Grade 8 Math Free Worksheets: 72 Free Printable PDFs with Step-by-Step Answer Keys

Eighth grade is the year math grows up. For most of elementary and middle school, the subject was a collection of dependable procedures — line up the numbers, follow the steps, get the answer, move on. Eighth grade does not let a student stay there. It asks for the structure underneath the steps: slope as a measure of how fast one quantity changes against another, a function as a rule that takes an input and returns exactly one output, an equation that can be true for one value, no value, or every value. There is a real difference between solving `9x + 2 = 29` and understanding why `9x + 2 = 9x – 5` can never be true — and Grade 8 is where that difference becomes the point.

The geometry changes in the same direction. This is the year the Pythagorean theorem arrives and turns out to be quietly useful everywhere — a missing leg of a right triangle, the distance between two points on a grid, a fast check on whether a corner is square. Students rotate, reflect, and translate figures across the coordinate plane and see why the rigid motions keep a shape exactly the same, while a dilation rescales it but keeps its shape. They learn the volume formulas for cylinders, cones, and spheres. And running underneath it all is a new fluency with the real number system: irrational numbers, scientific notation, and the properties of integer exponents.

These worksheets were built for that exact stretch of the year — where a perfectly capable student can feel lost simply because the kind of thinking has changed, not because they have fallen behind. For students everywhere, regardless of school, district, or state, each PDF gives one clear skill at a time, with enough practice to make the idea hold.

What’s on this page

Seventy-two single-skill PDFs, each aligned to Common Core-aligned Grade 8 mathematics standards. Every file targets one skill and nothing else — so a student working on systems of equations is not also wrestling with scientific notation. That focus matters, because eighth-grade trouble is almost always about one specific topic. When a student says “I don’t get functions,” the real issue is usually something narrow and nameable — telling a function from a non-function in a table, or reading an output off a graph — and a single-skill PDF lets practice land exactly there.

Each PDF opens with a one-page Quick Review that explains the skill in plain language with a fully worked example. Twenty practice problems follow, building from straightforward to genuinely challenging, plus four word problems that set the skill in a real context. The final page is a student-facing answer key — not just answers, but short, friendly explanations a student can read alone and actually learn from.

Real Numbers

• Rational and Irrational Numbers — [8.NS.1] tell a fraction-able number from one whose decimal never repeats
• Turning Repeating Decimals into Fractions — [8.NS.1] the algebra trick that turns 0.272727… into a clean fraction
• Estimating Irrational Numbers — [8.NS.2] pin a root like √20 between two whole numbers, then closer
• Estimating Expressions with Irrational Numbers — [8.NS.2] approximate whole expressions that mix roots and π
• Personal Financial Literacy — [8.PFL.1] real-money math: budgets, balances, and simple percent work
• Prime Factorization with Exponents — [8.NS.1] break a number all the way down and write it with exponents
• Density of Real Numbers — [8.NS.1] there is always another number between any two — find it

Exponents, Roots & Scientific Notation

• Properties of Integer Exponents — [8.EE.1] product, quotient, power, zero, and negative-exponent rules
• Square Roots and Cube Roots — [8.EE.2] undo a square or a cube, including the ± on x² equations
• Understanding Scientific Notation — [8.EE.3] move the decimal the right way for huge and tiny numbers
• Operations with Scientific Notation — [8.EE.4] multiply, divide, add, and subtract without losing the exponent
• Order of Operations with Radicals — [8.EE.2] where the radical bar fits in PEMDAS — it groups like parentheses

Linear Equations and Inequalities

• Graphing Proportional Relationships — [8.EE.5] read the unit rate straight off a proportional graph
• Slope as a Rate of Change — [8.EE.5] slope is just rise over run — a real-world rate
• Slope and the Equations of a Line — [8.EE.6] build y = mx + b from a slope and a point
• Solving Linear Equations in One Variable — [8.EE.7] multi-step solving: distribute, combine, isolate
• Solving Systems of Two Equations — [8.EE.8] find the point two lines share by substitution or elimination
• Solving Real Problems with Systems — [8.EE.8c] turn a word problem into two equations and solve it
• Solving Linear Inequalities — [8.EE.7] solve like an equation — but flip the sign when you divide by a negative
• Multiplying Linear Expressions and Factoring — [8.EE.1] distribute to expand, pull out a common factor to undo it
• Graphing Linear Inequalities in Two Variables — [8.EE.8] boundary line, solid or dashed, then shade the right side
• Parallel and Perpendicular Lines — [8.EE.6] equal slopes for parallel, negative reciprocals for perpendicular
• Point-Slope and Standard Form — [8.EE.6] two more ways to write a line — and when each one helps
• Literal Equations — [8.EE.7] solve a formula for a different letter
• Absolute Value Equations and Inequalities — [8.EE.7] split into two cases — and read ‘and’ vs ‘or’ correctly
• Equations with Special Solutions — [8.EE.7] spot ‘no solution’ and ‘all real numbers’ before you waste time

Functions and Sequences

• What Is a Function? — [8.F.1] every input gets exactly one output — and how to check
• Reading Function Values — [8.F.1] evaluate f(x) and read values from tables and graphs
• Comparing Two Functions — [8.F.2] compare functions given as equations, tables, and graphs
• Linear vs. Nonlinear Functions — [8.F.3] constant rate of change means linear — everything else does not
• Building Linear Functions — [8.F.4] write the function from a description, a table, or two points
• Sketching and Describing Function Graphs — [8.F.5] match a graph’s shape to a story: increasing, flat, falling
• Domain and Range of a Function — [8.F.1] the inputs you may use and the outputs you get back
• Arithmetic Sequences — [8.F.4] add the same step each time — and find the nth term
• Geometric Sequences — [8.F.4] multiply by the same ratio each time — and find the nth term

Geometry

• Rotations, Reflections, and Translations — [8.G.1] the three rigid motions and what each does to a figure
• Congruent Figures — [8.G.2] same size and shape — and the moves that prove it
• Transformations on the Coordinate Plane — [8.G.3] apply transformation rules to coordinates
• Similarity and Dilations — [8.G.4] scale a figure up or down and keep its shape
• Angles in Triangles and Parallel Lines — [8.G.5] the angle sum and the parallel-line angle pairs
• Pythagorean Theorem — [8.G.7] a² + b² = c² for any right triangle
• Distance with the Pythagorean Theorem — [8.G.8] find the distance between two points on the plane
• Volume of Cylinders, Cones, and Spheres — [8.G.9] the three curved-solid volume formulas, side by side
• Angle Relationships — [8.G.5] complementary, supplementary, vertical, and adjacent angles
• Surface Area of Prisms, Cylinders, and Pyramids — [8.G.9] add up every face — nets make it visible
• Volume of Pyramids — [8.G.9] one-third of the matching prism
• Composite Figures: Area and Perimeter — [8.G.9] break an odd shape into shapes you already know
• Interior Angles of Polygons — [8.G.5] the (n − 2) × 180° rule for any polygon
• Triangle Inequality Theorem — [8.G.5] which three lengths can actually close into a triangle
• Surface Area of Spheres — [8.G.9] the 4πr² formula and where it shows up
• Arc Length and Area of Sectors — [8.G.9] a slice of a circle — its curved edge and its area
• Cross Sections of 3D Figures — [8.G.9] the 2D shape you get when you slice a solid
• Parallel Lines and Transversals — [8.G.5] name and use every angle pair a transversal creates
• Applying the Pythagorean Theorem — [8.G.7] real-world right-triangle problems: ladders, ramps, diagonals
• Volume of Cones and Spheres — [8.G.9] focused practice on the two trickiest volume formulas

Statistics and Probability

• Scatter Plots — [8.SP.1] read clustering, outliers, and the direction of a trend
• Fitting a Line to Data — [8.SP.2] draw a trend line and find its slope and intercept
• Using a Linear Model — [8.SP.3] use the trend line to predict and to interpret slope
• Two-Way Tables — [8.SP.4] organize categorical data and read relative frequencies
• Mean Absolute Deviation — [8.SP.4] measure how spread out a data set really is
• Probability: Simple and Compound — [8.SP.4] single-event probability and combining events
• Counting Principle and Permutations — [8.SP.4] count outcomes by multiplying — and when order matters
• Box Plots and IQR — [8.SP.4] the five-number summary, the box, and the spread of the middle
• Random Sampling — [8.SP.4] why a fair sample beats a biased one, and how to scale up
• Effect of Data Changes — [8.SP.4] what adding or scaling values does to mean, median, and range
• Probability of Compound Events — [8.SP.4] and/or events, with and without replacement

Financial Literacy

• Simple Interest — [8.PFL.1] I = Prt — interest that grows on the original amount only
• Compound Interest — [8.PFL.2] interest that earns interest, period after period
• Percents: Tax, Discount, and Markup — [8.PFL.3] the everyday percent problems behind every receipt
• Cost of Credit and Loans — [8.PFL.4] what borrowing really costs once interest is counted
• Payment Methods — [8.PFL.5] cash, debit, credit, and checks — the math and the trade-offs
• Saving for College — [8.PFL.6] set a goal, plan a monthly amount, and let growth help

How to use these worksheets at home

You do not need a study plan that spans the whole school year. A steady weekly rhythm beats a frantic catch-up session every time. Pick two afternoons — one mid-week, one on a slow weekend morning — and treat each PDF as a single sitting. Most take fifteen to twenty minutes, short enough that a tired eighth grader will actually sit down and finish.

A pairing that works well: do a skill, then do the skill that stands on top of it. Run Slope as a Rate of Change one day and Slope and the Equations of a Line the next, and the second feels like a natural continuation. The same goes for Properties of Integer Exponents before Understanding Scientific Notation, or What Is a Function? before Reading Function Values. And hold back from rescuing too quickly: if a student stalls, send them back to the Quick Review and its worked example rather than to you.

Homework happens in every kind of setting — a kitchen table, a library, a bus, the quiet half hour before dinner. Print what you need the night before, keep the answer key for after the work is done, and let your student check their own thinking. That last step — finding their own slip, reading why the correct step is correct — is where most of the learning actually happens.

A note about Grade 8 math standards

Grade 8 mathematics is generally organized around a few connected strands: the number system, expressions and equations, functions, geometry, and statistics and probability. The defining feature of the year is the move into algebra and functions — linear equations in one and two variables, systems of equations, and a first formal definition of what a function is. A student who is steady there is steady in eighth grade, and walks into high school algebra on solid ground.

These standards are worth taking seriously on their own terms, whether or not a particular test is on the calendar. They describe what a well-prepared eighth grader should be able to do before a high school algebra course — interpret a graph, set up an equation from a word problem, reason about a geometric figure, and choose the approach that fits the question. Those are reasoning tasks, not arithmetic tasks, and that skill set carries forward for years.

Because every PDF here targets one Grade 8 skill, you can use the whole set as a checklist. If a student is shaky on functions or on the Pythagorean theorem, that gap shows plainly — and you can put time into exactly those PDFs rather than re-reviewing material already in hand. Since this is general practice rather than test prep, it works any time of year — a fall tune-up, a winter reset, a summer stretch, or steady support alongside whatever the classroom is covering that week.

Want everything in one bundle?

If you would rather have a full, organized program than a scattered set of files, the bundle pulls everything together into a single, coherent path through Grade 8 — full-length practice that strings the skills together.

Grade 8 Math Preparation Bundle — four practice-test books, full-length practice tests, and complete answer keys with step-by-step explanations.

A short closing

Eighth-grade math is a climb, but it is a steady one — a student gets there one skill, one afternoon at a time. Bookmark this page, print a single PDF tonight, and let your student start somewhere small. Kids do hard things well when the next step is clear, and a worksheet on the table is about as clear as it gets.