Pre-Algebra
The bridge from arithmetic to algebra: a balance scale that stays level, and the inequality sign flipping for a visible reason.
15 units · 83 topics · 388 questions
Where numbers below zero come from, how the number line orders them, and the four operations extended to negatives.
The Number Line and Negative Numbers · Comparing and Ordering Integers · Absolute Value · Adding Integers on the Number Line · +3 more
What a repeated-multiplication shorthand buys you, and how it scales all the way from atoms to galaxies.
What Exponents Mean · Multiplying and Dividing Powers with the Same Base · Negative Exponents · Powers of Ten · +2 more
Undoing a square, undoing a cube, and the strange numbers that show up when neither one comes out even.
Perfect Squares and Square Roots · Estimating Square Roots That Aren't Perfect · Cube Roots and Perfect Cubes · Irrational Numbers · +1 more
What a letter standing in for a number buys you, and the two moves — distribute and combine — that simplify anything.
What a Variable Is · Terms, Coefficients, and Constants · Writing Expressions from Words · Evaluating Expressions · +2 more
The balance scale that keeps both sides equal, and every move — one step to many, one variable to two — that uncovers what x is.
The Balance Scale Model of an Equation · One-Step Equations · Two-Step Equations · Multi-Step Equations · +3 more
What changes — and what famously flips — when an equation's equals sign becomes greater than or less than.
What an Inequality Means · Solving One-Step and Two-Step Inequalities · Why Multiplying or Dividing by a Negative Flips an Inequality · Graphing Inequalities on a Number Line · +1 more
Comparing two quantities, boiling a rate down to one unit, and the straight line through the origin that a proportional relationship always draws.
What a Ratio Is · Unit Rates · Proportional Relationships and Their Graphs · The Constant of Proportionality · +1 more
Percent as a ratio out of 100, and the everyday math of change, interest, tax, and tip built on top of it.
What Percent Means · Percent of a Number · Percent Increase and Decrease · Simple Interest · +1 more
Plotting points in all four quadrants, reading slope as rise over run, and finding where two lines cross.
The Coordinate Plane and Its Four Quadrants · Graphing Linear Relationships · Slope as Rise Over Run · Slope-Intercept Form · +2 more
What makes an input-output rule a function, how to spot one on a graph, and the patterns that repeat with a fixed rule.
What a Function Is · Function Tables · The Vertical Line Test · Sequences and Patterns
Every angle two lines can make, how a triangle's three angles are locked together, and the theorem hiding in a tilted square.
Complementary and Supplementary Angles · Vertical Angles · Angles Formed by Parallel Lines and a Transversal · Triangle Angle Sum · +3 more
Circles, combined shapes, and the leap from flat area into the volume and surface area of solids you can hold.
Area and Circumference of Circles · Composite Area · Volume and Surface Area of Prisms and Cylinders · Volume of Cones and Pyramids · +2 more
Sliding, flipping, and turning a shape without changing it, and what happens when a shape grows while its angles stay put.
Translations, Reflections, and Rotations · Congruence and Rigid Transformations · Dilations and Similarity · Scale Drawings
Boiling a whole data set down to one typical number, and the displays that show its shape, spread, and outliers.
Sampling and Why It Matters · Mean, Median, and Mode · Range and Mean Absolute Deviation · Box Plots · +1 more
Whether two quantities move together, how a table sorts two categories at once, and the chances behind combined events.
Scatter Plots and Association · Line of Best Fit · Two-Way Tables · Basic Probability · +1 more