Examining Powers and Bases
- Identify the base and the exponent in an expression written with powers.
- Write the full multiplication that a power represents (like 5^3 means 5×5×5).
- Evaluate simple powers of integers to find the value.
8th Grade Algebra Worksheets
Free algebra worksheets with answer key. No login or account needed. Below are a variety of topics from simplifying expressions or identifying coefficients to solving inequalities, graphing lines, and finding combinations. A grading column and quick grade scale maker grading a breeze and a modified pages help with lower level learners or when just introducing a topic. Great for teachers or for homeschool.
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About these worksheets
These worksheets introduce students to the concept of variables and algebraic thinking. Activities include using substitution to evaluate expressions, writing and graphing inequalities on a number line, identifying numerical coefficients, solving for unknown values using all four operations, and exploring powers, bases, and slope. Aligned with sixth through eighth grade standards, these resources build the foundation for pre-algebra and algebra.
Examining Slope Attributes
- Find the slope of a line by comparing the rise and run shown with two triangles on a graph.
- Compare two slopes to tell which line is steeper and explain why using rise/run.
- Write slope as a ratio or fraction and simplify it when possible.
About these worksheets
These worksheets cover a wide range of algebraic expression skills, from simplifying and expanding to factoring. Students practice combining like terms, using the distributive property, rewriting expressions as multiples of a sum, solving linear equations with variables on both sides, and expanding polynomials using the box method. Topics also include perfect square trinomials and matching equivalent expressions, making these resources ideal for sixth through eighth grade algebra.
Linear Equations with Variables on Both Sides
- Solve linear equations where the variable shows up on both sides of the equals sign.
- Combine like terms to simplify each side before solving.
- Use the distributive property to clear parentheses in an equation.
- Move terms across the equals sign using addition, subtraction, and multiplication to isolate the variable.
- Handle equations that need more than one step to get the variable alone.
About these worksheets
These worksheets bring together coordinate geometry and algebraic reasoning. Students use similar triangles to find missing coordinates and rise values, rotate shapes around the origin, and identify points of intersection by solving systems of equations. Aligned with eighth grade standards, these activities strengthen graphing skills and spatial reasoning on the coordinate plane.
Finding Rise using Similar Triangles
- Use similar triangles on a graph to figure out a missing rise between two points on a line.
- Set up and solve a proportion using rise and run to keep the slope the same.
- Check that your answer makes sense by comparing slopes from different triangles on the same line.
Finding Missing Coordinates Using Similar Triangles
- Find a missing x- or y-coordinate on a graph by using similar triangles.
- Set up and solve a proportion from matching side lengths in two similar triangles.
Identifying Point of Intersection with Equations
- Find the exact point where two lines cross by solving both equations together.
- Use substitution to plug one equation into the other and solve for x and y.
- Use elimination to combine equations and solve for the ordered pair.
- Check your solution by plugging the x and y values back into both equations.
About these worksheets
Students apply mathematical formulas to solve geometry problems involving right and non-right triangles. These worksheets cover the Pythagorean theorem for finding missing side lengths and the Law of Cosines for calculating unknown angles. Designed for eighth grade and above, these resources connect algebraic computation with geometric understanding.
Using Pythagorean theorem
- Identify the hypotenuse and the two legs in a right triangle.
- Use the Pythagorean theorem (a² + b² = c²) to find the missing side c.
- Square the leg lengths and add them correctly before solving for c.
- Take a square root to get the final length of c.
About these worksheets
These worksheets explore number concepts essential for middle school math, including square roots, cube roots, rational and irrational numbers, laws of exponents, scientific notation, radicals, and powers of ten. Students practice estimating radical values, simplifying expressions with exponents, and performing operations in scientific notation. Aligned with eighth grade Common Core standards, these resources build a strong number sense foundation for high school math.
Examining Square Roots
- Recognize the perfect squares that are closest to a given square root.
- Decide which two whole numbers a square root falls between.
- Use nearby perfect squares to make a quick estimate of a square root’s size.
Identifying Rational and Irrational Numbers
- Decide whether a number is rational or irrational.
- Recognize that fractions, integers, and whole numbers are rational because they can be written as a ratio of integers.
- Tell that terminating decimals and repeating decimals are rational numbers.
- Identify common irrational numbers like pi and square roots that do not simplify to a fraction.
Examining Square Root Relative Values
- Decide which two whole numbers a square root falls between.
- Use nearby perfect squares to judge whether a square root is closer to the lower or higher whole number.
- Compare the sizes of different square roots by thinking about their values.
Finding Radicals on a Numberline
- Place square roots on a number line by figuring out which two whole numbers they fall between.
- Estimate the decimal value of a square root well enough to plot it in the right spot.
- Use nearby perfect squares (like 16 and 25) to judge how close a square root is to a whole number.
Rewriting Using the Laws of Exponents
- Rewrite expressions with exponents using the product and quotient rules.
- Simplify powers raised to powers by multiplying exponents.
- Rewrite expressions with zero and negative exponents using reciprocals.
Solving Using the Laws of Exponents
- Practice rewriting negative exponents as fractions (e.g., 3⁻² becomes 1/3²)
- Multiply powers with the same base by adding their exponents, even when some exponents are negative
- Raise fractions to a power by applying the exponent to both the numerator and denominator
- Simplify expressions step by step to reach a final whole number or fraction
Solving with Squared and Cubed
- Evaluate expressions with squared and cubed numbers.
- Solve simple equations where a number is squared or cubed to find the missing value.
- Recognize perfect squares and perfect cubes and match them to their roots.
Solving with Negative Powers
- Rewrite negative exponents as reciprocals so the exponent becomes positive.
- Evaluate expressions with negative powers to get the correct fraction or decimal value.
- Work with negative exponents on whole-number bases, fractions, and powers of 10.
Rewriting Factors as Squares
- Break a number into factors and spot pairs that make a perfect square.
- Use exponents to write repeated factors more simply, like 3×3 as 3^2.
Simplifying Radicals
- Practice rewriting square roots by pulling out perfect-square factors.
- Use factor pairs to break a number under a radical into simpler parts.
- Simplify radicals all the way to a number times a square root (like 3√2).
- Recognize which radicals are already in simplest form.
Expressing Numbers using Powers of 10
- Rewrite whole numbers and decimals as one digit times a power of 10.
- Use place value to decide how many places the decimal point moves when converting.
- Work with both positive and negative exponents to show very large and very small numbers.
- Read and write numbers in a scientific-notation style and convert back to standard form.
Finding Relative Value with Powers of Ten
- Compare two powers of ten and decide which one is larger or smaller.
- Figure out how many times bigger one power of ten is than another.
- Connect powers of ten to place value shifts, like moving the decimal left or right.
Multiplying with Scientific Notation
- Multiply two numbers written in scientific notation.
- Multiply the coefficients and combine the powers of 10 using exponent rules.
- Rewrite answers in proper scientific notation by shifting the decimal and adjusting the exponent.