Vermont SBAC Grade 8 Math Free Worksheets: Free Printable PDF Worksheets with Worked Solutions

Somewhere in the first stretch of eighth grade, Vermont students tend to hit a quiet realization: the math is not just bigger, it is different. The work has shifted from finding answers to understanding rules. That is the move from arithmetic to algebra, and it is the whole reason eighth grade exists as its own distinct year rather than a slightly harder version of seventh.

The change threads through every topic. Slope becomes a rate of change — something you read and interpret, not only something you calculate. A function becomes a dependable rule, pairing each input with exactly one output. An equation might resolve to one solution, to none, or to infinitely many, and learning to recognize which is now part of the work. Geometry moves the same way: the Pythagorean theorem, rigid transformations on the coordinate plane, and the volume of cylinders, cones, and spheres show up as relationships to reason through instead of formulas to recite. And the real number system grows to include irrational numbers, scientific notation, and the laws of exponents.

These worksheets were built for that exact part of the year. Whether your student is in Burlington, Essex, Rutland, or Montpelier, the plan does not change — one clear skill at a time, with enough practice that it holds before the next idea comes along.

What’s on this page

This page holds seventy-two single-skill PDFs, each aligned to the Vermont Mathematics Standards at Grade 8. The format is deliberately tight: one skill per file, with nothing else crowding in. A student practicing linear inequalities is not also being tested on volume, and a student on the Pythagorean theorem is not getting diverted into two-way tables. That focus is what lets a wobbly skill turn into a solid one.

Each PDF begins with a one-page Quick Review — the skill explained in plain language, with one example worked all the way through. Twenty practice problems follow, sequenced so they open gently and build toward something genuinely demanding, plus four word problems that put the skill into a real-world setting. The final page is a student-facing answer key, written to be read alone: short, friendly explanations rather than a bare list of answers.

Real Numbers

• Rational and Irrational Numbers — [8.NS.A, 8.NS.A.1] tell a fraction-able number from one whose decimal never repeats
• Turning Repeating Decimals into Fractions — [8.NS.A, 8.NS.A.1] the algebra trick that turns 0.272727… into a clean fraction
• Estimating Irrational Numbers — [8.NS.A, 8.NS.A.2] pin a root like √20 between two whole numbers, then closer
• Estimating Expressions with Irrational Numbers — [8.NS.A, 8.NS.A.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.A, 8.EE.A.1] product, quotient, power, zero, and negative-exponent rules
• Square Roots and Cube Roots — [8.EE.A, 8.EE.A.2] undo a square or a cube, including the ± on x² equations
• Understanding Scientific Notation — [8.EE.A, 8.EE.A.3] move the decimal the right way for huge and tiny numbers
• Operations with Scientific Notation — [8.EE.A, 8.EE.A.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.B, 8.EE.B.5] read the unit rate straight off a proportional graph
• Slope as a Rate of Change — [8.EE.B, 8.EE.B.5] slope is just rise over run — a real-world rate
• Slope and the Equations of a Line — [8.EE.B, 8.EE.B.6] build y = mx + b from a slope and a point
• Solving Linear Equations in One Variable — [8.EE.C.7a, 8.EE.C.7b, 8.EE.C.8b] multi-step solving: distribute, combine, isolate
• Solving Systems of Two Equations — [8.EE.C.8a, 8.EE.C.8b] find the point two lines share by substitution or elimination
• Solving Real Problems with Systems — [8.EE.C, 8.EE.C.8, 8.EE.C.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.C.7b] 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.A, 8.F.A.1] every input gets exactly one output — and how to check
• Reading Function Values — [8.F.A, 8.F.A.1] evaluate f(x) and read values from tables and graphs
• Comparing Two Functions — [8.F.A, 8.F.A.2] compare functions given as equations, tables, and graphs
• Linear vs. Nonlinear Functions — [8.F.A, 8.F.A.3] constant rate of change means linear — everything else does not
• Building Linear Functions — [8.F.B, 8.F.B.4] write the function from a description, a table, or two points
• Sketching and Describing Function Graphs — [8.F.B, 8.F.B.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.A.1a, 8.G.A.1b, 8.G.A.1c] the three rigid motions and what each does to a figure
• Congruent Figures — [8.G.A, 8.G.A.2] same size and shape — and the moves that prove it
• Transformations on the Coordinate Plane — [8.G.A, 8.G.A.3] apply transformation rules to coordinates
• Similarity and Dilations — [8.G.A, 8.G.A.4] scale a figure up or down and keep its shape
• Angles in Triangles and Parallel Lines — [8.G.A.5] the angle sum and the parallel-line angle pairs
• Pythagorean Theorem — [8.G.B, 8.G.B.6, 8.G.B.7] a² + b² = c² for any right triangle
• Distance with the Pythagorean Theorem — [8.G.B, 8.G.B.8] find the distance between two points on the plane
• Volume of Cylinders, Cones, and Spheres — [8.G.C, 8.G.C.9] the three curved-solid volume formulas, side by side
• Angle Relationships — [8.G.B, 8.G.B.7] 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.A.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.A.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.C, 8.G.C.9] focused practice on the two trickiest volume formulas

Statistics and Probability

• Scatter Plots — [8.SP.A, 8.SP.A.1] read clustering, outliers, and the direction of a trend
• Fitting a Line to Data — [8.SP.A, 8.SP.A.2] draw a trend line and find its slope and intercept
• Using a Linear Model — [8.SP.A, 8.SP.A.3] use the trend line to predict and to interpret slope
• Two-Way Tables — [8.SP.A, 8.SP.A.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 sprawling plan. You need a steady one. A student who works two short PDFs a week, every week, will be in much better shape by spring than one who tries to cram a stack into a single weekend. Find two times your week already holds — a weeknight after supper, a slow morning on Saturday — and treat each worksheet as one focused sitting. Most take fifteen to twenty minutes, short enough that even a tired eighth grader will sit down for it.

It helps to pair worksheets so each leans on the one before. Run Properties of Integer Exponents, then Understanding Scientific Notation a day or two on, and the second feels like a natural step instead of a fresh climb. The same works for Scatter Plots before Fitting a Line to Data, or Rotations, Reflections, and Translations before Transformations on the Coordinate Plane. Each pairing hands your student a foothold before asking for the next reach.

Vermont winters make the indoor table the center of a lot of evenings, which is not a bad thing for math practice. Whether that table is in a Burlington apartment or a farmhouse kitchen out in a hill town, the routine is the same: print the night before so morning stays calm, keep the answer key until the work is done, then let your student grade their own page. Reading the explanation behind a missed problem is the moment the learning really lands.

A note about SBAC at Grade 8

Vermont eighth graders take the Vermont SBAC — Mathematics in the spring. It is built on the Vermont Mathematics Standards, so the skills these worksheets practice and the skills the test measures come from the same framework.

The Grade 8 SBAC asks for more than computation. It is a computer-based test that expects students to interpret graphs, translate word problems into equations, reason about geometric figures, and select the strategy that genuinely fits the problem. It uses a range of question types — including ones that ask students to explain or show their reasoning — and it leans firmly into the algebra-and-functions work that anchors eighth-grade math.

Because every PDF here targets one Vermont standard, the run-up to spring works as a checklist. If your student is steady on geometry but shaky on functions, you will see it clearly, and you can spend your time on the functions PDFs instead of re-reviewing skills they already have down.

A short closing

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

Best Bundle to Ace the Vermont SBAC Grade 8 Math Test

Want the fastest path through Vermont SBAC Grade 8 math? This bundle pulls it together — four full practice-test books with complete, step-by-step answer keys, instant PDF download.

Vermont VTCAP Grade 8 Math Preparation Bundle

Download

$64.99 Original price was: $64.99.$49.99Current price is: $49.99.