Montana MAST Grade 8 Math Free Worksheets: Free Printable PDF Worksheets with Full Solutions

Eighth grade is the year math quietly changes its nature. For most of elementary and middle school, the work was arithmetic — get the right number, move on. In eighth grade, the right number is only half the job. Now a Montana student has to handle the structure behind the answer: slope as a genuine rate of change, a function as a rule that pairs every input with one and only one output, an equation that might resolve to one solution, no solution, or infinitely many. That is a real shift in thinking, and it asks more of a kid than the grades before it did.

The geometry moves in the same direction. Eighth grade introduces the Pythagorean theorem, transformations across the coordinate plane, and the volume of cylinders, cones, and spheres — and it treats them as relationships to reason about, not formulas to recite. Running under all of it is a fresh comfort with the real number system: irrational numbers, scientific notation, and the laws of exponents that make scale manageable. It is a lot, and it all lands in the same year.

These worksheets were built for that exact climb. Whether your student is in Billings, Missoula, Great Falls, or Bozeman, the design never changes: one clear skill at a time, with enough practice to make it hold.

What’s on this page

You will find 72 single-skill PDFs here, each aligned to the Montana Mathematics Standards for Grade 8. Every file targets exactly one skill. A student working through linear inequalities is not simultaneously being tested on volume, and a student on the Pythagorean theorem is not being pulled into two-way tables. That focus is intentional — it is the cleanest path from a shaky skill to a sure one.

Each PDF begins with a one-page Quick Review that explains the skill in plain language and walks through one fully worked example. Then come 20 practice problems that build from approachable to genuinely challenging, followed by 4 word problems that set the skill in a real context. The final page is a student-facing answer key — not bare answers, but short, friendly explanations a student can read independently and actually learn from.

Real Numbers

• Rational and Irrational Numbers — [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] 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.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] 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] 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.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.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 across the whole year. A steady weekly rhythm does far more good than a panicked weekend before a deadline. Pick two afternoons — perhaps one midweek and one on a slow weekend — and treat each PDF as a single sitting. Most take fifteen to twenty minutes, brief enough that a tired eighth grader will actually finish.

The pairing that works best is doing a skill and then the skill that grows out of it. Run Properties of Integer Exponents one day and Understanding Scientific Notation the next, and the second worksheet feels like a step rather than a wall. The same is true for What Is a Function? before Linear vs. Nonlinear Functions, or Pythagorean Theorem before Applying the Pythagorean Theorem. Building in order keeps a student moving instead of stalling.

Montana is enormous, and homework gets done across all of it — at a kitchen table in Billings, in a ranch house out on the Hi-Line, in the last quiet hour of an evening in a small town near the mountains. Print what you need the night before, set the answer key aside until the work is done, and let the student check their own reasoning afterward. Reading those explanations — comparing their thinking to a clear walkthrough — is where most of the learning actually happens.

A note about MAST at Grade 8

Montana uses the Montana Aligned to Standards Through-year — Mathematics, known as MAST. Unlike a single spring exam, MAST is a through-year model: students take it across three windows during the school year — fall, winter, and spring — so the picture of how a student is doing builds up over time rather than landing all at once at the end. It is built on the Montana Mathematics Standards, the same source these worksheets are aligned to.

That through-year structure changes how you can use this page. Because the test checks in more than once, the worksheets work as steady support all year long, not just as a March-and-April scramble. The Grade 8 MAST still asks students to do more than compute — to interpret a graph, set up an equation from a word problem, reason about a geometric figure, and choose the approach that fits — and it leans hard on the algebra-and-functions strand that defines eighth-grade math.

Because every PDF here is tied to one Grade 8 standard, each MAST window can serve as a checkpoint. After a fall or winter window, you will have a clearer sense of which skills are solid and which need work — and you can pull exactly those PDFs, instead of re-reviewing everything.

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. Montana 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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