algebra tiles

There are two sets of algebraic identities usually taught at the school level - (i) the quadratic ones and (ii) the cubic ones. Both can be modeled in a low-cost way. Nets of solids can be used for the cubic identities. Layouts of both are included along with links to uses.

Algebra tiles are a powerful manipulatives to understand algebraic expressions in single variable up to degree 2. They prevent some misconceptions and can be used all the way till middle-term factorization. They can be easily made from cardboard boxes.

2D base 10 blocks, popularly known as Flats-Longs-Units (FLU) are the most useful of all manipulatives for numbers. They can be extended to decimals through fractions as well as to algebra tiles.

These pre-grouped proportional manipulatives can be used to introduce numbers up to 999 and the four operations - addition, subtraction, multiplication and division. In fact, they can be used to understand the division algorithm to find the square root!

Here are the remaining 3 proofs of algebraic identities

(a + b)(a - b) = (a2 - b2)

(a + b)2 + (a - b)2 = 2(a2 + b2)

(a + b)2 - (a - b)2 = 4ab by using algebra tiles. 

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