Algebra tiles support the representation and manipulation of constant, linear and quadratic expressions. Expressions are built up from tiles corresponding to each of x2, −x2, x, −x, 1, and −1, where the shape and colour indicates the class of tile.

Solving equations involves working with expressions on each side of an equals sign simultaneously. The activity below supports this by providing an upper staging area where any tiles added will be added to both given expressions. Use the staging area to isolate the unknown (that is any x tiles) on one side, and any unit tiles on the other. Once this is done, the solution can be read by arranging the tiles so that each x tile matches up with the same number of unit tiles.



Linear Equations and Algebra Tiles
Solving linear equations visually


Completed

About the activity

Good visual models illustrate mathematical concepts with clarity—bridging the concrete and the abstract. Algebra tiles are one such model, supporting interactive modelling and problem solving in directed number arithmetic, binomial expansion and factorisation, completing the square and linear equations. Thus they are extremely useful tools for introduction and early work in these important and fundamental topics.

The development of these algebra tile activities was inspired by William Emeny's Great Maths Teaching Ideas blog entry Algebra Tiles - from counting to completing the square.