Colorado CMAS Grade 6 Math Free Worksheets: Printable Grade 6 Math Practice with Full Solutions

Sixth-grade math has a way of sneaking up on a family. The homework looks roughly like it always has — numbers, a few words, a box for the answer — but the thinking underneath has changed. A student is suddenly asked to compare quantities with a ratio, to divide one fraction by another, to make sense of a number below zero, and to treat a letter as a stand-in for something unknown. None of it is impossible. All of it is new.

What sixth grade is really doing is laying foundations. Ratios, rates, and percents become the groundwork for proportional reasoning. Negative numbers and the coordinate plane open up the full number system. Expressions, one-step equations, and inequalities are the first real algebra. Area, volume, surface area, and nets build spatial reasoning, and the year ends with statistics — mean, median, spread, dot plots, box plots — and an introduction to probability. Strong foundations, but a lot of them, poured in one year.

These 72 worksheets let a student pour one section at a time. Whether your sixth grader is in Denver, Colorado Springs, Aurora, or Boulder, each PDF gives them a single skill, a clear example, and the practice to set it firmly.

What’s on this page

Seventy-two single-skill PDFs, each aligned to the Colorado Mathematics Standards at Grade 6. Each file holds to one skill. A student practicing unit rates is not also being asked about box plots, and a student working through nets is not being pulled into equations. The focus is the feature.

Every PDF opens with a one-page Quick Review — the skill explained plainly, with one example worked all the way through. Then 20 practice problems that build from easy to genuinely challenging, then 4 word problems that anchor the skill in a real situation. The last page is a student-facing answer key with short, friendly explanations, written so a sixth grader can check their work and understand a mistake without help.

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

Pick a rhythm and keep it. Two afternoons a week, one worksheet each, is enough to make steady progress without making math the enemy. The PDFs take about fifteen to twenty minutes — short by design, because a focused short page beats a long unfocused one every time.

Pair related skills so each page sets up the next. “Understanding Integers” before “Graphing Points on the Coordinate Plane” puts the negatives in place before the four quadrants need them. “Writing Algebraic Expressions” before “Solving One-Step Equations” gives a student the language before the task. Sequencing the skills this way turns the worksheets into a staircase instead of a pile.

In Colorado, homework happens between a lot of other things — practices, the drive home from the mountains, the early dark of a winter afternoon in Boulder or Aurora. The routine fits anyway: print the page the night before, keep the answer key until the work is finished, and then hand it over so your student can grade their own thinking. Reading the explanation after a miss is the part that actually teaches.

When you sit down together, try to keep your own role light. The instinct to jump in the second a sixth grader hesitates is strong, but a few seconds of productive struggle is where the thinking happens. If they are truly stuck, point them back to the worked example at the top of the page rather than walking them through the answer — the example was put there for exactly that moment. A student who learns to get themselves unstuck has gained something more durable than a single correct answer.

A note about CMAS at Grade 6

Colorado students take CMAS — the Colorado Measures of Academic Success — for Mathematics in the spring. It is built on the Colorado Mathematics Standards, the same framework these worksheets are aligned to, so practice here points directly at what the test asks.

The Grade 6 CMAS expects students to reason as well as compute. A student might need to interpret a ratio in context, work with negative numbers on the coordinate plane, write and solve a one-step equation, find area, volume, or surface area, or describe the center and spread of a data set. Because each PDF isolates a single standard, the spring window doubles as a checklist — you can spot the few skills that still need work and spend your time precisely there.

A short closing

Sixth-grade math is a foundation a student builds one section at a time, and no single section is out of reach. Bookmark this page, print one PDF tonight, and let your sixth grader start small. Colorado kids do solid, steady work when the next step is clear — and a worksheet on the table is a clear next step.

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