Method One: ‘The Dissecting Method’
The children often like to name their methods and this one was explained as follows:
“If you dissect (partition) the 23 into 10, 10 and 3. Rather than multiply by 20, it is easier to multiply by 10. Once you have found that 113 X 10 = 1130, you then repeat it to get to 20. 113 X 3 could be similarly done with the hundreds, tens and ones multiplied separately. You then add them up to find the total amount of apples”.
Method Two: ‘The Standard Written Method’
he pupils found that there was a long way and a short way of tackling this calculation when using a written method. While the shorter method was familiar (from back in our own school days), the longer version showed the children’s relational understanding. In this version, they were able to demonstrate the value of each number that they were multiplying. They could also explain why we “put on a zero when multiplying by the 2” and why “the 3 was crossed out once we had finished multiplying with it”.
Method Three: ‘The Use What You Know Method’
Some children could also explain their method by telling the class: “having doubled 113 to find 226, you put on a zero because that’s what you did with the 2”.
We then tried to prove the calculation using smaller numbers: 4 x 2 = 8 and 4 x 20 = 80. 113 x 3 was worked out in two stages and the totals were then added together.
Each method told us the answer was that 23 boxes was enough for the 2500 apples. There would be 99 apples spare which, according to this year 6 class, could be used to make cider!
We drew the anchor task to a close by comparing our methods with those in the textbook. There was a different dissecting method – the textbook had split 113, we had split 23. The standard written form was there albeit with minor variations but our method three wasn’t included at all. This made the children feel really good about themselves!