Geometrical interpretation of An Algebraic identity- (a+b)2- (a-b)2 = 4ab

Jun 30 2016

Source: vascsc-tts-guj

## Topic:

Algebra

## Workplace Skills:

Problem Solving

### Estimated Time Required:

1-2 hours

### Target Grade (Ages):

Grade 6 (Ages 11-12)

Grade 7 (Ages 12-13)

Grade 8 (Ages 13-14)

### Diversity Indicators:

Teachers and students

## Tab Wrapper

### Goals:

To give an understanding of the identity

### Prerequisites:

- A student must know the basic concept of Algebra and mensuration

### Background:

If a relation between the basic concept of Algebra and Mensuration is established then the visualization of the algebraic identities become easier.

### Materials:

**Material required**: A thick card board, a thin card board, scale, pencil, scissor(or cutter), coloured papers and glue.

### Procedure:

- Cut a square out of thick cardboard .
- Cut about half a centimeter wide four strips with length as the length of the square.
- Glue the strips along the border of the square to make a square tray as shown in the figure.
- Now cut the thin card board to make a square which fits in to the tray.
- Now cut this square into a square and four congruent rectangles as shown in the figure.
- Denote the length and breadth of a rectangles as ‘a’ and ‘b’ respectively.
- Glue coloured papers on one side of these pieces.( use one colour for a square and another another colour for four rectangles ).
- Your model for verifying the above identity is ready.

**How to use it:**

- Arrange all the five pieces and fill the tray.
- Note the length and breadth of the rectangles as ‘a’ and ‘b’ respectively.
- What is the length of the whole square and that of the small square piece?
- What is the area of the whole square?
- What is the area of the small square piece?
- Remove the small square piece from the arrangement.
- What is the area of the remaining part?
- Note that this area is made up of 4 congruent rectangles.
- What is the area of each rectangle?
- What is the sum of areas of rectangle?
- From steps 7 and 10, can you see the result?
- The above identity is verified.

## Original Resources

### Worksheets

The attached file is lesson plan for algebraic identity of (a+b)2- (a-b)2 = 4ab in Gujarati Language

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