Free math simulations

Completing the square

Build the expression with algebra tiles, then find the tiles that complete the square.

About this simulation

Students build a quadratic expression with algebra tiles and arrange the x-tiles around the x² tile to make a square. They fill the missing corner with extra tiles, take the same amount away, and write each step the way they would on paper, ending in vertex form. Each one goes in a table. They then write the working before building, and try it with no tiles. Three spice levels add negatives, odd numbers and more than one x².

Who it's for

MYP years 4–5 (ages 14–16), especially extended mathematics.

How to use it

  1. Choose a spice level. The simulation gives you an expression.
  2. Drag the x-tiles into the dotted square, then fill the empty corner with extra tiles.
  3. Write it down: type the numbers, or drag the corner, strips or unit tiles into the boxes.
  4. Look for the pattern, write it before you build, then try No tiles.
BranchNumerical and abstract reasoningSpatial reasoningTopicsQuadraticsCompleting the squareVertex formAlgebraic expressions

Steps

My results

ExpressionPerfect square insideTaken awayVertex form