Chapter 11 The Study Of Numbers Up To 1000—Ii
isolated numbers to be multiplied or divided (as occurs in our conventional teaching of arithmetic), but he consolidates the idea of repeated doublings, redoublings and halvings using new starting points. Exercises 17 and 18 include the following: Start with 5 and go on doubling. Start with 4, with 6, and go on doubling. Go backwards till you reach the number you started with. Start with 7, with 11, with 13, with 15. Go on doubling till you almost reach 1000.
Multiplying By 5 Pupils have already mastered multiplications by 10 and by 100 (when discovering the multiples of 100 and of 10), and, having now gained confidence with doublings and halvings, their skill is applied to other multiplications. They are reminded that the relation of 5 to 10 is , that 5 = of 10. They understand that the tan-yellow cross is equivalent to the pink-orange cross, that is, that 8 × 5 = 4 × 10. Therefore, says Gattegno in exercise 20, to multiply by 5, first multiply by
The Cuisenaire Gattegno method of teaching Mathematics