ABSTRACT
Work out the answers to the following calculations mentally. Avoid writing anything down at this point:
1 1 + 6 = 28 - 9 = 20 * 5 = 57 * 3 =
Now ask yourself, ‘how did I carry out the calculation?’ You may think ‘I just did it’, but let’s think more deeply. Did you just know that 11 and 6 made 17, or did you add 6 and 1 to make 7 then add that to 10? Did you partition 9 into 8 + 1 so you could take 8 away from 28 to get 20 and then take away another 1 to give 19? Did you multiply 10 by 5 and then double the answer to get 100, did you add 20 + 20 + 20 + 20 + 20, or is this a fact you know? And, finally, did you work out 3 * 50 and 3 * 7 and then add 150 + 21 to give you 171, or did you use the algorithm, or rule, you were taught in school? In your head you might have said something like ‘3 * 7 = 21; put the 1 down and carry 2; 3 * 5 is 15, add 2 is 17. So the answer is 171’. This models the written algorithm.
