Arizona AASA Grade 8 Math Worksheets: 72 Free Printable PDFs

72 free printable Arizona AASA Grade 8 math worksheets covering the grade 8 skills: real numbers, exponents and scientific notation, linear equations and inequalities, functions, geometry, statistics and probability, and financial literacy. Choose a topic, open the PDF, and print.

For a lot of Arizona families, eighth grade is the year math gets harder to help with at the kitchen table, and that is not a sign anything is going wrong. It is the year arithmetic turns into algebra. A student who used to chase a single answer now has to handle the structure behind it: slope as a rate of change, a function as a rule that pairs each input with one output, an equation that might have one solution, no solution, or infinitely many. That is a real change in how a kid has to think, and almost all of them feel it.

The geometry pushes the same way. Eighth grade brings the Pythagorean theorem, transformations on the coordinate plane, and the volume of cylinders, cones, and spheres, not as formulas to memorize cold, but as relationships to reason through. And underneath all of it is a new ease with the real number system: irrational numbers, scientific notation, and the laws of exponents.

These worksheets were built for that exact stretch. Whether your student is in Phoenix, Tucson, Mesa, or Flagstaff, 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 Arizona Mathematics Standards for 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 getting sidetracked by scatter plots.

Each PDF opens with a one-page Quick Review that explains the skill in plain language, with a fully worked example to follow along with. Twenty practice problems come next, building from straightforward up to genuinely challenging, plus four word problems that put the skill into 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, [8.NS.A, 8.NS.A.1, 8.NS.A.3] 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, 8.EE.C.7] multi-step solving: distribute, combine, isolate
• Solving Systems of Two Equations, [8.EE.C, 8.EE.C.7, 8.EE.C.8] find the point two lines share by substitution or elimination
• Solving Real Problems with Systems, [8.G.C, 8.G.C.9] turn a word problem into two equations and solve it
• Solving Linear Inequalities, [8.EE.C, 8.EE.C.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.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, 8.G.A.1] 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.B, 8.SP.B.5] 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 step rather than a jump. The same idea works for Properties of Integer Exponents before Operations with Scientific Notation, or Pythagorean Theorem before Applying the Pythagorean Theorem. Each pair lets the harder skill stand on something the student already knows.

Arizona is a state of long afternoons, and homework happens everywhere, at a table in a Phoenix apartment, on a cooler evening in Flagstaff, in the quiet stretch before dinner in Tucson. Print what you need the night before, hold onto the answer key until the work is done, and let the student check their own thinking. That last step, actually reading the explanations, is where most of the learning happens.

A note about AASA at Grade 8

Arizona students take Arizona’s Academic Standards Assessment, known as AASA, in Mathematics in the spring. It is built on the Arizona Mathematics Standards, so the skills on these worksheets and the skills on the test come from the same place.

The Grade 8 AASA asks students to do more than compute. It asks them 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 in front of them. It leans hard on the algebra-and-functions work that defines eighth-grade math, so a student who is comfortable with functions, slope, and linear equations is in good shape walking in.

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

Want everything in one bundle?

If your student is heading toward the spring AASA and you would rather have a full, organized program than a stack of separate files, the bundle pulls it all together.

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

Related free worksheets: 8th grade math worksheets · Common Core grade 8 math worksheets

Arizona 8th Grade Math Standards: What Students Learn

Arizona’s grade 8 math standards were adopted by the State Board of Education in December 2016. The Arizona Department of Education updated the grade 8 document on January 29, 2025. The update marks certain Essential Standards that will get more test questions on the AASA starting in the 2025-2026 school year. The content falls into five domains:

Every grade also includes the eight Standards for Mathematical Practice, such as making sense of problems and explaining reasoning. Use the worksheet chapters above as a checklist: if a domain in this table feels shaky, start with the matching chapter.

Frequently Asked Questions

What are the Arizona 8th grade math standards?

Arizona’s 8th grade math standards cover five domains: The Number System, Expressions and Equations, Functions, Geometry, and Statistics and Probability. Students work with irrational numbers, exponents and scientific notation, linear equations and systems, slope, transformations, the Pythagorean theorem, volume of cylinders, cones and spheres, and scatter plots. The standards were adopted in 2016 and updated in January 2025.

What is a function in math in 8th grade?

A function is a rule that gives exactly one output for each input. For y = 2x + 3, an input of 1 gives 5 and an input of 2 gives 7, and no input ever gives two different outputs. On a graph, a function passes the vertical line test. Arizona 8th graders compare functions in tables, graphs and equations, and decide whether they are linear.

Is there an Arizona AASA sample test?

Yes. The Arizona Department of Education posts AASA sample tests so students can see the question types and practice with the online testing tools before spring testing. Have your 8th grader try one at a computer, then go back to the matching single-skill worksheets for any topic that caused trouble, such as systems of equations or transformations.

How can my child practice for the AASA 8th grade math test?

Work one skill at a time first, then mix topics. Short daily sessions on single-skill worksheets build accuracy in areas like slope, exponents and the Pythagorean theorem. In the last few weeks, add a sample test or a mixed review each week so your child gets used to switching between algebra, geometry and statistics questions.

How do you place irrational numbers on a number line in 8th grade?

Estimate the value between two whole numbers, then refine it. For √20, note that 4² = 16 and 5² = 25, so √20 is between 4 and 5. Since 4.5² = 20.25, it is a little less than 4.5, about 4.47. Plot it just left of the halfway point between 4 and 5. Rational numbers like 3/4 or −2.5 are placed exactly.