Expressions & Equations Worksheets

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use Focus to pick the grouping level, or Mix All.

Write a numerical expression that records a calculation in words ("add 8 and 7, then multiply by 2" is 2 × (8 + 7)), and interpret an expression without evaluating it.

Write repeated multiplication using an exponent, expand an exponent back into factors, and evaluate expressions containing one.

Substitute a given value for a single variable and evaluate the resulting expression.

Reason about order of operations by building and comparing expressions: insert operations and parentheses to make an equation true, and compare two groupings of the same numbers, and explain number tricks with algebra.

Name the parts of an expression — term, coefficient, constant and factor — and describe a product as a single factor times a sum.

Evaluate multi-step expressions that combine parentheses, exponents, and all four operations.

Translate a short verbal phrase into a one-variable algebraic expression using the correct operation.

Decide whether two expressions are equivalent — equal for every value of the variable — and justify it, testing a value to check.

Substitute values to find which make an equation or inequality true — the idea behind what solving actually asks.

Choose a variable for the unknown quantity in a real situation, write an expression using it, and say what the expression means.

Solve one-step linear equations using addition, subtraction, multiplication, or division.

Write an inequality (x > c, x < c, ≥, ≤) for a constraint and graph its solution set on a number line — open circle for strict, closed for inclusive.

Two quantities that change together, in words, a table, a graph and an equation: each problem carries one situation through them — name the variables, plot and read graphs, write the equation and use it forwards and backwards.

Substitute values for two variables, including powers, and evaluate the expression.

Complete or analyze an input-output table governed by a two-step rule (multiply then add/subtract).

Solve one-step inequalities and express the solution, flipping the sign when dividing by a negative.

Work with linear expressions three ways: expand a bracket, take out the greatest common factor, and collect like terms — including when a whole bracket is subtracted.

Rewrite an expression in an equivalent form and say what the new form reveals — that taking 20% off means multiplying by 0.80, or that two successive discounts do not simply add.

Solve multi-step problems using positive and negative numbers in any form — whole numbers, fractions, decimals and percents — then check that the answer is reasonable.

Solve two-step linear equations of the form ax + b = c using inverse operations.

Solve two-step inequalities of the form ax + b < c, correctly reversing the sign with negative coefficients.

Evaluate whole-number bases raised to exponents from -4 to 4, including zero and negative exponents (which give unit fractions).

Simplify expressions using product, quotient, and power-of-a-power rules with integer exponents.

Solve equations of the form x squared = p and x cubed = p, and know why a square gives two solutions while a cube gives one.

Compare two proportional relationships given in different forms — a table against an equation — by reducing each to its unit rate, the slope.

Solve multi-step linear equations in one variable — with variables on both sides, distributing where needed, and recognizing equations with one, no, or infinitely many solutions.

Find the slope of a line from two points or from its graph, and write a line as y = mx + b by reading its slope and y-intercept (8.EE.B.5).

Solve systems of two linear equations by graphing (the solution is the point where the lines cross), by substitution, and by elimination, including real-world problems.

Translate real situations into a system of two linear equations and solve (8.EE.C.8).