Virginia SOL Grade 8 Math Free Worksheets: Printable SOL-Aligned Practice, No Signup Needed

Plenty of Virginia parents notice the same thing around the start of eighth grade: helping with math homework gets harder, and not because their student is struggling. It is because the subject itself has changed. Eighth grade is the crossing point from arithmetic to algebra. A student who used to be measured by whether they got the answer now has to understand the structure that produces it — the rule, the reasoning, the edge cases.

That turn shows up in every strand of the course. Slope becomes a rate of change you interpret rather than a number you simply compute. A function becomes a rule that pairs each input with exactly one output. An equation might have one solution, no solution, or infinitely many — and figuring out which has become part of the work. Geometry takes the same direction: the Pythagorean theorem, transformations on the coordinate plane, and the volume of cylinders, cones, and spheres arrive as relationships to reason about, not formulas to memorize. And the real number system widens to take in irrational numbers, scientific notation, and the laws of exponents.

These worksheets were built for that climb. Whether your student is in Virginia Beach, Norfolk, Richmond, or Chesapeake, the approach stays constant — one clear skill at a time, with enough practice that it holds before the next concept arrives.

What’s on this page

You will find seventy-two single-skill PDFs on this page, each aligned to the Virginia Standards of Learning (SOL) for Mathematics at Grade 8. Every file is built around one skill and nothing else. A student working on systems of equations is not also being quizzed on scientific notation, and a student on volume is not being pulled toward scatter plots. That narrow focus is exactly what turns a shaky skill into a reliable one.

Each PDF opens with a one-page Quick Review — the skill in plain language, with a single example worked from beginning to end. Twenty practice problems follow, arranged to start approachable and climb to genuinely challenging, plus four word problems that put the skill into a real context. The closing page is a student-facing answer key: short, friendly explanations a student can read on their own and actually learn from, not just a column of answers.

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.2] the algebra trick that turns 0.272727… into a clean fraction
• Estimating Irrational Numbers — [8.NS.1] pin a root like √20 between two whole numbers, then closer
• Estimating Expressions with Irrational Numbers — [8.NS.1] 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.PFA.1] product, quotient, power, zero, and negative-exponent rules
• Square Roots and Cube Roots — [8.NS.1] undo a square or a cube, including the ± on x² equations
• Understanding Scientific Notation — [8.NS.1] move the decimal the right way for huge and tiny numbers
• Operations with Scientific Notation — [8.NS.1] 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.CE.1, 8.PFA.3] read the unit rate straight off a proportional graph
• Slope as a Rate of Change — [8.PFA.3] slope is just rise over run — a real-world rate
• Slope and the Equations of a Line — [8.PFA.3] build y = mx + b from a slope and a point
• Solving Linear Equations in One Variable — [8.PFA.4] multi-step solving: distribute, combine, isolate
• Solving Systems of Two Equations — [8.PFA.4] find the point two lines share by substitution or elimination
• Solving Real Problems with Systems — [8.PFA.4] turn a word problem into two equations and solve it
• Solving Linear Inequalities — [8.PFA.5] 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.PFA.2] every input gets exactly one output — and how to check
• Reading Function Values — [8.PFA.2] evaluate f(x) and read values from tables and graphs
• Comparing Two Functions — [8.PFA.2] compare functions given as equations, tables, and graphs
• Linear vs. Nonlinear Functions — [8.PFA.3] constant rate of change means linear — everything else does not
• Building Linear Functions — [8.PFA.3] write the function from a description, a table, or two points
• Sketching and Describing Function Graphs — [8.PFA.3] 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.MG.3] the three rigid motions and what each does to a figure
• Congruent Figures — [8.MG.3] same size and shape — and the moves that prove it
• Transformations on the Coordinate Plane — [8.MG.3] apply transformation rules to coordinates
• Similarity and Dilations — [8.MG.3] scale a figure up or down and keep its shape
• Angles in Triangles and Parallel Lines — [8.MG.1] the angle sum and the parallel-line angle pairs
• Pythagorean Theorem — [8.MG.4] a² + b² = c² for any right triangle
• Distance with the Pythagorean Theorem — [8.MG.4] 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.MG.1] complementary, supplementary, vertical, and adjacent angles
• Surface Area of Prisms, Cylinders, and Pyramids — [8.MG.2] add up every face — nets make it visible
• Volume of Pyramids — [8.MG.2] one-third of the matching prism
• Composite Figures: Area and Perimeter — [8.MG.5] 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.MG.2] focused practice on the two trickiest volume formulas

Statistics and Probability

• Scatter Plots — [8.PS.3] read clustering, outliers, and the direction of a trend
• Fitting a Line to Data — [8.PS.3] draw a trend line and find its slope and intercept
• Using a Linear Model — [8.PS.3] use the trend line to predict and to interpret slope
• Two-Way Tables — [8.PS.3] 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.PS.1] 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.PS.2] 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

The thing that works is rhythm, not bulk. A student who does two short PDFs a week, consistently, will be far better prepared by spring than one who tries to power through a stack in one weekend. Pick two slots your week already provides — a weeknight after dinner, a calmer morning on the weekend — and let each worksheet be a single focused sitting. Most run fifteen to twenty minutes, brief enough that even a tired eighth grader will do one.

Pairing worksheets so they build on one another makes a real difference. Try Properties of Integer Exponents first, then Understanding Scientific Notation a couple of days later, and the second stops feeling like a new mountain and starts feeling like the next step. The same logic works for What Is a Function? before Comparing Two Functions, or Pythagorean Theorem before Applying the Pythagorean Theorem. Each pair gives your student a foothold before the next reach.

Virginia covers a lot of ground, and homework happens across all of it — a table in a Tidewater neighborhood near the water, a kitchen in the Piedmont, a quiet half hour somewhere in the Valley with the Blue Ridge in view. Print what you need the night before so the morning is not rushed. Keep the answer key until the work is finished, then let your student check their own page. Reading the explanation behind a missed problem is where the understanding genuinely settles in.

A note about SOL at Grade 8

Virginia eighth graders take the Standards of Learning — Mathematics assessment, known as the SOL, in the spring. As the name signals, the test is built directly on the Virginia Standards of Learning (SOL) for Mathematics — so the standards these worksheets follow and the standards the test measures are one and the same.

The Grade 8 SOL asks for more than computation. It expects students to interpret a graph, set up an equation from a word problem, reason through a geometric figure, and decide which of several approaches actually fits the question. It is a computer-based test that uses a mix of question types, and it leans firmly on the algebra-and-functions content that defines eighth-grade math — so comfort with slope, functions, and linear equations carries a student a long way through it.

Because each PDF here targets one SOL standard, the lead-up to spring works neatly as a checklist. If your student has geometry handled but functions are still loose, you will spot it, and you can spend your time on the functions PDFs instead of re-covering what they already own.

A short closing

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

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