District of Columbia DC CAPE Grade 6 Math Free Worksheets: 72 Free Printable Math Practice PDFs

Sixth grade is the year math starts asking why as often as it asks how much. A student who could once divide on autopilot now has to explain what it means to divide by a fraction. A kid who memorized multiplication facts is suddenly asked to compare two ratios, to extend a number line below zero, and to write a relationship as an expression with a letter standing in for something unknown. It is a genuine shift in thinking, and most sixth graders feel the ground move a little under them.

In a city as compact and various as Washington, that transition happens in a hundred different settings — a row house in Petworth, an apartment near Capitol Hill, a kitchen in Anacostia where a parent is helping with homework between shifts. Wherever the table is, the math is the same: ratios and rates and percents, fluent operations with multi-digit and decimal numbers, the coordinate plane stretched into all four quadrants, one-step equations and inequalities, area and volume and surface area, and the first real taste of statistics.

These worksheets were built for that exact stretch of the year. Each one hands a student a single skill, with enough practice to make it stick before the next idea arrives.

What’s on this page

Seventy-two single-skill PDFs, each aligned to the District of Columbia Mathematics Standards at Grade 6. Every file targets one skill and only that skill — so a student working on unit rate is not also untangling area of a triangle, and a student practicing how to divide mixed numbers is not pulled sideways into box plots.

Each PDF opens with a one-page Quick Review that lays out the skill in plain language, with one example worked all the way through. Then come twenty practice problems that climb from gentle to genuinely challenging, followed by four word problems that drop the skill into a real situation. The last page is a student-facing answer key — not a bare list of answers, but short, friendly explanations a sixth grader can read alone and actually learn something 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

You do not need an elaborate schedule. A short, steady rhythm beats a long Saturday cram every time. Pick two afternoons a week, treat each PDF as one sitting, and stop when it is done — most take fifteen to twenty minutes, which is about the honest attention span of a sixth grader at the end of a school day.

The most useful trick is to pair a skill with the skill that grows out of it. Run “What Is a Ratio?” one day and “Finding the Unit Rate” the next, and the second sheet feels like a natural next step rather than a fresh wall. The same goes for “Dividing Fractions by Fractions” before “Dividing Mixed Numbers,” or “Plotting Points on the Coordinate Plane” before you reach into the negative quadrants. Skills that were taught together review well together.

DC families move through a lot of routines in a small footprint — the Metro ride, the after-school program, the walk home past the same corner store. Fold the worksheet into one of those routines instead of fighting for a brand-new slot in the day. Print what you need the night before, keep the answer key aside until the work is finished, and let your child check their own thinking. That last step, reading the explanation for a missed problem, is where most of the real learning lives.

A note about DC CAPE at Grade 6

Students in the District take the DC Comprehensive Assessment of Performance and Equity — the DC CAPE — in mathematics in the spring. It is built on the District of Columbia Mathematics Standards, which are aligned to the Common Core, so the skills practiced on these worksheets and the skills measured on the test trace back to the same source.

At Grade 6, the DC CAPE asks for more than a correct number. It asks students to reason about a ratio, to set up and solve a one-step equation from a word problem, to interpret a data display, and to choose an approach that actually fits the question in front of them. Because every PDF here targets a single standard, you can treat the spring window as a checklist: if your child is shaky on dividing fractions or on the coordinate plane, you will see it plainly and can work just those files, instead of re-reviewing everything they already have down.

Want everything in one bundle?

If your child is heading toward the spring DC CAPE and you would rather have one organized program than a growing stack of separate files, the bundle pulls it all together.

District of Columbia DC CAPE 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 climb, but it is a steady one — a student gets up it one skill, one afternoon at a time. Bookmark this page, print a single PDF tonight, and let your child start somewhere small and winnable. DC kids do hard things when the next step is clear, and a worksheet on the table is about as clear as a next step gets.