Vermont SBAC Grade 6 Math Free Worksheets: Free Printable PDF Worksheets with Worked Solutions

Sixth-grade math is where a lot of the ideas a student will use for years quietly get introduced. The negative numbers that will matter all through algebra. The coordinate plane that geometry and functions will live on. The variable that turns a sentence into an equation. None of it is presented with fanfare — it just appears in the year’s work, one topic after another, and a student who gets a real grip on each one walks into seventh grade with the ground already solid under them.

The year asks for a lot at once: ratios, rates, and percents; dividing a fraction by a fraction; fluent multi-digit and decimal arithmetic; integers and the four-quadrant coordinate plane; algebraic expressions, one-step equations, and inequalities; area, volume, and surface area, including nets; and the beginnings of statistics — mean, median, spread, dot plots, box plots, and a first taste of probability. The trick is not speed. It is patience, one skill at a time.

These worksheets were built with exactly that patience in mind. Whether your student is in Burlington, Essex, Rutland, or Montpelier, they hand over one clear skill at a time, with enough practice for it to take hold.

What’s on this page

Seventy-two single-skill PDFs, each aligned to the Vermont Mathematics Standards at Grade 6. Every file stays on one skill and nothing more — so a student working on dividing decimals is not also fighting through box plots, and a student learning the coordinate plane is not pulled sideways into surface area.

Each PDF starts with a one-page Quick Review that explains the skill in plain language and walks through a single worked example. Twenty practice problems follow, climbing from easy to genuinely challenging, then four word problems that put the skill into a real setting. The last page is a student-facing answer key — short, friendly explanations a sixth grader can read alone and actually learn from, not just a column of answers.

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 way to make these count is to work them in related pairs. Sixth-grade skills sit close to one another, and doing two connected sheets in the same week lets the second build on the first instead of starting cold. Try “Understanding Percent” then “Percent of a Number.” Try “Adding and Subtracting Integers” then “Plotting Points in Four Quadrants.” Try “Writing Expressions” then “Solving One-Step Equations.” The connection between them is doing some of the teaching for you.

Keep the sessions short and steady — fifteen to twenty minutes, twice a week. That rhythm outworks a long, dreaded cram, and a sixth grader is much more likely to agree to something that finishes soon. Let your student work the whole page first, then go through the answer key together. The checking is not a formality; reading why a step works is usually where the understanding actually arrives.

Vermont has long, quiet evenings for a good part of the year, and a single worksheet fills twenty minutes of one without any drama. Print what you need ahead of time, keep the answer key for after, and let the student do the reasoning out loud. When a sheet turns out to be hard, treat it as a signpost rather than a setback — it has just told you precisely which skill needs another pass, and a single named skill is far easier to face again than a vague sense of being behind. It also helps to mark progress out loud. Sixth graders keep a quiet tally of what they can and cannot do, and naming a skill they have clearly mastered makes them more willing to open the next file.

A note about SBAC at Grade 6

Vermont students take the SBAC — the Smarter Balanced Assessment Consortium test — in Mathematics each spring. It is built on the Vermont Mathematics Standards, so the skills these worksheets practice and the skills the test measures are drawn from the same standards.

The Grade 6 SBAC is not a recall test. It asks students to interpret a ratio or rate in context, reason about negative quantities, set up an equation from a word problem, and choose an approach that genuinely fits the question. It pairs selected-response items with problems that ask a student to show or explain their thinking. Because each PDF here maps to a single standard, the spring window doubles as a checklist — find the shaky skills, work just those pages, and leave the steady ones alone.

Want everything in one bundle?

If the spring SBAC is ahead and you would rather have one organized program than a folder of loose files, the bundle pulls everything together.

Vermont SBAC 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 built quietly, one skill at a time, and that is exactly how a student should approach it. Bookmark this page, print a single PDF tonight, and let your child start small and specific. Vermont kids do patient, steady work well — and a worksheet on the table turns a large year into one clear, doable next step.