District of Columbia DC CAPE Grade 8 Math Free Worksheets: 72 Free Printable Math Practice PDFs

Somewhere in eighth grade, math quietly changes its job description. For years it has been about getting the number — adding, dividing, converting, finishing. Then a DC student opens a unit on functions and suddenly the question is not “what is the answer” but “what is the rule.” Slope becomes a rate, not a fraction to compute. An equation can have one solution, no solution, or every solution at once. That is a different kind of thinking, and almost every kid feels the ground shift a little when it arrives.

The geometry moves the same way. Eighth grade is when students meet the Pythagorean theorem, slide and spin and reflect figures across a coordinate plane, and reason about the volume of cylinders, cones, and spheres. None of it is meant to be memorized cold — it is meant to be understood as a set of relationships that hold up no matter what numbers you plug in. And underneath the whole year sits a fuller picture of the real number system: irrational numbers, scientific notation, and the laws of exponents that make very large and very small numbers manageable.

These worksheets were built for that specific stretch. Whether your student walks to school in Capitol Hill, takes the bus from Petworth, or studies at a kitchen table in Anacostia, the goal is the same — one clear skill at a time, with enough honest practice to make it hold.

What’s on this page

You will find seventy-two single-skill PDFs, each aligned to the District of Columbia Mathematics Standards for Grade 8. Every file does one job. A student practicing systems of equations is not also being quizzed on scatter plots, and a student working through volume is not getting pulled sideways into exponent rules. That focus is the whole point — it keeps practice from turning into a blur.

Each PDF opens with a one-page Quick Review that lays out the skill in plain words, followed by a fully worked example so the student can see the steps before trying their own. Then come twenty practice problems that climb from warm-up to genuinely demanding, plus four word problems that drop the skill into a real situation. The last page is a student-facing answer key — not bare answers, but short, friendly explanations a student can read on their own and actually learn something from.

Real Numbers

• Rational and Irrational Numbers — [8.NS.1, 8.NS.2] 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, 8.EE.4] 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, 8.SP.3] build y = mx + b from a slope and a point
• Solving Linear Equations in One Variable — [8.EE.7, 8.EE.8] 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, 8.F.4, 8.F.5] 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.2, 8.G.3, 8.G.4] 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.6, 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, 8.SP.2] 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.F.2, 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 an elaborate system. A calm, repeatable weekly rhythm will always beat a frantic weekend catch-up. Pick two slots — maybe a weekday afternoon and a quiet stretch on the weekend — and treat each PDF as one sitting. Most run fifteen to twenty minutes, short enough that a worn-out eighth grader will still sit down for it.

A pairing trick that works: do a skill, then immediately do the skill that leans on it. Run Properties of Integer Exponents one day and Understanding Scientific Notation the next, and the second one feels like a logical next step rather than a brand-new wall. The same holds for Slope as a Rate of Change before Slope and the Equations of a Line, or What Is a Function? before Reading Function Values. You are building a staircase, not scattering bricks.

DC is small on a map and dense with learning — museums on the Mall, libraries in every quadrant, a Metro ride that can turn into review time if you let it. Print what you need the night before so the morning is not a scramble. Keep the answer key aside until the work is done, then hand it over and let your student check their own reasoning. That last move — reading the explanations and seeing where a step went sideways — is where the real learning tends to happen.

A note about DC CAPE at Grade 8

District of Columbia students take the DC Comprehensive Assessment of Performance and Equity (DC CAPE) in Mathematics in the spring. It is built on the District of Columbia Mathematics Standards, so the skills these worksheets target and the skills the test measures are drawn from the same well.

The Grade 8 DC CAPE asks for more than clean arithmetic. It expects a student to read a graph and say what it means, build an equation out of a word problem, reason carefully about a geometric figure, and choose which approach actually fits the question in front of them. It mixes question types and leans heavily on the algebra-and-functions strand that defines eighth-grade math.

Because every PDF here is tied to a single Grade 8 standard, the spring window can double as a checklist. If your student is solid on the Pythagorean theorem but wobbly on comparing functions, you can see that plainly and spend your time exactly there — instead of re-reviewing things they already own.

A short closing

Eighth-grade math is a climb, but it is the kind you make one step at a time. Bookmark this page, print a single PDF tonight, and let your student begin somewhere small and specific. DC kids handle hard things well when the next move is clear — and a worksheet sitting on the table is about as clear as a next move gets.

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