Pennsylvania PSSA Grade 8 Math Free Worksheets: Free Printable PDF Worksheets for Every Skill

There is a turning point in eighth grade that catches a lot of Pennsylvania students off guard. The math used to be about producing a number. Now it is about the relationship that produces the number — slope as a rate of change, a function as a rule that gives back exactly one output for each input, an equation that may have one solution, none, or infinitely many. That is a real change in how a kid has to think, and most eighth graders feel it well before they could explain it.

The geometry takes the same turn. Eighth grade brings the rigid motions — translations, reflections, rotations — and frames congruence as the thing those motions create rather than a label handed down. It adds dilations and similarity, the Pythagorean theorem, and the volume of cylinders, cones, and spheres — all of them relationships to reason about, not formulas to memorize cold. And running through the whole year is a deeper sense of the real number system: irrational numbers, scientific notation, and the laws of exponents.

These worksheets were built for that exact stretch of the year. Whether your student is in Philadelphia, Pittsburgh, Allentown, or Erie, each PDF gives them one clear skill at a time, with enough practice to make it stick.

What’s on this page

Seventy-two single-skill PDFs, each aligned to the Pennsylvania Core Standards for Mathematics at Grade 8. Every file targets one skill and nothing else — so a student working on systems of equations is not also wrestling with scientific notation, and a student on volume is not distracted by scatter plots. The single-skill focus is what makes a student’s progress easy to read.

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 put 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 — [CC.2.1.8, CC.2.1.8.E, CC.2.1.8.E.1] tell a fraction-able number from one whose decimal never repeats
• Turning Repeating Decimals into Fractions — [CC.2.1.8, CC.2.1.8.E, CC.2.1.8.E.4] the algebra trick that turns 0.272727… into a clean fraction
• Estimating Irrational Numbers — [CC.2.1.8, CC.2.1.8.E, CC.2.1.8.E.4] pin a root like √20 between two whole numbers, then closer
• Estimating Expressions with Irrational Numbers — [CC.2.1.8, CC.2.1.8.E, CC.2.1.8.E.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 — [CC.2.2.8, CC.2.2.8.B, CC.2.2.8.B.1] product, quotient, power, zero, and negative-exponent rules
• Square Roots and Cube Roots — [CC.2.2.8, CC.2.2.8.B, CC.2.2.8.B.3] undo a square or a cube, including the ± on x² equations
• Understanding Scientific Notation — [CC.2.2.8, CC.2.2.8.B, CC.2.2.8.B.1] move the decimal the right way for huge and tiny numbers
• Operations with Scientific Notation — [CC.2.1.8, CC.2.1.8.E, CC.2.1.8.E.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 — [CC.2.4.8, CC.2.4.8.B, CC.2.4.8.B.1] read the unit rate straight off a proportional graph
• Slope as a Rate of Change — [CC.2.4.8, CC.2.4.8.B, CC.2.4.8.B.2] slope is just rise over run — a real-world rate
• Slope and the Equations of a Line — [CC.2.2.8, CC.2.2.8.B, CC.2.2.8.B.2] build y = mx + b from a slope and a point
• Solving Linear Equations in One Variable — [CC.2.2.8, CC.2.2.8.B, CC.2.2.8.B.3] multi-step solving: distribute, combine, isolate
• Solving Systems of Two Equations — [CC.2.2.8, CC.2.2.8.B, CC.2.2.8.B.3] find the point two lines share by substitution or elimination
• Solving Real Problems with Systems — [CC.2.3.8, CC.2.3.8.A, CC.2.3.8.A.1] turn a word problem into two equations and solve it
• Solving Linear Inequalities — [CC.2.2.8.B] 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? — [CC.2.4.8, CC.2.4.8.B, CC.2.4.8.B.2] every input gets exactly one output — and how to check
• Reading Function Values — [CC.2.2.8, CC.2.2.8.C, CC.2.2.8.C.1] evaluate f(x) and read values from tables and graphs
• Comparing Two Functions — [CC.2.4.8, CC.2.4.8.B, CC.2.4.8.B.2] compare functions given as equations, tables, and graphs
• Linear vs. Nonlinear Functions — [CC.2.2.8, CC.2.2.8.B, CC.2.2.8.B.3] constant rate of change means linear — everything else does not
• Building Linear Functions — [CC.2.2.8, CC.2.2.8.C, CC.2.2.8.C.2] write the function from a description, a table, or two points
• Sketching and Describing Function Graphs — [CC.2.2.8, CC.2.2.8.C, CC.2.2.8.C.2] 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 — [CC.2.3.8, CC.2.3.8.A, CC.2.3.8.A.1] the three rigid motions and what each does to a figure
• Congruent Figures — [CC.2.3.8, CC.2.3.8.A, CC.2.3.8.A.2] same size and shape — and the moves that prove it
• Transformations on the Coordinate Plane — [CC.2.2.8, CC.2.2.8.B, CC.2.2.8.B.2] apply transformation rules to coordinates
• Similarity and Dilations — [CC.2.3.8, CC.2.3.8.A, CC.2.3.8.A.2] 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 — [CC.2.3.8, CC.2.3.8.A, CC.2.3.8.A.3] a² + b² = c² for any right triangle
• Distance with the Pythagorean Theorem — [CC.2.3.8, CC.2.3.8.A, CC.2.3.8.A.3] find the distance between two points on the plane
• Volume of Cylinders, Cones, and Spheres — [CC.2.3.8.A.1] the three curved-solid volume formulas, side by side
• Angle Relationships — [CC.2.3.8, CC.2.3.8.A, CC.2.3.8.A.2] 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 — [CC.2.3.8.A.1] focused practice on the two trickiest volume formulas

Statistics and Probability

• Scatter Plots — [CC.2.4.8, CC.2.4.8.B, CC.2.4.8.B.1] read clustering, outliers, and the direction of a trend
• Fitting a Line to Data — [CC.2.2.8, CC.2.2.8.C, CC.2.2.8.C.2] draw a trend line and find its slope and intercept
• Using a Linear Model — [CC.2.4.8, CC.2.4.8.B, CC.2.4.8.B.2] use the trend line to predict and to interpret slope
• Two-Way Tables — [CC.2.4.8, CC.2.4.8.B, CC.2.4.8.B.2] 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 plan as long as the school year. A steady weekly rhythm beats a weekend cram every time. Pick two afternoons — maybe one mid-week after school and one on a slow Sunday — and treat each PDF as a single sitting. Most take fifteen to twenty minutes, short enough that a tired eighth grader will actually do it.

A pairing that works well: do a skill, then do the skill that builds on it. Run Solving Linear Equations in One Variable one day and Solving Systems of Two Equations the next, and the second worksheet feels like a natural step instead of a new mountain. The same goes for Properties of Integer Exponents before Understanding Scientific Notation, or Rotations, Reflections, and Translations before Transformations on the Coordinate Plane. When skills connect, work them in that order.

Pennsylvania runs from river city to ridge country, and homework happens everywhere across it — at a kitchen table in Philadelphia, on a back step in a Pittsburgh neighborhood, in the quiet hour before a Friday night game in a small town in the coal region. 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 — reading the explanations — is where most of the learning actually happens.

A note about the PSSA at Grade 8

Pennsylvania eighth graders take the Pennsylvania System of School Assessment (PSSA) in Mathematics in the spring. It is built on the Pennsylvania Core Standards for Mathematics, so the skills on these worksheets and the skills on the test come from the same source.

The Grade 8 PSSA asks students to do more than compute. They have to interpret a graph, set up an equation from a word problem, reason about a geometric figure, and decide which of several approaches actually fits the question. It mixes multiple-choice with open-ended items, and it leans hard on the algebra-and-functions strand — slope, linear equations, systems, and the function concept — that defines eighth-grade math.

Because every PDF here targets one Grade 8 standard, you can use the spring window as a checklist. If your student is shaky on functions or on the Pythagorean theorem, you can see it clearly and work just those PDFs, rather than re-reviewing things they already have down.

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. Pennsylvania kids do hard things well when the next step is clear, and a worksheet on the table is about as clear as it gets.

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