New York NYSTP Grade 6 Math Free Worksheets: 72 Free Printable Practice Worksheets with Keys

Ask a sixth grader in New York what changed about math this year and you may get a shrug, but the change is real. Fifth grade was mostly about getting numbers to behave — line up the decimals, find the common denominator, carry the one. Sixth grade asks something harder. It asks a student to compare quantities, to reason about what a number means, and to start describing the world with letters instead of just digits.

That shift shows up everywhere at once. Ratios and unit rates turn “how much” into “how much per.” Dividing fractions stops being a rule to memorize and becomes a question worth understanding. Negative numbers walk off the number line and onto a full coordinate grid. Expressions and one-step equations introduce the quiet idea that a letter can stand for something you do not know yet. And the geometry — area of triangles, volume of boxes, the surface area of a shape unfolded into a net — rewards students who can picture things, not just plug into formulas.

From a classroom in Buffalo to a kitchen table in Yonkers, from Rochester to a sixth-grade hallway in New York City, the work is the same: one skill at a time, with enough practice to make it feel ordinary. That is what these worksheets are built to do.

What’s on this page

You will find seventy-two single-skill PDFs, each one aligned to the New York Mathematics Standards at Grade 6. Every file holds to a single idea. A student practicing unit rates is not also being quizzed on box plots; a student working through area of triangles is not getting pulled sideways into negative numbers. One skill, one page of focus.

Each PDF opens with a one-page Quick Review that explains the skill in plain words and walks through a worked example step by step. Then come twenty practice problems, ordered so the early ones build confidence and the later ones stretch it. Four word problems follow, putting 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 on their own and actually learn 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

The best way to use these is not all at once. Pick a couple of steady afternoons a week and treat each PDF as one short sitting — most take fifteen or twenty minutes, which is about the honest attention span of a sixth grader after a full school day.

The real trick is pairing. Skills in sixth grade come in small families, and doing them back to back makes the second one feel easy. Try “What Is a Ratio?” one day and “Finding the Unit Rate” the next. Run “Dividing Fractions by Fractions” before “Dividing Mixed Numbers.” Do a worksheet on plotting points in all four quadrants before one on finding distances on the coordinate plane. Each pairing turns a new topic into a logical next step instead of a fresh wall.

New York is a state of very different places — a sixth grader doing homework in a Manhattan apartment and one doing it in a quiet house upstate are living different days. But the rhythm that works is the same everywhere. Print what you need the night before. Let the student do the work first and check the answer key after. That last step, reading the explanation for anything they missed, is where most of the learning actually lands.

A note about NYSTP at Grade 6

New York students take the New York State Testing Program — Mathematics assessment in the spring. It is built on the New York Mathematics Standards, which means the skills practiced on these worksheets and the skills measured on the test come from exactly the same place.

The Grade 6 NYSTP asks for more than quick computation. It asks students to interpret a ratio situation, to reason through a multi-step problem, to set up a simple equation from a description, and to make sense of a data display. Because each PDF on this page targets a single standard, you can use the spring window as a checklist. If your student is solid on fractions but wobbly on the coordinate plane or on writing expressions, that shows up clearly — and you can spend time exactly where it is needed instead of reviewing everything evenly.

Want everything in one bundle?

If your sixth grader is heading toward the spring test and you would rather have one organized program than a folder of loose files, the bundle gathers it all in order.

New York NYSTP 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 real climb, but it is a gentle one when the next step is always clear. Bookmark this page, print one PDF tonight, and let your student start somewhere small — a single skill, a single page. New York kids handle hard things well when nobody is rushing them, and a worksheet on the table is about as unhurried and clear as a starting point gets.