The Cuisenaire Gattegno Method Of Teaching Mathematics

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The remaining squares

How can the squares 132, 172, 192, 232, 262, 292 and 312 be found mentally when required? One method, of course, would be to multiply the number by itself but Gattegno proceeds to show our lower primary pupils a ‘special and simpler way’, one which involves the presentation and use of ideas normally left for secondary schooling. These may readily be recognized in their algebraic form as 1

(a + b)2 = a2 + b2 + 2 ab

2 (a – b)2 = a2 + b2 – 2 ab Gattegno, however, applies them to the arithmetic involved in such squares as 1

312 = (30 + 1)2 = 302 + 12 + 2 × 30 × 1

2 292 = (30 — 1)2 = 302 + 12 — 2 × 30 × 1 3 232 = (20 + 3)2 = 202 + 32 + 2 × 20 × 3 How can the Cuisenaire rods make ‘simple’ what has proved to be too difficult for primary grade pupils in the past? It can be first demonstrated with the rods that 92, which is equal to (4 + 5)2, is also equal to 42 + 52 + 2 × (4 × 5). After repeating this exercise with other smaller squares, pupils should be able to apply it to squares such as 312. First 92 is made using nine blue rods placed side by side. On top of this square and in one corner 42 is placed, made with four

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The Cuisenaire Gattegno method of teaching Mathematics

The Cuisenaire Gattegno method of teaching Mathematics

The Cuisenaire Gattegno method of teaching Mathematics

The Cuisenaire Gattegno method of teaching Mathematics