Montana MAST Grade 6 Math Free Worksheets: Free Printable PDF Worksheets with Full Solutions

Sixth grade is the year math starts to branch. For five years it ran more or less in one line — bigger numbers, more operations, a steady widening of the same basic toolkit. Then sixth grade arrives and the road forks several directions at once. Ratios and rates head one way. The coordinate plane and negative numbers head another. Algebraic expressions and one-step equations open a third path, and the geometry of area, volume, and surface area a fourth. A student is suddenly traveling several routes in the same week.

That is not a problem to fix; it is just the shape of the year. But it does mean a sixth grader benefits from practice that takes one route at a time. From Billings to Missoula, from Great Falls to Bozeman, the students who do best with this material are usually not the ones who rush — they are the ones who give each new idea a clear, uncrowded space to settle.

These 72 worksheets are built to provide exactly that space. One skill per page, with enough practice to make it familiar.

What’s on this page

Seventy-two single-skill PDFs, each aligned to the Montana Mathematics Standards at Grade 6. Every file holds to one skill and nothing else. A student working on the unit rate is not also being tested on dot plots; a student practicing surface area from a net is not being pulled into fraction division. That focus is the whole point — it is what lets a fifteen-minute session actually move the needle.

Each PDF begins with a one-page Quick Review: the skill explained simply, with one example carried all the way through. Then 20 practice problems build from approachable to demanding, and 4 word problems follow to anchor the skill in something real. The last page is a student-facing answer key — written so a sixth grader can read it alone, see not just the answer but the thinking behind it, and correct course without waiting for 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

A little, often. That is the whole strategy. One worksheet is about fifteen minutes of focused work, and two sessions a week — say a weeknight and a weekend morning — add up faster than anyone expects. The goal is a habit, not a heroic effort. A sixth grader who does one page twice a week will have worked through dozens of skills by spring, and will have done it without a single exhausting study marathon.

When you choose the next page, choose with the connections in mind. Skills that lean on each other are best done close together. Pair “What Is a Ratio?” with “Finding the Unit Rate.” Pair “Dividing Fractions by Fractions” with “Dividing Mixed Numbers.” Do “Writing Algebraic Expressions” before “Solving One-Step Equations,” and “Plotting Points on the Coordinate Plane” before anything that asks for distance on the grid. Done in order, the second worksheet feels like a continuation, not a cliff.

Montana is a state of long distances and small towns, and homework happens wherever the day ends — a ranch kitchen, a table in a Bozeman apartment, the quiet hour after practice in Great Falls. Print the page ahead of time, keep the answer key until the work is done, then let your student grade themselves. That last step, reading the explanation and finding their own slip, is where a worksheet turns into actual understanding.

A note about MAST at Grade 6

Montana students take the MAST — Montana Aligned to Standards Through-year — in mathematics across three through-year windows in the fall, winter, and spring. Rather than one high-stakes session, it checks in on student progress more than once over the year, which fits naturally with steady, ongoing practice.

MAST is built on the Montana Mathematics Standards, so the skills on these worksheets and the skills on the assessment come from the same source. At Grade 6, that means reasoning with ratios and rates, dividing fractions, working with negative numbers and the coordinate plane, writing and solving expressions and equations, finding area and volume, and interpreting data. Because every PDF maps to a single standard, you can use the through-year rhythm as a series of checkpoints — and target the worksheets to whatever a given window reveals.

A short closing

The branching paths of sixth-grade math are not as daunting as they first look — a student covers them one at a time, one afternoon at a time. Bookmark this page, print a single PDF tonight, and let your student start small. Montana kids are used to steady going over long ground, and a worksheet on the table is simply the next clear step on the way.

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