New Mexico NM-MSSA Grade 8 Math Free Worksheets: Printable Grade 8 Math PDFs with Worked Solutions

Eighth grade is the year math quietly trades arithmetic for algebra. For most of a student’s life, the work has been about producing the right number. In eighth grade, the right number becomes only part of the task — what counts now is the structure underneath it. A New Mexico student has to start treating slope as a rate of change, a function as a rule that gives every input exactly one output, and an equation as something that might have one solution, none, or infinitely many. That is a real shift in thinking, and most kids feel the weight of it.

Geometry climbs the same way. This is the year the Pythagorean theorem becomes a working tool, the year figures slide, flip, and turn across the coordinate plane, and the year volume reaches past rectangular boxes into cylinders, cones, and spheres. The goal is never to memorize a formula and forget the why — it is to reason about the relationship the formula captures. And running beneath everything is a new comfort with the real number system: irrational numbers, scientific notation, and the laws of exponents that make outsized and minuscule numbers manageable.

These worksheets were built for that exact part of the year. Whether your student is in Albuquerque, Las Cruces, Rio Rancho, or Santa Fe, the design stays the same: one clear skill at a time, with enough practice that the skill genuinely holds before the next one arrives.

What’s on this page

This page offers 72 single-skill PDFs, each aligned to the New Mexico Mathematics Standards for Grade 8. Every file does exactly one job. A student working on functions is not also being quizzed on surface area, and a student on the Pythagorean theorem is not being pulled into random sampling. That focus is deliberate — it is the cleanest path from a shaky skill to a steady one.

Each PDF opens with a one-page Quick Review that explains the skill in plain language and works through a single example from start to finish. 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 a bare list of answers, but short, friendly explanations a student can read alone and actually learn from.

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 plan that runs the length of the school year. A reliable weekly rhythm does far more than a panicked weekend. Pick two afternoons — perhaps one midweek after school and one on an unhurried weekend morning — and treat each PDF as a single sitting. Most take fifteen to twenty minutes, short enough that even a tired eighth grader will sit down and finish.

The pairing that helps most is doing a skill and then the skill that builds on it. Run Slope as a Rate of Change one day and Slope and the Equations of a Line the next, and the second sheet feels like a natural step rather than a new wall. The same works for What Is a Function? before Linear vs. Nonlinear Functions, or Properties of Integer Exponents before Understanding Scientific Notation. When the worksheets follow a sensible order, the student spends less energy lost and more energy actually working.

New Mexico spreads across a wide and varied landscape, and homework happens all over it — at a kitchen table in Albuquerque, in a house on the mesa outside Santa Fe, in the cool of an evening in a small town down near Las Cruces. Print what you need the night before so the morning runs smoothly, and keep the answer key set aside until the work is done. Then let the student check their own reasoning and read the explanations. That last step — comparing their thinking to a clear walkthrough — is where most of the real learning happens.

A note about NM-MSSA at Grade 8

New Mexico eighth graders take the New Mexico Measures of Student Success and Achievement — Mathematics, the NM-MSSA, in the spring. It is built on the New Mexico Mathematics Standards, so the skills these worksheets target and the skills the test measures come from the same source. Nothing on this page is a detour from what the state actually expects.

The Grade 8 NM-MSSA asks students to do far more than compute. It expects 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 mixes shorter items with longer, multi-step tasks, 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, you can use the spring window as a checklist. If your student is steady on geometry but uneven on functions or on the real number system, that shows up clearly — and you can spend your time exactly there, rather than re-reviewing things they already have down.

Want everything in one bundle?

If the spring NM-MSSA is coming and you would rather follow one organized program than manage a stack of loose files, the bundle pulls everything together.

New Mexico NM-MSSA Grade 8 Math Preparation Bundle — four practice-test books, full-length practice tests, and complete answer keys with step-by-step explanations.

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