Grade 8•Math skills checklist

What should an 8th grader know in math?

The complete grade 8 math skills checklist

Eighth grade is the gateway to high school mathematics. Students master linear relationships, encounter the Pythagorean theorem, and explore transformational geometry. Success here determines readiness for Algebra I.

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The Number System

Understand irrational numbers

Know that numbers like √2 and π are irrational and cannot be written as fractions.

Examples: √2 ≈ 1.414... (non-repeating), π ≈ 3.14159...

Approximate irrational numbers

Locate irrational numbers on a number line and estimate their values.

Examples: √5 is between 2 and 3 (closer to 2.2), √10 ≈ 3.16

Work with integer exponents

Apply rules for multiplying, dividing, and raising powers to powers.

Examples: x³ × x⁴ = x⁷, (x²)³ = x⁶, x⁵ ÷ x² = x³

Use scientific notation

Express and compute with very large and very small numbers.

Examples: 3,500,000 = 3.5 × 10⁶, 0.00042 = 4.2 × 10⁻⁴

Expressions & Equations

Solve linear equations in one variable

Solve equations with variables on both sides, including those with no or infinite solutions.

Examples: 3x + 5 = 2x + 12, 2(x - 3) = 2x - 6 (infinite solutions)

Solve systems of linear equations

Find the intersection of two lines using graphing or algebraic methods.

Examples: y = 2x + 1 and y = -x + 7, Solve by substitution or elimination

Understand slope

Calculate slope as rise/run and interpret it as rate of change.

Examples: Slope = (y₂ - y₁)/(x₂ - x₁), m = 3 means "up 3 for every 1 right"

Graph linear equations

Plot lines using slope-intercept form y = mx + b.

Examples: y = 2x - 3: slope is 2, y-intercept is -3

Functions

Understand function definition

Know that a function assigns exactly one output to each input

Examples: f(x) = 2x + 1, Vertical line test

Use function notation

Evaluate f(x) and interpret function notation

Examples: f(3) = 7, g(x) = x^2

Compare functions

Compare functions in tables, graphs, equations, and verbal descriptions

Examples: Which has greater slope?, Which grows faster?

Linear vs nonlinear

Identify if a function is linear from its equation, graph, or table

Examples: y = 3x - 2 is linear, y = x^2 is nonlinear

Geometry

Understand transformations

Perform and describe translations, reflections, rotations, and dilations.

Examples: Reflect over y-axis: (x,y) → (-x,y), Rotate 90° clockwise

Understand congruence and similarity

Know that congruent figures have same shape and size; similar figures have same shape.

Examples: Corresponding angles equal, Corresponding sides proportional

Apply the Pythagorean theorem

Use a² + b² = c² to find missing sides of right triangles.

Examples: Legs 3 and 4 → hypotenuse = 5, Find distance between two points

Find volume of 3D shapes

Calculate volume of cylinders, cones, and spheres.

Examples: Cylinder: V = πr²h, Sphere: V = (4/3)πr³, Cone: V = (1/3)πr²h

Statistics & Probability

Construct and interpret scatter plots

Plot bivariate data and describe patterns.

Examples: Identify positive/negative/no correlation

Use lines of best fit

Informally fit a line and use it to make predictions.

Examples: Draw trend line through scatter plot, Predict y value for given x

Interpret two-way tables

Construct and analyze two-way frequency tables.

Examples: Find conditional frequencies, Identify associations

Where grade 8 students often struggle

  • Confusing √x with x/2 (square root is NOT dividing by 2)
  • Adding exponents when they should multiply: (x²)³ = x⁶, not x⁵
  • Forgetting that vertical line test checks if graph is a function
  • Mixing up Pythagorean theorem sides: c is always the hypotenuse (longest side)
  • Scientific notation errors with negative exponents
  • Not recognizing when equations have no solution or infinite solutions

Signs your child is on track

  • Fluently applies exponent rules without looking them up
  • Graphs lines quickly from y = mx + b form
  • Uses Pythagorean theorem confidently in both directions
  • Solves multi-step equations with variables on both sides
  • Distinguishes functions from non-functions
  • Interprets slope as rate of change in context

Coming in grade 9

Mastering these grade 8 skills prepares your child for:

Linear functions in depth (Algebra I)
Solving and graphing systems of equations
Quadratic functions and equations
Exponential functions introduction
Statistical inference
Formal geometric proofs

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