North Carolina EOG Grade 6 Math Free Worksheets: Printable EOG-Ready Practice, Answers Included

There is a moment in sixth grade when a student realizes math has quietly raised its expectations. The arithmetic is still there, but it is no longer the point. The point is reasoning — comparing two quantities and seeing the relationship, taking a fraction apart by dividing it, looking at a string of symbols and reading it the way you would read a sentence.

Sixth grade in North Carolina pulls a lot of new threads into one year. Ratios, rates, and percents teach students to think proportionally. Dividing fractions asks them to understand a rule instead of just obeying it. Negative numbers stretch the number line in both directions and then anchor it to a coordinate plane with four quadrants. Algebraic expressions and one-step equations bring in the idea of an unknown. Geometry turns toward area of triangles and quadrilaterals, the volume of rectangular prisms with fractional edges, and surface area built from nets. And statistics arrives in earnest — mean, median, the spread of a data set, dot plots and box plots, and a first honest look at probability.

Whether your student is in Charlotte or Raleigh, Greensboro or Durham, or a smaller town somewhere between them, the path through all of that is the same: take one skill, practice it until it is steady, then move to the next. These worksheets are made for exactly that.

What’s on this page

This page holds seventy-two single-skill PDFs, each aligned to the North Carolina Mathematics Standards at Grade 6. Each file does one job. A student working on percent problems is not also fielding questions about surface area; a student practicing how to write an expression is not being tested on dot plots at the same time. The focus stays narrow on purpose.

Every PDF begins with a one-page Quick Review — the skill explained simply, with one example worked all the way through. After that come twenty practice problems arranged from gentle to genuinely demanding, then four word problems that drop the skill into a real-world setting. The final page is a student-facing answer key written for the student: short explanations, friendly tone, the kind of thing a sixth grader can read alone and come away understanding why an answer is what it is.

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 system. What you need is consistency, and consistency at this age means small and frequent. Two afternoons a week, one PDF each, fifteen to twenty minutes a sitting — that beats a long Saturday session that everyone dreads by Friday.

Lean on the natural order of the skills. A lot of sixth-grade math is built in pairs, where the second skill is just the first one taken one step further. Do “Understanding Percent” before “Percent of a Number.” Run “Writing Algebraic Expressions” the day before “Evaluating Algebraic Expressions.” Practice “Area of Triangles” before tackling “Area of Composite Figures.” When you stack related worksheets like that, the harder one stops feeling hard.

North Carolina families fit homework into busy evenings — between practices, before dinner, in the half hour after a long bus ride home in Durham or Greensboro. The worksheets are built to survive that reality: short, printable, self-contained. Print one the night before, hand it over, and keep the answer key for after. Letting the student check their own work, and read the explanation for whatever they missed, is the quiet engine of the whole thing.

A note about EOG at Grade 6

North Carolina students take the End-of-Grade Mathematics Test in the spring. It is built on the North Carolina Mathematics Standards, so the skills your student practices here line up directly with what the EOG will ask.

The Grade 6 EOG is not a speed-arithmetic test. It asks students to interpret a ratio or rate, to solve a multi-step problem and explain the path, to work with negative numbers and the coordinate plane, and to make sense of a data display rather than just read a number off it. Because each worksheet on this page targets one standard, you can treat the spring window as a checklist. Strong on fraction division but uneasy with expressions and equations? That gap becomes visible, and you can work it directly instead of reviewing everything at the same flat pace.

Want everything in one bundle?

If you would rather hand your student a complete, ordered program than manage a pile of individual PDFs, the bundle pulls everything together in sequence.

North Carolina EOG 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 rewards patience more than speed. Bookmark this page, print a single PDF tonight, and let your student begin with one skill on one page. North Carolina kids do steady, careful work well when the next step is laid out plainly in front of them — and a worksheet on the kitchen table is exactly that kind of plain, clear start.