Algebra tile

They have also been used to prepare prison inmates for their General Educational Development (GED) tests.

They give students another way to solve algebraic problems other than just abstract manipulation.

[1] The National Council of Teachers of Mathematics (NCTM) recommends a decreased emphasis on the memorization of the rules of algebra and the symbol manipulation of algebra in their Curriculum and Evaluation Standards for Mathematics.

According to the NCTM 1989 standards "[r]elating models to one another builds a better understanding of each".

[1] For example, eight positive unit tiles can be added to both sides.

[1] Zero pairs of unit tiles are removed from the left side, leaving one positive

For example, seven positive unit tiles can be removed from both sides.

Once the sides of the rectangle are represented by the algebra tiles, one would then try to figure out which algebra tiles would fill in the rectangle.

For instance, if one had x×x, the only algebra tile that would complete the rectangle would be x2, which is the answer.

Multiplication of binomials can also be thought of as creating a rectangle where the factors are the length and width.

In order to factor using algebra tiles, one has to start out with a set of tiles that the student combines into a rectangle, this may require the use of adding zero pairs in order to make the rectangular shape.

[1] In a sense this is the reverse of the procedure for multiplying polynomials.