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Grade 8

What Math Does a 8th Grader Learn? All 27 Topics, in Order

By Knomi Learning · Updated

The short answer

A 8th grader learns 27 math topics, in 8 units: Roots and Exponents, Equations in One Variable, Transformations, Lines and Slope, Systems of Equations, Functions, Pythagoras and Volume and Data and Scatter Plots. That is 94 smaller skills in all, taught in the order below, each building on earlier ones.

  • The earlier topics 8th grade leans on most: Coordinate Plane (Grade 6), Two-Variable Equations (Grade 6), Exponents (Grade 6), One-Step Equations (Grade 6) and Two-Step Equations (Grade 7).
  • All 94 skills are matched to a Common Core standard.
  • Every one of them has a full lesson on Knomi.

Unit 1: Roots and Exponents

1

Square and Cube Roots

Undo squaring and cubing: find the side of a square from its area and the edge of a cube from its volume. These roots are the tool behind the Pythagorean theorem and the volume problems later in the year.

What it covers

  • Square Roots of Perfect Squares
  • Estimating Square Roots
  • Cube Roots
  • Roots of Fractions and Decimals
  • Equations with Squares and Cubes

Builds on

  • Grade 7: Signs of Products and Powers
  • Grade 7: Negative Times Negative
  • Grade 6: Powers of Whole Numbers
  • Grade 6: Multiplying Decimals
  • Grade 6: Powers of Fractions
  • Grade 6: Equations and Solutions
  • and 5 more
Square and Cube Roots on the 8th grade map
2

Irrational Numbers

Every fraction becomes a decimal that stops or repeats. Numbers like √2 and π never do either, so they cannot be written as fractions. Your kid learns to tell the two kinds apart and to pin an irrational number down on the number line.

What it covers

  • Fractions as Repeating Decimals
  • Repeating Decimals as Fractions
  • Rational or Irrational
  • Comparing Real Numbers

Builds on

  • Grade 7: Decimals That Repeat
  • Grade 7: Solving Two-Step Equations
  • Grade 7: Quotients of Integers
  • Grade 6: Decimal Quotients
  • Grade 6: Factors and Prime Factorization
  • Grade 6: Combining Like Terms
  • and 4 more
Irrational Numbers on the 8th grade map
3

Exponent Rules

Find the shortcuts for multiplying and dividing powers by writing out the repeated factors and counting them. The rules come from what an exponent means, so your kid can rebuild one if memory slips.

What it covers

  • Powers with Negative Bases
  • Multiplying and Dividing Powers
  • Powers of Powers and Products

Builds on

  • Grade 7: Signs of Products and Powers
  • Grade 6: Powers of Whole Numbers
  • Grade 6: Powers of Fractions
  • Grade 6: Order with Exponents
  • Grade 6: Meaning of Exponents
  • Grade 4: Making Equivalent Fractions
Exponent Rules on the 8th grade map
4

Integer Exponents

What could 5^0 or 2^−3 mean? Your kid follows the pattern of the exponent rules downward and finds that zero and negative exponents are forced to mean 1 and 'one over'.

What it covers

  • Zero Exponents
  • Negative Exponents
  • Rules with Integer Exponents

Builds on

  • Grade 7: Adding the Opposite
  • Grade 7: Adding Integers Fluently
  • Grade 6: Meaning of Exponents
  • Grade 6: Reciprocals and Mixed Numbers
  • Grade 6: Identifying Equivalent Expressions
  • Grade 5: Generating and Comparing Number Patterns
Integer Exponents on the 8th grade map
5

Scientific Notation

Scientists write huge and tiny numbers as a number from 1 up to 10 times a power of 10. Your kid learns to read, write, compare and calculate with them, from the distance to the sun to the width of a cell.

What it covers

  • Estimating with Powers of Ten
  • Writing Scientific Notation
  • Multiplying and Dividing
  • Adding and Subtracting
  • Scientific Notation Word Problems

Builds on

  • Grade 6: Multiplying Decimals
  • Grade 6: Dividing by a Decimal
  • Grade 6: Adding Decimals
  • Grade 6: Rates and Unit Rates
  • Grade 6: Converting Units
  • Grade 5: Decimals and Powers of Ten
  • and 3 more
Scientific Notation on the 8th grade map

Unit 2: Equations in One Variable

6

Multi-Step Equations

Solve equations that take several moves: the unknown on both sides, parentheses, fractions. Every step keeps the two sides balanced. This is the algebra the rest of the year runs on, from angle puzzles to systems.

What it covers

  • Variables on Both Sides
  • Equations with Parentheses
  • Fraction and Decimal Coefficients
  • Multi-Step Equation Word Problems
  • Rearranging Formulas

Builds on

  • Grade 7: Solving Two-Step Equations
  • Grade 7: Like Terms with Negatives
  • Grade 7: Expanding Expressions
  • Grade 7: Equations with Parentheses
  • Grade 7: Equations with Rational Numbers
  • Grade 7: Solving Two-Step Word Problems
  • and 8 more
Multi-Step Equations on the 8th grade map
7

Number of Solutions

Not every equation has exactly one answer. Some are true for every number and some for none. Your kid learns to tell which, often before finishing the algebra, and meets the same three cases again with pairs of lines.

What it covers

  • One, None or Infinitely Many
  • Building Equations by Solution Count

Builds on

  • Grade 7: Expressions in Different Forms
  • Grade 6: Equations and Solutions
  • Grade 6: Identifying Equivalent Expressions
Number of Solutions on the 8th grade map

Unit 3: Transformations

8

Rigid Transformations

Slides, flips and turns. Your kid moves shapes around the coordinate plane, describes each move exactly enough that someone else could repeat it, and finds out what these moves never change.

What it covers

  • Translations
  • Reflections
  • Rotations
  • Properties of Rigid Motions

Builds on

  • Grade 7: Adding Integers Fluently
  • Grade 6: Four Quadrants
  • Grade 6: Drawing Polygons with Coordinates
  • Grade 6: Reflections Across the Axes
  • Grade 4: Line Symmetry
  • Grade 4: Parallel and Perpendicular Lines
  • and 1 more
Rigid Transformations on the 8th grade map
9

Congruence

Two shapes are congruent when one can be moved exactly onto the other with slides, flips and turns. Your kid chains moves together and uses them to show that two shapes match, or that they cannot.

What it covers

  • Sequences of Transformations
  • Congruent Figures

Builds on

  • Grade 7: One Triangle, Many or None
  • Grade 6: Four Quadrants
Congruence on the 8th grade map
10

Angles and Parallel Lines

Why do the angles made by parallel lines match up, and why do a triangle's angles always add to 180°? Your kid finds the reasons, then uses them to chase down missing angles like a detective.

What it covers

  • Parallel Lines and Transversals
  • Triangle Angle Sum
  • Exterior Angles of Triangles
  • Angle Sums of Polygons

Builds on

  • Grade 7: Complementary and Supplementary Angles
  • Grade 7: Vertical and Adjacent Angles
  • Grade 6: Substituting Values
  • Grade 5: Classifying Quadrilaterals
  • Grade 4: Parallel and Perpendicular Lines
  • Grade 4: Classifying Triangles
  • and 1 more
Angles and Parallel Lines on the 8th grade map
11

Dilations

A dilation enlarges or shrinks a shape without changing its angles, like zooming in on a photo. Your kid learns how a center and a scale factor fix exactly where every point goes.

What it covers

  • Scale Factor and Center
  • Dilations with Coordinates

Builds on

  • Grade 7: Scaled Copies
  • Grade 7: Positive Times Negative
  • Grade 6: Four Quadrants
  • Grade 5: Multiplying Fractions by Fractions
  • Grade 4: Times-as-Many Comparisons
Dilations on the 8th grade map
12

Similarity

Similar shapes are the same shape at different sizes: equal angles, and sides in one steady ratio. Your kid uses that to find lengths that cannot be measured, and gets the reason slope works in the next unit.

What it covers

  • Similar Figures
  • Side Lengths in Similar Figures
  • Angle-Angle Similarity

Builds on

  • Grade 7: Lengths from a Scale
  • Grade 7: Solving Proportions
  • Grade 6: Ratio Tables
  • Grade 4: Making Equivalent Fractions
Similarity on the 8th grade map

Unit 4: Lines and Slope

13

Lines Through the Origin

Your kid revisits proportional relationships like cost per pound and sees the unit rate show up as the steepness of a line through the origin. It is the bridge from ratios to the algebra of lines.

What it covers

  • Graphing Proportional Relationships
  • Unit Rate as Slope
  • Comparing Proportional Relationships

Builds on

  • Grade 7: Graphs Through the Origin
  • Grade 7: Constant of Proportionality
  • Grade 7: Unit Rate on a Graph
  • Grade 7: Comparing Proportional Relationships
  • Grade 6: Graphing and Comparing Ratios
  • Grade 6: Rates and Unit Rates
  • and 2 more
Lines Through the Origin on the 8th grade map
14

Slope

Slope is one number that says how steep a line is and which way it tilts. Your kid measures it from a graph and from two points, and learns why it comes out the same anywhere on the line.

What it covers

  • Slope from a Graph
  • Slope Triangles
  • Slope from Two Points
  • Negative, Zero and Undefined Slope

Builds on

  • Grade 7: Adding the Opposite
  • Grade 7: Quotients of Integers
  • Grade 6: Distance on the Plane
  • Grade 6: Absolute Value
  • Grade 4: Making Equivalent Fractions
  • Grade 3: Division as Sharing and Grouping
Slope on the 8th grade map
15

Slope-Intercept Form

Every slanted line has an equation y = mx + b: a slope and a starting height. Your kid learns to read a line's story straight from its equation and to write the equation from its graph.

What it covers

  • Meaning of y = mx + b
  • Graphing y = mx + b
  • Equations from Graphs
  • Equations from Two Points

Builds on

  • Grade 7: Solving Two-Step Equations
  • Grade 6: Tables from Equations
  • Grade 6: Graphs of Relationships
  • Grade 6: Substituting Values
Slope-Intercept Form on the 8th grade map
16

Graphing Linear Equations

Lines do not always arrive as y = mx + b. Your kid learns that a line is the picture of every (x, y) pair that makes an equation true, and handles equations like 2x + 3y = 12, intercepts, and flat and upright lines.

What it covers

  • Solutions of Two-Variable Equations
  • Intercepts
  • Solving for y
  • Horizontal and Vertical Lines

Builds on

  • Grade 7: Solving Two-Step Equations
  • Grade 6: Tables from Equations
  • Grade 6: Equations and Solutions
  • Grade 6: Four Quadrants
Graphing Linear Equations on the 8th grade map

Unit 5: Systems of Equations

17

Systems of Equations

Two equations, two unknowns, one question: what makes both true at once? Your kid sees the answer as the point where two lines cross, and learns what it means when they never do.

What it covers

  • Solutions of a System
  • Solving Systems by Graphing
  • Number of Solutions of a System

Builds on

  • Grade 6: Equations and Solutions
  • Grade 4: Parallel and Perpendicular Lines
Systems of Equations on the 8th grade map
18

Solving Systems

Graphs can be fuzzy, so your kid learns exact ways to solve two equations at once: swap one into the other, or add them so a variable disappears. Then the methods go to work on real problems.

What it covers

  • Substitution
  • Elimination
  • Systems Word Problems

Builds on

  • Grade 7: Adding and Subtracting Expressions
  • Grade 6: Substituting Values
  • Grade 6: Least Common Multiple
Solving Systems on the 8th grade map

Unit 6: Functions

19

Functions

A function is a rule that gives exactly one output for each input, like a machine that never surprises you. Your kid learns to spot functions in tables, graphs and everyday rules.

What it covers

  • Function Rules
  • Functions in Tables
  • Functions on Graphs

Builds on

  • Grade 6: Independent and Dependent Variables
  • Grade 6: Substituting Values
  • Grade 6: Tables from Equations
  • Grade 6: Graphs of Relationships
  • Grade 6: Four Quadrants
  • Grade 5: Generating and Comparing Number Patterns
Functions on the 8th grade map
20

Linear Functions

The simplest functions grow by the same amount every step, and their graphs are straight lines. Your kid learns to recognize them, compare them, and turn a phone plan or a draining pool into one.

What it covers

  • Linear or Nonlinear
  • Rate of Change and Initial Value
  • Comparing Linear Functions
  • Writing Linear Functions
  • Interpreting Linear Models

Builds on

  • Grade 7: Proportional or Not
  • Grade 6: Rates and Unit Rates
  • Grade 6: Expressions from Situations
  • Grade 6: Graphs of Relationships
Linear Functions on the 8th grade map
21

Graphs That Tell Stories

A graph can tell a story with no numbers at all: speeding up, levelling off, heading back. Your kid learns to read those stories and to sketch a graph from one.

What it covers

  • Describing Graphs
  • Sketching Graphs from Stories

Builds on

  • Grade 6: Graphs of Relationships
  • Grade 6: Independent and Dependent Variables
Graphs That Tell Stories on the 8th grade map

Unit 7: Pythagoras and Volume

22

Pythagorean Theorem

In any right triangle, the squares on the two short sides add up to the square on the long side. Your kid sees why it is true and uses it to find a missing side.

What it covers

  • Squares on the Sides
  • Finding the Hypotenuse
  • Finding a Leg
  • Converse of the Theorem

Builds on

  • Grade 7: Solving Two-Step Equations
  • Grade 7: Triangle Side Lengths
  • Grade 6: Area of Triangles
  • Grade 6: Addition and Subtraction Equations
  • Grade 4: Classifying Triangles
  • Grade 4: Perimeter and Area of Rectangles
Pythagorean Theorem on the 8th grade map
23

Pythagorean Applications

Ladders against walls, shortcuts across a field, the diagonal of a screen. Your kid finds the hidden right triangle in real problems, between points on a grid, and inside boxes.

What it covers

  • Right Triangle Word Problems
  • Distance Between Two Points
  • Pythagorean Theorem in 3D

Builds on

  • Grade 7: Slicing Prisms
  • Grade 6: Area of Triangles
  • Grade 6: Distance on the Plane
  • Grade 6: Perimeter and Area on the Plane
  • Grade 3: Finding Perimeter
  • Grade 2: Solid Shapes
Pythagorean Applications on the 8th grade map
24

Volume of Round Solids

Cans, ice cream cones and basketballs. Your kid learns the volume formulas for cylinders, cones and spheres, sees how they are related, and uses them on real containers.

What it covers

  • Volume of Cylinders
  • Volume of Cones
  • Volume of Spheres
  • Volume Word Problems
  • Surface Area of Cylinders

Builds on

  • Grade 7: Area of a Circle
  • Grade 7: Volume of Right Prisms
  • Grade 7: Circumference
  • Grade 7: Surface Area of Prisms
  • Grade 6: Volume of Prisms
  • Grade 6: Formulas and Several Variables
  • and 5 more
Volume of Round Solids on the 8th grade map

Unit 8: Data and Scatter Plots

25

Scatter Plots

Does more practice go with higher scores? Your kid plots two measurements for each person or thing and learns to describe the pattern the cloud of points makes.

What it covers

  • Making Scatter Plots
  • Describing Association
  • Clusters and Outliers

Builds on

  • Grade 6: Four Quadrants
  • Grade 6: Independent and Dependent Variables
  • Grade 6: Dot Plots and Frequency Tables
  • Grade 6: Shape of a Distribution
  • Grade 6: Choosing Mean or Median
Scatter Plots on the 8th grade map
26

Lines of Best Fit

When a scatter plot looks roughly like a line, your kid draws the line that best follows the trend, writes its equation, and uses it to predict and to explain what the numbers mean.

What it covers

  • Fitting a Line
  • Equation of a Fitted Line
  • Interpreting Slope and Intercept
Lines of Best Fit on the 8th grade map
27

Two-Way Tables

Do kids with a curfew also tend to have chores? Your kid sorts category data into a table and uses percentages to see whether two things go together.

What it covers

  • Reading and Building Two-Way Tables
  • Relative Frequencies
  • Association in Two-Way Tables

Builds on

  • Grade 7: Relative Frequency
  • Grade 6: Dot Plots and Frequency Tables
  • Grade 6: Finding the Percent
  • Grade 6: Part and Whole Ratios
  • Grade 4: Subtracting Multi-Digit Numbers
  • Grade 4: Comparing with Unlike Denominators
  • and 1 more
Two-Way Tables on the 8th grade map

Questions parents ask

How many math topics are in 8th grade?

On Knomi's map, 8th grade math has 27 topics in 8 units, made of 94 smaller skills.

What should a student know before starting 8th grade math?

The earlier topics 8th grade leans on most are Coordinate Plane (Grade 6), Two-Variable Equations (Grade 6), Exponents (Grade 6), One-Step Equations (Grade 6) and Two-Step Equations (Grade 7). A student who is quick and sure with those is ready. Each topic below lists exactly what it builds on.

Is this 8th grade math list aligned to Common Core?

Common Core is the spine. All 94 skills carry a Common Core reference, and the order follows the usual US course.

Does Knomi teach 8th grade math?

Every one of them has a full lesson on Knomi. The 8th grade map is open to anyone, with no account needed to look around.

See 8th 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 8 map

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