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Learning by Doing

objective: To solve a linear equation, say 2x + 5 = 7
Materials required: Green and yellow chart papers/rubber sheets, scissors, ruler,
pencil, eraser, cardboard, white paper, adhesive.
Method of construction:

• Take a piece of cardboard and cover it with a sheet of white paper. 1
1 1
• Cut several green and yellow rectangular pieces of size x × 1 (say x x x 1 1
= 5) and a few green and yellow square pieces size 1 × 1 from chart
paper, as shown in Fig. 1. Fig. 1
• Use each green rectangular piece to represent (+x) and each yellow rectangular piece
to represent (–x). Similarly, let each green square piece represent (+1) and each yellow
square piece represent (−1).
Procedure:
• For the equation 2x + 5 = 7, arrange 2 rectangular and 12 green square pieces on the
cardboard in the following manner (Fig. 2).
• Add five yellow small square pieces on both sides (Fig. 3).

• Pair each green square with a yellow square as shown in Fig. 3.
x x
x x
= =

Fig. 2 Fig. 3

• Remove the pairs of green and yellow from both sides to obtain Fig. 4.
• Take the half the number of pieces on both sides we get Fig. 5.
x
=
x x =
Fig. 4 Fig. 5

• Thus, solution of the equation 2x + 5 = 7 is x = 1.
This activity may be repeated by taking some more linear equations since this application
is useful in explaining the process of solving an equation.
For example, repeat the activity for following equations and fill the observations.

Equation Pieces in LHS Pieces in rHS Pieces added on Solution
both sides

rectangle Square rectangle Square rectangle Square
2x – 5 = 3 2 green 5 yellow 5 green x = 4

2x – 7 = 5 – 2x 2 yellow 2 green

53 Linear Equations in One Variable