New Hampshire NH SAS Grade 6 Math Free Worksheets: Printable Standards-Aligned Practice with Answers

If you want to know what sixth-grade math feels like from the inside, watch a student work a percent problem for the first time. They know what a fraction is. They know what a decimal is. And now they are being told that percent is a third way of saying the same thing — and that all three can be traded for one another mid-problem. The math is not impossible. It is just asking the student to hold more ideas at once and to move between them flexibly. That, more than any single new topic, is the real demand of sixth grade.

You can see that demand at work in classrooms from Manchester to Nashua, from Concord to Dover. The year stretches a student across ratios and rates, the division of fractions, negative numbers and the coordinate plane, algebraic expressions and one-step equations and inequalities, the geometry of area and volume and surface area, and the beginnings of real statistics. None of it is out of reach — but all of it goes better when a student can practice one strand at a time, without the others crowding in.

These 72 worksheets give a student that uncrowded room. One skill, one page, enough practice to make it stick.

What’s on this page

Seventy-two single-skill PDFs, each aligned to the New Hampshire Mathematics Standards at Grade 6. Every file is built around one skill and only that skill. A student working on the unit rate is not simultaneously being quizzed on surface area; a student practicing one-step equations is not being pulled into dot plots. That deliberate narrowness is what makes a fifteen-minute sitting actually count.

Each PDF opens with a one-page Quick Review: the skill explained in plain language, with one example carried fully through. Then 20 practice problems build from gentle to genuinely tough, and 4 word problems follow to root the skill in something a student can picture. The last page is a student-facing answer key — written so a sixth grader can read it alone, see the reasoning and not just the result, and correct their own course.

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 a long schedule, only a steady one. A worksheet is about a fifteen-minute commitment — short enough that a sixth grader will actually do it on a school night — and two a week, done reliably, beats a single long session by a wide margin.

The habit worth building is doing connected skills together. The worksheets fall into natural pairs, and a pair worked back to back makes the second one feel like a continuation instead of a fresh start. Pair “Understanding Percent” with “Percent of a Number.” Pair “Dividing Fractions by Fractions” with “Dividing Mixed Numbers.” Do “Writing Algebraic Expressions” before “Solving One-Step Equations,” and learn to plot points before measuring distances on the grid. Each pairing turns two lessons into one idea that holds together.

Homework in New Hampshire happens wherever the evening lands — a kitchen table in a Manchester neighborhood, a quiet house outside Concord, the hour after dinner in Dover. Print the page the night before, keep the answer key aside until the work is finished, then let your student grade their own thinking against it. That self-check, reading the explanation and finding their own mistake, is the part of the practice where the learning actually settles.

A note about NH SAS at Grade 6

New Hampshire students take the NH SAS — the New Hampshire Statewide Assessment System — in mathematics in the spring. It is built on the New Hampshire Mathematics Standards, which means the skills on these worksheets and the skills on the assessment are drawn from the same expectations.

At Grade 6, the NH SAS asks students to do more than calculate. It asks them to reason through ratio and rate problems, work confidently with fractions and decimals, handle negative numbers and the coordinate plane, write and solve expressions and equations, find area and volume, and interpret real data sets. Because each PDF here targets a single standard, the whole collection works as a checklist — you can see plainly which skills are solid and which still want a few more passes before the spring window.

A short closing

The flexibility sixth-grade math asks for is built, not born — a student grows it one skill, one afternoon at a time. Bookmark this page, print a single PDF tonight, and let your student start somewhere small and clear. New Hampshire kids do careful, independent work well when the next step is in plain sight, and a worksheet on the table puts it there.

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