For example, at the beginning of the systematic work with multiplication by a fraction, let the following be printed clearly at the top of every relevant page of the textbook and displayed on the blackboard:—
When you multiply a number by anything more than 1 the result is larger than the number.
When you multiply a number by 1 the result is the same as the number.
When you multiply a number by anything less than 1 the result is smaller than the number.
Let the pupils establish the new habit by many such exercises as:—
|
18 × 4 = .... 4 × 4 = .... 2 × 4 = .... 1 × 4 = .... 1⁄2 × 4 = .... 1⁄4 × 4 = .... 1⁄8 × 4 = .... |
9 × 2 = .... 6 × 2 = .... 3 × 2 = .... 1 × 2 = .... 1⁄3 × 2 = .... 1⁄6 × 2 = .... 1⁄9 × 2 = .... |
In the case of division by a fraction the old harmful habit should be counteracted and refined by similar rules and exercises as follows:—
When you divide a number by anything more than 1 the result is smaller than the number.
When you divide a number by 1 the result is the same as the number.
When you divide a number by anything less than 1 the result is larger than the number.