Building Blocks

Algebra 1 · Axiom Academy

Every quadratic is a pile of tiles. Pack them into a rectangle with no gaps, and its two sides hand you the factors. Three kinds of tile, one hidden rectangle Algebra tiles turn a polynomial into something you can hold. A quadratic is built from just three shapes — a big square worth , skinny rectangles worth , and tiny unit squares worth . The shape's area is the term. The daring move: those scattered tiles always pack into one neat rectangle, and reading off its sides factors the polynomial for you. Watch the tiles for — one big square, five rectangles, six units — slide out of the scatter and lock into a single rectangle. When they settle, its width is and its height is : the factors. The tile counts are the coefficients; the rectangle's sides are the factors. That is the whole area model in one picture. Choose the sides, watch the polynomial appear Drag the two sliders to set the rectangle's width and height . The grid fills with exactly one tile, rectangles, and units — and the trinomial those tiles spell out is, automatically, the product of your two sides. Every whole-number rectangle works — the middle coefficient is always the two sides' sum, the constant always their product. When the rectangle is a square Make both sides equal and the rectangle becomes a square . Grow it with the slider: side on both edges gives — always one tile, an even rectangles, and a perfect-square block of units. That is what "perfect-square trinomial" looks like.

This is the written version of the interactive lesson above. See the full Algebra 1 course.