Alaska AK STAR Grade 8 Math Free Worksheets: Standards-Aligned Practice PDFs, No Signup Required

Somewhere in eighth grade, math stops being a list of procedures and starts being a way of reasoning. An Alaska student who has spent years getting the right number now has to think about the structure behind it — what slope actually measures, why a function is a rule and not just a picture, how an equation can have exactly one solution, none at all, or infinitely many. That shift is real, and most eighth graders feel the ground move a little under them.

The geometry shifts too. This is the year the Pythagorean theorem shows up and turns out to be useful everywhere — finding a missing side, measuring the distance between two points, checking whether a corner is truly square. Students rotate, reflect, and translate figures on the coordinate plane, and they learn to find the volume of cylinders, cones, and spheres. And threaded through all of it is a new relationship with the real number system: irrational numbers, scientific notation, and the laws of exponents.

These worksheets were made for that part of the year. Whether your student is in Anchorage, Fairbanks, Juneau, or Wasilla, each PDF gives them one clear skill at a time, with enough practice to make it settle in.

What’s on this page

Seventy-two single-skill PDFs, each aligned to the Alaska Mathematics Standards for Grade 8. Every file holds to one skill and one skill only — so a student working through systems of equations is not also tangled up in scientific notation, and a student on volume is not getting pulled away by scatter plots.

Each PDF starts with a one-page Quick Review that explains the skill in plain language and walks all the way through a worked example. Twenty practice problems follow, built to rise from straightforward to genuinely demanding, and then four word problems that set the skill inside a real context. The final page is a student-facing answer key — not just the answers, but short, approachable explanations a student can read alone and actually use to learn.

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.2] 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.3] 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.8] 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.7] 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.2] 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, 8.G.2, 8.G.4] the three rigid motions and what each does to a figure
• Congruent Figures — [8.G.1] 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.1] 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.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.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.3, 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

There is no need for a plan that stretches the whole school year. A steady weekly habit beats a last-minute scramble every single time. Choose two afternoons — maybe one in the middle of the week and one on a quiet weekend — and treat each PDF as a single sitting. Most take fifteen to twenty minutes, which is short enough that even a tired eighth grader will actually do it.

The pairing that works best is simple: do a skill, then do the skill built on top of it. Try Slope as a Rate of Change one day and Slope and the Equations of a Line the next, and the second worksheet feels like a natural next step rather than a brand-new mountain. The same goes for Scatter Plots before Fitting a Line to Data, or Rotations, Reflections, and Translations before Transformations on the Coordinate Plane. Each pairing lets the second, harder skill rest on something solid.

Alaska winters make for long, dark evenings, and that is honestly good news for homework — there is time and quiet for it. Math happens at a kitchen table in Fairbanks, by a woodstove in a small town off the road system, in the hour before dinner in Juneau. Print what you need the night before, keep the answer key until the work is finished, and let your student check their own thinking. Reading those explanations is where most of the learning really lands.

A note about AK STAR at Grade 8

Alaska students take the Alaska System of Academic Readiness — Mathematics, known as AK STAR, in the spring. It is built on the Alaska Mathematics Standards, so the skills on these worksheets and the skills on the test come from exactly the same source.

The Grade 8 AK STAR asks students to do more than crunch numbers. It wants them to interpret a graph, set up an equation from a word problem, reason carefully about a geometric figure, and choose the approach that genuinely fits the question. It leans hard on the algebra-and-functions strand at the heart of eighth-grade math, so a student who is steady on linear equations, functions, and slope walks in well prepared.

Because every PDF here targets one Alaska standard, you can treat the lead-up to the spring window as a checklist. If your student is unsteady on functions or the Pythagorean theorem, it will show plainly, and you can work just those PDFs rather than reviewing everything all over again.

A short closing

Eighth-grade math is a climb, but it is a steady one — a student gets there one skill and one afternoon at a time. Bookmark this page, print a single PDF tonight, and let your student begin somewhere small. Alaska 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 gets.

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