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Grade 6

What Math Does a 6th Grader Learn? All 27 Topics, in Order

By Knomi Learning · Updated

The short answer

A 6th grader learns 27 math topics, in 6 units: The Number System, Ratios and Percents, Negative Numbers, Expressions and Equations, Geometry and Statistics. That is 86 smaller skills in all, taught in the order below, each building on earlier ones.

  • The earlier topics 6th grade leans on most: Understanding Decimals (Grade 5), Multiplying Fractions (Grade 5), Multiplying Within 100 (Grade 3), Adding and Subtracting (Grade 4) and Multi-Step Problems (Grade 4).
  • All 86 skills are matched to a Common Core standard.
  • Every one of them has a full lesson on Knomi.

Unit 1: The Number System

1

Multi-Digit Division

Long division becomes a dependable, step-by-step routine for whole numbers of any size. It is the last of the four whole-number algorithms, and decimal division, unit rates and averages all run on it.

What it covers

  • Partial Quotients
  • Long Division
  • Remainders and Estimates

Builds on

  • Grade 5: Division with Two-Digit Divisors
  • Grade 5: Multiplying Large Numbers
  • Grade 5: Decimals and Powers of Ten
  • Grade 5: Fractions as Division
  • Grade 4: Subtracting Multi-Digit Numbers
  • Grade 4: Rounding Whole Numbers
  • and 2 more
Multi-Digit Division on the 6th grade map
2

Decimal Arithmetic

Add, subtract and multiply decimals of any length with the same pencil-and-paper methods used for whole numbers. Grade 5 did this with drawings; now it becomes quick, reliable routine, and almost everything else this year leans on it.

What it covers

  • Adding Decimals
  • Subtracting Decimals
  • Multiplying Decimals

Builds on

  • Grade 5: Decimal Place Value to Thousandths
  • Grade 5: Multiplying Large Numbers
  • Grade 5: Decimals and Powers of Ten
  • Grade 5: Rounding Decimals
  • Grade 4: Adding Multi-Digit Numbers
  • Grade 4: Subtracting Multi-Digit Numbers
Decimal Arithmetic on the 6th grade map
3

Dividing Decimals

Long division carried on past the decimal point: decimal answers, dividing a decimal, and dividing by a decimal. This is the skill behind unit prices, averages and most real-world rates.

What it covers

  • Decimal Quotients
  • Dividing by a Decimal
  • Decimal Division Word Problems

Builds on

  • Grade 5: Fractions as Division
  • Grade 5: Decimal Place Value to Thousandths
  • Grade 5: Decimals and Powers of Ten
  • Grade 5: Rounding Decimals
  • Grade 4: Making Equivalent Fractions
  • Grade 4: Multi-Step Word Problems
  • and 1 more
Dividing Decimals on the 6th grade map
4

Factors and Multiples

Find the greatest common factor and least common multiple of two numbers, and know which one a problem is asking for. These two ideas sit under fraction work now and under factoring in algebra later.

What it covers

  • Factors and Prime Factorization
  • Greatest Common Factor
  • Least Common Multiple
  • Factoring Sums

Builds on

  • Grade 5: Expressions and Grouping Symbols
  • Grade 4: Factor Pairs and Multiples
  • Grade 3: Multiplication Fact Fluency
  • Grade 3: Distributive Property with Arrays
Factors and Multiples on the 6th grade map
5

Dividing Fractions

What it means to divide a fraction by a fraction, and how to do it: pictures first, the 'multiply by the reciprocal' shortcut after. It completes the fraction arithmetic begun in Grades 3–5.

What it covers

  • Fractions and Whole Numbers
  • Meaning of Fraction Division
  • Reciprocals and Mixed Numbers
  • Fraction Division Word Problems

Builds on

  • Grade 5: Dividing Whole Numbers by Unit Fractions
  • Grade 5: Multiplying Fractions by Fractions
  • Grade 4: Making Equivalent Fractions
  • Grade 4: Mixed Numbers and Improper Fractions
  • Grade 4: Perimeter and Area of Rectangles
  • Grade 3: Division as Sharing and Grouping
Dividing Fractions on the 6th grade map

Unit 2: Ratios and Percents

6

Understanding Ratios

Compare two quantities with a ratio, like 2 cups of juice for every 3 cups of water. It is the biggest new idea of the year, and it grows into rates, percents and, later, slope.

What it covers

  • Ratio Language
  • Part and Whole Ratios

Builds on

  • Grade 4: Times-as-Many Comparisons
  • Grade 3: Multiplication Fact Fluency
Understanding Ratios on the 6th grade map
7

Equivalent Ratios

2:3, 4:6 and 10:15 all describe the same relationship. Your kid uses tables, double number lines and graphs to scale a ratio up or down, which is how recipes get doubled and fair comparisons get made.

What it covers

  • Ratio Tables
  • Double Number Lines
  • Graphing and Comparing Ratios
  • Sharing in a Ratio

Builds on

  • Grade 5: Coordinate Plane Basics
  • Grade 5: Generating and Comparing Number Patterns
  • Grade 4: Making Equivalent Fractions
  • Grade 3: Multiplication Fact Fluency
  • Grade 2: Number Lines
Equivalent Ratios on the 6th grade map
8

Unit Rates

'How much for one?' The price of one ounce, the miles in one hour. With a unit rate your kid can compare deals, predict travel times and convert between units of measure.

What it covers

  • Rates and Unit Rates
  • Unit Price and Speed Problems
  • Comparing Rates
  • Converting Units

Builds on

  • Grade 5: Fractions as Division
  • Grade 5: Decimal Place Value to Thousandths
  • Grade 5: Converting Metric Units
  • Grade 4: Multi-Step Word Problems
Unit Rates on the 6th grade map
9

Percents

Percent means 'per 100'. With that one idea your kid finds a percent of an amount and works backwards to the whole, so discounts, test scores and battery levels all start to make sense.

What it covers

  • Meaning of Percent
  • Percents, Fractions and Decimals
  • Percent of a Quantity
  • Finding the Whole
  • Finding the Percent

Builds on

  • Grade 5: Decimals and Powers of Ten
  • Grade 5: Multiplying Fractions by Fractions
  • Grade 4: Decimals and Fractions on Number Lines
  • Grade 4: Making Equivalent Fractions
Percents on the 6th grade map

Unit 3: Negative Numbers

10

Negative Numbers

Numbers below zero: temperatures, depths, debts. Place negative whole numbers, fractions and decimals on a number line and see every number as having an opposite.

What it covers

  • Positive and Negative Quantities
  • Integers and Opposites
  • Negative Fractions and Decimals

Builds on

  • Grade 4: Decimals and Fractions on Number Lines
  • Grade 4: Mixed Numbers and Improper Fractions
  • Grade 3: Placing Fractions on the Number Line
  • Grade 2: Number Lines
Negative Numbers on the 6th grade map
11

Order and Absolute Value

Compare and order positive and negative numbers, and learn absolute value: a number's distance from zero. Your kid also learns to keep two ideas apart: which number is greater, and which is bigger in size.

What it covers

  • Comparing Rational Numbers
  • Absolute Value
  • Absolute Value and Order

Builds on

  • Grade 5: Decimal Place Value to Thousandths
  • Grade 4: Comparing with Unlike Denominators
  • Grade 4: Decimals and Fractions on Number Lines
  • Grade 2: Number Lines
Order and Absolute Value on the 6th grade map
12

Coordinate Plane

The grid from Grade 5 grows to all four quadrants, using negative coordinates. Your kid plots points, spots reflections and finds distances, which sets up graphing for the rest of school.

What it covers

  • Four Quadrants
  • Reflections Across the Axes
  • Distance on the Plane

Builds on

  • Grade 5: Coordinate Plane Basics
  • Grade 4: Line Symmetry
Coordinate Plane on the 6th grade map

Unit 4: Expressions and Equations

13

Exponents

A short way to write repeated multiplication, such as 2^5 for 2 × 2 × 2 × 2 × 2. Exponents show up right away in area and volume formulas and stay through all of algebra.

What it covers

  • Meaning of Exponents
  • Powers of Whole Numbers
  • Powers of Fractions

Builds on

  • Grade 5: Decimals and Powers of Ten
  • Grade 5: Multiplying Large Numbers
  • Grade 5: Multiplying Fractions by Fractions
  • Grade 4: Perimeter and Area of Rectangles
  • Grade 3: Multiplication Fact Fluency
Exponents on the 6th grade map
14

Order of Operations

The agreed order for working out a calculation with several steps: parentheses, then exponents, then multiplying and dividing, then adding and subtracting. It makes sure everyone reads the same expression the same way.

What it covers

  • Order with Exponents
  • Expressions with Fractions and Decimals

Builds on

  • Grade 5: Expressions and Grouping Symbols
  • Grade 5: Writing and Interpreting Expressions
  • Grade 5: Unlike Denominators
  • Grade 4: Decimals and Fractions on Number Lines
Order of Operations on the 6th grade map
15

Writing Expressions

Letters start standing for numbers, and phrases like '5 less than a number' become n − 5. This is the first real step into algebra.

What it covers

  • Variables and Parts of Expressions
  • Expressions from Words
  • Expressions from Situations

Builds on

  • Grade 5: Writing and Interpreting Expressions
  • Grade 5: Fractions as Division
  • Grade 4: Multi-Step Word Problems
  • Grade 3: Missing Factors and Divisors
Writing Expressions on the 6th grade map
16

Evaluating Expressions

Plug numbers into expressions and formulas and work out the result. It is how a formula for area, cost or distance turns into an actual answer.

What it covers

  • Substituting Values
  • Formulas and Several Variables

Builds on

  • Grade 5: Volume of Rectangular Prisms
  • Grade 4: Perimeter and Area of Rectangles
Evaluating Expressions on the 6th grade map
17

Equivalent Expressions

Expressions can look different and still mean the same thing, like 3(x + 2) and 3x + 6. Your kid uses number properties they already know to rewrite expressions in simpler or more useful forms.

What it covers

  • Distributive Property with Variables
  • Combining Like Terms
  • Identifying Equivalent Expressions

Builds on

  • Grade 3: Distributive Property with Arrays
Equivalent Expressions on the 6th grade map
18

One-Step Equations

Solving an equation means finding the number that makes it true. Your kid solves equations like x + 7 = 12 and 3x = 18 by keeping both sides balanced, and writes equations for real problems.

What it covers

  • Equations and Solutions
  • Equations with Models
  • Addition and Subtraction Equations
  • Multiplication and Division Equations
  • Equations with Fractions and Decimals
  • Equation Word Problems

Builds on

  • Grade 5: Fractions as Division
  • Grade 5: Unlike Denominators
  • Grade 4: Subtracting Multi-Digit Numbers
  • Grade 4: Multi-Step Word Problems
  • Grade 3: Missing Factors and Divisors
  • Grade 3: Relating Multiplication and Division
One-Step Equations on the 6th grade map
19

Inequalities

Describe limits such as 'taller than 48 inches' or 'under 20 dollars' with an inequality like h > 48, and show all the numbers that work on a number line.

What it covers

  • Writing and Testing Inequalities
  • Graphing Inequalities
Inequalities on the 6th grade map
20

Two-Variable Equations

Two quantities that change together, like hours worked and money earned. Your kid describes the link with an equation, a table and a graph, and moves between the three.

What it covers

  • Independent and Dependent Variables
  • Tables from Equations
  • Graphs of Relationships

Builds on

  • Grade 5: Generating and Comparing Number Patterns
  • Grade 5: Coordinate Plane Basics
Two-Variable Equations on the 6th grade map

Unit 5: Geometry

21

Area of Polygons

Move beyond rectangles to the area of parallelograms, triangles, trapezoids and odd-shaped figures. The big idea: any shape can be cut up and rearranged into shapes your kid already knows.

What it covers

  • Area of Parallelograms
  • Area of Triangles
  • Trapezoids and Other Quadrilaterals
  • Composite Figures

Builds on

  • Grade 5: Multiplying Fractions by Fractions
  • Grade 5: Classifying Quadrilaterals
  • Grade 4: Perimeter and Area of Rectangles
  • Grade 4: Parallel and Perpendicular Lines
  • Grade 4: Multi-Step Word Problems
Area of Polygons on the 6th grade map
22

Polygons on the Plane

Draw shapes on a coordinate grid from the coordinates of their corners, then use those coordinates to find side lengths, perimeter and area.

What it covers

  • Drawing Polygons with Coordinates
  • Perimeter and Area on the Plane

Builds on

  • Grade 5: Classifying Quadrilaterals
  • Grade 3: Finding Perimeter
Polygons on the Plane on the 6th grade map
23

Volume with Fractions

Find the volume of boxes whose sides are fractions, like 2 1/2 by 1 1/2 by 3 inches. Packing the box with tiny fraction-sized cubes shows why multiplying the three edges still works.

What it covers

  • Packing with Fraction Cubes
  • Volume of Prisms

Builds on

  • Grade 5: Volume of Rectangular Prisms
  • Grade 5: Multiplying Fractions by Fractions
  • Grade 4: Mixed Numbers and Improper Fractions
Volume with Fractions on the 6th grade map
24

Nets and Surface Area

Unfold boxes and pyramids into flat patterns called nets, and use them to find how much surface a solid has. It is the math of wrapping paper, paint and packaging.

What it covers

  • Nets of Solid Figures
  • Surface Area from Nets
  • Surface Area Word Problems

Builds on

  • Grade 5: Classifying Quadrilaterals
  • Grade 5: Expressions and Grouping Symbols
  • Grade 5: Volume of Rectangular Prisms
  • Grade 4: Perimeter and Area of Rectangles
  • Grade 4: Multi-Step Word Problems
  • Grade 2: Solid Shapes
Nets and Surface Area on the 6th grade map

Unit 6: Statistics

25

Data Distributions

Real statistics begins: ask questions whose answers vary, collect data, and picture it with dot plots and histograms. Your kid learns to describe what a whole set of data looks like, not just read single values.

What it covers

  • Statistical Questions
  • Dot Plots and Frequency Tables
  • Histograms
  • Shape of a Distribution

Builds on

  • Grade 5: Line Plots with Fractional Data
  • Grade 3: Scaled Bar Graphs
Data Distributions on the 6th grade map
26

Mean and Median

Two ways to sum up a set of data with one typical number: the mean (the fair-share average) and the median (the middle value). Your kid also learns when each one tells the truer story.

What it covers

  • Mean
  • Median
  • Choosing Mean or Median

Builds on

  • Grade 5: Division with Two-Digit Divisors
  • Grade 5: Decimal Place Value to Thousandths
  • Grade 4: Adding Multi-Digit Numbers
  • Grade 2: Number Lines
Mean and Median on the 6th grade map
27

Spread and Box Plots

Measure how spread out a set of data is, and draw a box plot that sums up a whole data set with five numbers. Two classes can share the same average and still look very different; this is how to see it.

What it covers

  • Range and Interquartile Range
  • Box Plots
  • Mean Absolute Deviation

Builds on

  • Grade 4: Subtracting Multi-Digit Numbers
Spread and Box Plots on the 6th grade map

Questions parents ask

How many math topics are in 6th grade?

On Knomi's map, 6th grade math has 27 topics in 6 units, made of 86 smaller skills.

What should a student know before starting 6th grade math?

The earlier topics 6th grade leans on most are Understanding Decimals (Grade 5), Multiplying Fractions (Grade 5), Multiplying Within 100 (Grade 3), Adding and Subtracting (Grade 4) and Multi-Step Problems (Grade 4). A student who is quick and sure with those is ready. Each topic below lists exactly what it builds on.

Is this 6th grade math list aligned to Common Core?

Common Core is the spine. All 86 skills carry a Common Core reference, and the order follows the usual US course.

Does Knomi teach 6th grade math?

Every one of them has a full lesson on Knomi. The 6th grade map is open to anyone, with no account needed to look around.

See 6th grade math as a map.

Every topic above, with lines to what it needs first. Open it and look around, no account needed.

Open the Grade 6 map

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