Chapter 11 The Study Of Numbers Up To 1000—Ii

With the object of carrying out the operation mentally, Gattegno analyses squares into 1 Squares which can easily be found using previous knowledge These give no difficulty, as pupils already know the squares of numbers up to 10 and can easily find 202 and 302. 2

Squares easy to work out from previous knowledge 1

Even numbers squared are multiples of 4; e.g.: 182 = 22 × 92 = 81 doubled and redoubled to 324.

2 Multiples of 5, when squared, are multiples of 25; e.g.: 152 = 52 × 32 = 25 × 9 = × 900 = × 450 = 225 3 Multiples of 4, when squared, are multiples of 16; e.g.: 242 = 42 × 62 = 36 doubled and then this answer redoubled three times to 576. 4 Multiples of 7, 8, 9 and 11 can easily be decomposed into their factors; (e.g. 222 = 112 × 22 = 121 × 4 = 484). Thus, the majority of squares less than 1000 are easy to work out using their factors and the squares of their factors. In the ‘table of squares’ that pupils are building they would now have all the squares of numbers up to 10 plus 122,142,152,162,182, 202, 212, 222, 242, 252, 272, 282, and 302. All of these can be worked out mentally.

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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