting two-way tables.

Analyze and describe patterns of association between two variables in a scatter plot, including whether the association is linear or nonlinear, and identify positive, negative, or no association.

Construct and interpret a linear function (e.g., a line of best fit) to model relationships between two variables that exhibit a linear association, and assess the model's fit.

Use the equation of a linear model to solve problems and interpret the meaning of the slope and y-intercept in the context of the data.