Grade 6 Math Free Worksheets: 72 Free Printable PDFs with Step-by-Step Answer Keys

Sixth grade is the hinge year in a student’s math life. Up to this point, the work has mostly been arithmetic — adding, subtracting, multiplying, dividing, and knowing the facts cold. Sixth grade keeps all of that, but it asks for something new on top of it: the ability to see how numbers relate, not just what they equal. A ratio compares two quantities. A rate ties one of them to time or distance. A percent is that same comparison scaled to a hundred. A student who used to ask “what’s the answer?” now has to ask “how do these pieces connect?”

That shift runs through the whole year. Negative numbers pull the number line out past zero in both directions, and the coordinate plane opens into all four quadrants. Dividing by a fraction stops being a rule to memorize and becomes a move a student can reason through. Variables move into expressions, one-step equations, and inequalities, standing in for a value that has to be found. Geometry grows into area, volume, and surface area, with nets that fold flat shapes into solids. And statistics arrives in earnest — real data, with honest questions about its center and its spread.

These 72 worksheets were built to make that big year walkable, one skill at a time. Wherever a sixth grader is learning, each PDF hands them a single idea, a clear example, and enough practice to make the idea feel ordinary.

What’s on this page

Seventy-two single-skill PDFs, each aligned to Grade 6 mathematics standards. Every file does exactly one job. A student practicing unit rates is not also being quizzed on surface area, and a student working through one-step equations is not being pulled sideways into box plots. One skill, one page of focused practice, one clear target.

Each PDF opens with a one-page Quick Review that explains the skill in plain language and walks through a fully worked example. Then come 20 practice problems that build from easy to genuinely challenging, followed by 4 word problems that put the skill in a real situation. The last page is a student-facing answer key — not bare answers, but short, friendly explanations a sixth grader can read on their own and actually learn from.

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 single most useful habit with these PDFs is sequencing them well. Sixth-grade skills arrive in families, and a worksheet always lands softer when the page before it built the foundation. Run “What Is a Ratio?” before “Finding the Unit Rate” — once a student sees that a rate is a ratio with a “per” in it, the second page reads like the next step rather than a fresh subject. Pair “Dividing Fractions by Fractions” with “Dividing Mixed Numbers” on back-to-back days, since the second is the first with one extra wrinkle. “Writing Expressions” before “Solving One-Step Equations” works the same way.

Keep the sessions short. Most of these worksheets take fifteen to twenty minutes — about the length of a sixth grader’s dependable focus on a school night. Two steady afternoons a week will carry a student further than one long, joyless weekend marathon. Keep a pencil and scratch paper handy, and resist correcting mid-problem; the answer key is there for afterward, and it does that job better than a hovering adult.

The rhythm is the same everywhere: pick the skill, do the page, check the work. That last step is where understanding settles in, so hand over the answer key and let your student grade their own thinking. Reading the explanations is not a formality — it is where most of the real learning happens.

A note about Grade 6 math standards

Grade 6 mathematics standards, across most states, organize the year into a few big strands: ratios and proportional reasoning; the number system, now stretched to include negative numbers and fraction division; expressions and equations, where variables first do real work; geometry built on area, surface area, and volume; and statistics, with real data sets and questions about their shape, center, and spread.

What ties those strands together is a move away from pure computation and toward reasoning. A sixth grader is expected to set up a ratio from a word problem, plot and interpret points across all four quadrants of the coordinate plane, solve a one-step equation or inequality, work with the area and volume of real figures, and describe what a data set actually shows. Because every PDF on this page targets exactly one of those skills, you can use the full set as a checklist. If a student is solid on percents but shaky on dividing fractions, that gap shows up clearly — and you can spend your time only where it is needed, rather than reviewing what is already secure.

Want everything in one bundle?

If you would rather hand a student a full, organized program than manage a stack of separate files, the bundle gathers everything in one place.

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 is a year of big new ideas, but no student has to meet them all at once. Bookmark this page, print a single PDF tonight, and let your sixth grader start with one skill. The year is long, but it is built from small, steady steps — and a worksheet waiting on the table is about as clear as a next step gets.