Arizona AASA Grade 6 Math Free Worksheets: Printable Practice for Every Sixth-Grade Math Skill

Ask a sixth grader what they did in math today and you might hear a dozen unrelated-sounding things: ratios, then negative numbers, then something about a coordinate plane, then dividing one fraction by another. It can feel scattered. It isn’t. Sixth grade is the year math widens out from arithmetic into the four big ideas — proportional reasoning, the rational number system, algebraic thinking, and statistics — that the rest of school math is built on.

The widening is real, though, and most students feel the stretch. A ratio asks them to compare instead of count. A negative number asks them to think below zero. An expression with a letter in it asks them to hold a number they don’t know yet. And a box plot asks them to summarize a whole list of numbers in one picture. Each idea is reasonable on its own — the difficulty is meeting all of them in a single year.

That is exactly what these 72 worksheets are for. Whether your student is in Phoenix, Tucson, Mesa, or Flagstaff, each PDF takes one of those ideas, breaks off a single skill, and gives a student a clear path through it.

What’s on this page

Seventy-two single-skill PDFs, each aligned to the Arizona Mathematics Standards at Grade 6. Each file is built around one skill and nothing else, so practice stays focused. A student working on percent problems is not also fielding questions about nets, and a student on mean and median is not being asked about inequalities at the same time.

Every PDF begins with a one-page Quick Review: the skill in plain language, plus one example worked from start to finish. After that come 20 practice problems arranged easy to hard, then 4 word problems that show the skill at work in a real setting. The closing page is a student-facing answer key with short, friendly explanations — written so a sixth grader can check the work and learn from a mistake on their own.

Ratios, Rates, and Percents

• What Is a Ratio? — [6.RP.1] compare two quantities and write the comparison three ways
• Using Ratio Language — [6.RP.1] describe a ratio in words — ‘for every,’ ‘to,’ and ‘per’
• What Is a Rate? — [6.RP.2] a ratio that compares two different units, like miles per hour
• Finding the Unit Rate — [6.RP.2] divide to find the cost or amount for exactly one
• Tables of Equivalent Ratios — [6.RP.3] build a ratio table and fill in the missing values
• Graphing Ratios — [6.RP.3] plot a ratio table and see the straight line it makes
• What Is a Percent? — [6.RP.3] a percent is just a ratio out of 100 — and how to read it
• Solving Percent Problems — [6.RP.3] find the part, the percent, or the whole
• Solving Rate and Ratio Word Problems — [6.RP.3] turn a real-world story into a ratio you can solve
• Converting Measurement Units — [6.RP.3] use ratios to switch between units like feet and inches
• Personal Financial Literacy — [6.RP.3] real-money math: prices, tips, and simple percent work
• Proportional vs. Non-Proportional Relationships — [6.RP.2] tell which relationships keep a constant ratio and which don’t
• Financial Literacy: Budgeting and Saving — [6.RP.3] plan a budget, track spending, and set a savings goal
• Ratios with Scale Drawings — [6.RP.3] use a scale to move between a drawing and real life

The Number System

• Dividing Fractions by Fractions — [6.NS.1] multiply by the reciprocal — and understand why it works
• Multi-Digit Division — [6.NS.2] the standard algorithm for dividing large whole numbers
• Decimal Operations — [6.NS.3] add, subtract, multiply, and divide decimals cleanly
• Greatest Common Factor and Least Common Multiple — [6.NS.4] find the GCF and LCM and know when to use each
• The Distributive Property with Common Factors — [6.NS.4] rewrite a sum by pulling out the greatest common factor
• Understanding Positive and Negative Numbers — [6.NS.5] what negative numbers mean in temperature, money, and elevation
• Opposites and Absolute Value — [6.NS.7] opposites flip the sign; absolute value is distance from zero
• Rational Numbers on the Number Line — [6.NS.6] place fractions, decimals, and negatives exactly where they go
• The Coordinate Plane — [6.NS.6] plot points in all four quadrants using ordered pairs
• Comparing and Ordering Rational Numbers — [6.NS.7] use the number line to order positives, negatives, and fractions
• Distance on the Coordinate Plane — [6.NS.8] find the distance between two points that share a line
• Integer Addition and Subtraction — [6.NS.5] add and subtract positives and negatives with confidence
• Integer Multiplication and Division — [6.NS.5] the sign rules for multiplying and dividing integers
• Compute with Integers in Context — [6.NS.5] real situations where negative numbers do the work

Expressions and Equations

• Exponents and Order of Operations — [6.EE.1] evaluate powers and run PEMDAS in the right order
• Translating Words into Expressions — [6.EE.2] turn a phrase into an algebraic expression
• Terms, Factors, and Coefficients — [6.EE.2] name the parts of an expression so you can talk about them
• Evaluating Expressions — [6.EE.2] substitute a value for the variable and compute
• Equivalent Expressions — [6.EE.3] use properties to show two expressions are the same
• Variables in Real-World Problems — [6.EE.6] let a letter stand for an unknown and model a situation
• Solving One-Step Equations — [6.EE.7] undo one operation to isolate the variable
• Writing Inequalities — [6.EE.8] translate ‘at least,’ ‘no more than,’ and ‘fewer than’ into symbols
• Graphing Inequalities on a Number Line — [6.EE.8] open or closed circle, then shade the right direction
• Two Quantities That Change Together — [6.EE.9] independent and dependent variables, tables, and graphs

Geometry

• Area of Triangles — [6.G.1] one-half base times height — for every kind of triangle
• Area of Parallelograms and Trapezoids — [6.G.1] the area formulas for two more four-sided shapes
• Volume of Rectangular Prisms — [6.G.2] volume with fractional edge lengths, using unit cubes
• Polygons on the Coordinate Plane — [6.G.3] draw a polygon from coordinates and find its side lengths
• Finding Area on the Coordinate Plane — [6.G.3] use coordinates to find the area of a plotted figure
• Nets and Surface Area — [6.G.4] unfold a solid into a net and add up every face
• Transformations on the Coordinate Plane — [6.G.3] slide and reflect figures and track the new coordinates
• Area of Circles Introduction — [6.G.1] a first look at radius, diameter, and the area of a circle

Statistics and Probability

• Statistical Questions — [6.SP.1] tell a question that has variability from one that does not
• Describing Data: Center, Spread, and Shape — [6.SP.2] the three things every data set has — and how to name them
• Mean and Median — [6.SP.3] two measures of center and when each one tells the truth
• Measures of Spread — [6.SP.3] range and mean absolute deviation — how spread out the data is
• Dot Plots and Histograms — [6.SP.4] two ways to picture how often each value shows up
• Box Plots — [6.SP.4] the five-number summary and the box it builds
• Summarizing Data and Making Comparisons — [6.SP.5] describe a data set in a sentence and compare two of them
• Introduction to Probability — [6.SP.5] how likely is it — from impossible to certain, as a number
• Stem-and-Leaf Plots — [6.SP.4] organize a data set while keeping every original value
• Circle Graphs — [6.SP.4] read a pie chart and connect each slice to a percent
• Data Displays Extended — [6.SP.4] choose the right graph and read it carefully

Number and Operations Practice

• Writing Ratios in Different Forms — [6.RP.1] the same ratio as a fraction, with a colon, and in words
• Equivalent Ratios — [6.RP.3] scale a ratio up or down and keep it the same
• Comparing Unit Rates — [6.RP.2] find the better buy by comparing rates for one
• Proportions and Cross Multiplication — [6.RP.3] set two ratios equal and solve for the missing value
• Simplifying Fractions — [6.NS.4] divide out the common factor to write a fraction lowest-terms
• Adding Fractions with Unlike Denominators — [6.NS.4] find a common denominator, then add
• Subtracting Fractions with Unlike Denominators — [6.NS.4] find a common denominator, then subtract
• Adding and Subtracting Mixed Numbers — [6.NS.4] work with the whole and fraction parts, including regrouping
• Multiplying Fractions — [6.NS.1] multiply across — and simplify before or after
• Multiplying Mixed Numbers — [6.NS.1] rename as improper fractions, then multiply
• Dividing Fractions — [6.NS.1] keep, change, flip — divide by multiplying the reciprocal
• Dividing Mixed Numbers — [6.NS.1] rename as improper fractions, then divide
• Decimal Place Value — [6.NS.3] name each digit’s value, from tenths to thousandths
• Comparing and Ordering Decimals — [6.NS.7] line up the place values and order decimals correctly
• Area of Rectangles and Squares — [6.G.1] length times width — including fractional and decimal sides

How to use these worksheets at home

The simplest plan is the one that actually happens. Choose two afternoons a week and protect them. Each worksheet is one sitting, usually fifteen to twenty minutes, and that short length is the point — a sixth grader will finish a focused page far more reliably than an open-ended hour of “do some math.”

Lean on the way the skills connect. Run “What Is a Ratio?” first, then “Finding the Unit Rate,” and a student sees the unit rate as just a ratio simplified to one. Do “Dividing Fractions by Fractions” before “Dividing Mixed Numbers,” and the harder page becomes a small extension instead of a new wall. When skills are practiced as families, momentum builds on its own.

Arizona homework happens in a lot of settings — a cooled kitchen after a hot Phoenix afternoon, a porch in Flagstaff where the evening is already crisp. Wherever it lands, the routine holds: print the page ahead of time, keep the answer key for afterward, and let your student grade their own work. The few minutes spent reading why an answer was wrong are the minutes that teach.

If a worksheet exposes a gap, treat it as good news rather than bad. A single-skill page that goes poorly has done its job — it found the weak spot precisely, while there is still plenty of year left to fix it. Set that one PDF aside, work a skill your student is steadier on to rebuild some confidence, and circle back to the hard one a few days later. Spaced out like that, a stubborn skill usually gives way, and your student learns that struggling with a page is part of the process, not a verdict on whether they are “a math person.”

A note about AASA at Grade 6

Arizona students take AASA — Arizona’s Academic Standards Assessment — for Mathematics in the spring. It is built on the Arizona Mathematics Standards, the very framework these worksheets are aligned to, so what your student practices on this page and what the test measures are drawn from the same place.

The Grade 6 AASA expects more than getting an answer. It asks students to interpret a ratio in context, reason with positive and negative numbers, locate points across the coordinate plane, write and solve a one-step equation, work with area, surface area, and volume, and describe a data set’s center and spread. Since every PDF here isolates one standard, the spring window can function as a checklist: identify the handful of skills that still need work and aim your time precisely there.

Want everything in one bundle?

If a complete, organized program sounds better than juggling separate files, the bundle brings it all together.

Arizona AASA Grade 6 Math Preparation Bundle — four practice-test books, full-length practice tests, and complete answer keys with step-by-step explanations.

A short closing

Sixth-grade math only looks scattered from a distance; up close it is one clear skill after another. Bookmark this page, print a single PDF tonight, and let your student begin somewhere small. Arizona kids do steady, serious work when the next step is laid out in front of them — and a worksheet on the table lays it out plainly.