Doing it the easy way

If a pupil is allowed to imagine the problem/puzzle, then they can rearrange the facts to make the puzzle easier. An simple example of this is when a pupil is asked to calculate 4 + 7 + 6. It is an easier sum to add 4 + 6 + 7, because 4 + 6 canbe recognised as being equal to 10, and 10 + 7 is then a trivial sum. But the principle applies to more complex situations and calculations. Another advantage of imagining the problem/puzzle, is that one can use analogous situations to make the calculation easier. When I was at primary school the class was given a nasty question which involved distances in many different units of measurement. As I struggled with it, the boy I sat next to told me it was easy and that I could use my ruler to find the answer. I misunderstood him and looked for the answer in the writing that was stamped on the rulers [it comprised facts like “10 chains = 1 furlong” and “8 furlongs = 1 mile”]. I quickly determined that there was nothing there which I didn’t already know and that he was either mad, or he had a different type of ruler from the ones in my possession, but neither was true. What he had done was use the scale on the edge of the ruler as a number line, which had aided him in working out the answer. So while I was trying to understand the problem and trying to sort out a solution, he just counted up and down his ruler and arrived at an answer in a fraction of the time it took me. (If I remember rightly, I ran out of time and never did solve that particular question). This ability to find and use an analogue for the content of a maths problem is an important skill which aids children’s maths ability enormously. At Puppet Maths, we teach children to use their imaginations, and to use analogies, the better for arriving at the correct solution with facility. We like to think that we are the home of imaginative thinking in maths.