TwiddleLab / Courses / Math
Algebra in Motion
Balance scales, undo steps and slide parabolas until equations solve themselves.
Best after: Functions You Can See
Lessons
- Keep It Balanced (5 min): An equation is a level scale: both sides weigh the same.
- Undo, Undo (7 min): Every step has an inverse operation that undoes it: + undoes −, × undoes ÷.
- Letters on Both Sides (7 min): With the letter on both sides, take the same amount of it from both sides until it's on one side only.
- Two Unknowns, Two Scales (7 min): Two equations with the same two unknowns make a system. Its solution makes both true at once.
- Inequalities Are Regions (7 min): An inequality like h > 140 has many solutions: a whole region of the number line, its solution set.
- Rearranging Formulas (7 min): A formula is an equation with letters. Rearranging it means getting a different letter alone.
- Area Model: Multiplying Brackets (7 min): To expand brackets, build the rectangle: (x + a)(x + b) is one x², a + b strips and a × b unit squares.
- Factoring: Find the Rectangle (7 min): To factor x² + bx + c, fold its tiles into a rectangle: its sides are the factors (x + p)(x + q).
- Zeros: Where the Parabola Lands (7 min): A zero of a function is an x where its value is 0: where the graph meets the x axis.
- Completing the Square (7 min): Completing the square: split the strips in half, fill the corner, and owe back what you added. x² + 6x + 4 = (x + 3)² − 5.
- The Quadratic Formula (7 min): Completing the square with letters gives the quadratic formula: x = (−b ± √(b² − 4ac)) ÷ 2a.
- Project: Hit the Target (8 min): Where a shot lands is a root: solve c + bx − 0.05x² = height of the target.
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