X as a placeholder

The frame is a step towards the literal symbol, and the child should, at this point, readily accept the idea of x as a placeholder. Children need to understand such phrases as

(i) 3x which means 3 times x used instead of x X 3

(ii) x/3 which means x divided by 3 (x over 3) used instead of ? of x.

These might be introduced through reference to ? X 3 and 3 X ? which the pupils know are equivalent by the commutative law.

Constant practice should be given in solving the simple type of equations, involving addition, subtraction, multiplication and division, only one process being involved in each equation at first:

x – 3 = 7 add 3

x + 3 = 7 subtract 3

x.3 = 12 multiply by 3

3x = 12 divide by 3.

A typical assignment for this purpose might be:

To win a game of Snakes and Ladders, Tom has to score a total of 100 exactly.

His last score was 5, and he won the game on that score.

What was his score immediately before his last throw of the die?

Gradually, equations involving two operations should be introduced e.g. 2y – 7 = 9; 3t / 2 = 6.

Teacher-contrived problems involving equations of this type should be presented for solution. Problems that will be found very useful are the “I thought of a number” type and the “unequal sharing” type: