Math Ladder · Middle school · Grade 8

Pre-Algebra (Grade 8)

Exponents and roots, linear equations and functions, systems, transformations and the Pythagorean theorem.

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53 topics in 11 units. Builds on Grade 7. Leads to Algebra 1. It also opens the way to Physical Science on the Physics Ladder. Not sure this is the right course? Find your rung.

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Unit 1 Exponents and Scientific Notation

8 topics

Learn the exponent rules, including zero and negative exponents, and compute in scientific notation.

  1. Multiplying Powers
  2. Dividing Powers
  3. Powers of Powers and Products
  4. Zero and Negative Exponents
  5. Using All the Exponent Rules
  6. Scientific Notation
  7. Comparing Very Large and Small Numbers
  8. Operations in Scientific Notation

Unit 2 Roots and Irrational Numbers

6 topics

Use square and cube roots, and meet numbers that are not fractions.

  1. Square Roots and Perfect Squares
  2. Cube Roots
  3. Solving x² = p and x³ = p
  4. Repeating Decimals as Fractions
  5. Irrational Numbers
  6. Estimating Square Roots

Unit 3 Linear Equations

3 topics

Solve multi-step equations and tell whether an equation has one, no, or infinitely many solutions.

  1. Multi-Step Equations
  2. Variables on Both Sides
  3. One, None or Infinitely Many Solutions

Unit 4 Functions

3 topics

Understand functions, compare them in different forms, and describe graphs in words.

  1. What Is a Function?
  2. Functions as Tables, Graphs and Rules
  3. Describing Graphs in Words

Unit 5 Slope and Lines

9 topics

Understand slope as a rate, find it from graphs and points, and write y = mx + b.

  1. Unit Rate as Slope
  2. Slope as Rate of Change
  3. Rise Over Run from a Graph
  4. Why Slope Is the Same Everywhere
  5. The Slope Formula
  6. Slope-Intercept Form
  7. Linear and Nonlinear Functions
  8. Comparing Functions in Different Forms
  9. Building Linear Models

Unit 6 Systems of Linear Equations

5 topics

Solve pairs of linear equations by graphing and substitution.

  1. What a System's Solution Means
  2. Solving Systems by Graphing
  3. Solving Systems by Substitution
  4. Parallel and Identical Lines
  5. Systems Word Problems

Unit 7 Transformations, Congruence and Similarity

6 topics

Move figures with translations, reflections, rotations and dilations, and use them to define congruence and similarity.

  1. Translations
  2. Reflections
  3. Rotations
  4. Congruence by Rigid Motions
  5. Dilations
  6. Similar Figures

Unit 8 Angles and Triangles

3 topics

Use parallel lines, triangle angle sums and angle-angle similarity.

  1. Parallel Lines Cut by a Transversal
  2. Triangle Angle Sum and Exterior Angles
  3. Angle-Angle Similarity

Unit 9 The Pythagorean Theorem

4 topics

Prove and use the Pythagorean theorem and its converse, including for distance.

  1. The Pythagorean Theorem
  2. The Converse
  3. Pythagorean Theorem in 2D and 3D
  4. Distance Between Two Points

Unit 10 Volume of Curved Solids

3 topics

Find the volume of cylinders, cones and spheres.

  1. Volume of Cylinders
  2. Volume of Cones
  3. Volume of Spheres

Unit 11 Data in Two Variables

3 topics

Make scatter plots, fit lines, use the line to predict, and read two-way tables.

  1. Scatter Plots and Association
  2. Lines of Fit
  3. Two-Way Tables
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