Schedule first lesson

Free simulation · MYP 4–5

Completing the Square

Build x² + bx with algebra tiles, find the corner that completes the square, and write the working down step by step.

By Shannon Mellon · Last updated 3 November 2026

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.

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.

Branch of mathematics: numerical and abstract reasoning. Topics: quadratics, completing the square, vertex form, algebraic expressions.

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