Algebra Identity for School Maths Lab

Quick Answer: Algebra Identity for School Maths Lab is a set of pieces representing squares and rectangles whose side lengths stand for algebraic terms such as a and b. With this algebra identity kit, students arrange the pieces to show that identities such as (a + b)² = a² + 2ab + b² are statements about area.

Identities as Areas

An algebraic identity is true for every value of its letters, and the quickest way to see why (a + b)² = a² + 2ab + b² is to build it. A square with side a + b splits into one square of side a, one square of side b and two rectangles measuring a by b. When students lay the four pieces together and see that they fill the large square exactly, the middle term 2ab stops being a rule to memorise and becomes the two rectangles they have just placed.

Kits of this kind are also used for (a − b)², where the pieces show a square of side a with strips removed, and for a² − b² = (a + b)(a − b), where the L-shaped region left after taking a small square from a large one is rearranged into a rectangle. Which identities this particular kit models should be confirmed at the time of ordering, together with the material and the number of pieces.

A useful lesson step is to give the letters values. With a = 5 cm and b = 3 cm the large square has an area of 64 cm², and the pieces measure 25, 15, 15 and 9 cm², which add to the same total. Checking one numerical case builds confidence before students apply the identity to expand expressions such as (2x + 3)².

Applications

• Proving (a + b)² = a² + 2ab + b² by fitting area pieces into a larger square
• Showing (a − b)² and a² − b² geometrically, where the kit includes those models
• Checking an identity numerically by measuring the pieces and adding their areas
• Moving from area models to symbolic expansion of expressions such as (2x + 3)²

Specifications

Care & Handling

• Keep the pieces for each identity together in a labelled bag or tray, since a missing rectangle makes the model impossible to complete.
• Store pieces flat, away from heat and direct sun, so they stay square and fit edge to edge.
• Clean with a dry or slightly damp cloth; avoid solvents that could lift any printed labels such as a² or ab.

Why Choose LabEquip

Maths teachers in middle and secondary classes use an identity kit when algebra first moves from arithmetic to symbols. It sits in LabEquip’s Mathematics School Lab Products range beside the general-purpose Algebra Tiles and the three-dimensional Cubic Identities (a+b)3 model; send your requirement through the contact page.

Frequently Asked Questions

How does the kit prove (a + b)² = a² + 2ab + b²?

Students build a square of side a + b from one a-by-a square, one b-by-b square and two a-by-b rectangles. Because the four pieces fill the large square with no gaps, its area must equal their sum, which is exactly the right-hand side of the identity.

Why is the middle term 2ab and not ab?

When the large square is built, there are two rectangles of size a by b, one along the top and one down the side. Students who forget the middle term, or write it as ab, can see the second rectangle sitting on the desk.

How is a² − b² shown with area pieces?

Remove a b-by-b square from the corner of an a-by-a square. The remaining L-shape is cut into two rectangles and rearranged into one rectangle measuring (a + b) by (a − b), so the area left over equals (a + b)(a − b).

How is an identity kit different from algebra tiles?

An identity kit is built around specific identities, with pieces sized for those proofs. Algebra tiles are a general set of unit, x and x² tiles used to model any expression, multiply binomials and factorise quadratics. The identity kit suits a first lesson on identities; tiles suit broader practice afterwards.

Does the geometric proof work for negative values?

The area model needs positive lengths, so it demonstrates the identity for positive a and b. The algebraic proof, multiplying out (a + b)(a + b), then shows that the identity holds for all values, which is a useful point to discuss once students have seen the model.

What should students record during the activity?

A labelled sketch of the arrangement, the area of each piece in terms of a and b, the total area written two ways, and a numerical check with chosen values. This matches the aim, materials, procedure and conclusion format used in many maths lab record books.

Last Updated: September 2026