20th January 2017 - Lynne’s logic - Multiplication
Happy New Year everyone and welcome to 2017, which – of course – you will all know is a prime number; in fact, the 306th prime number! The last prime number year was 2011, and there will not be another prime number year till 2027. (Just in case you were wondering!)
Well, multiplication is the name of the game today, (cue a song for any oldies reading this!).
I remember attending a workshop led by a well-respected mathematician, who began by telling us multiplication does not exist in nature. Shock, horror! But I later understood what he meant. Do you agree?
- 3 + 2 can be shown easily in its concrete form; just use three fingers and two fingers. Now think about 3 x 2; you have three fingers and another three fingers. The child looking to see two fingers somewhere will be sadly disappointed. Multiplication is a number being used as a process rather than as a finite quantity, which is a big step from addition and subtraction, hence its appearance in the phase 2 materials. We will, therefore, require our learners to think in a different way when dealing with multiplication.
- Then we compound the problem by reading the same calculation from different views. Is 3 x 2 three two times (or twice), or is it three lots of two? In the same way, is 4 x 3 four trebled (three times), or is it four lots of three? You will know it is both, but this can be a lot for some learners to cope with. It is important they recognise and understand this dual view, best shown by lots of arrays using a wide range of verbalisations so they understand it is just a different way of interpreting an array; the answer will be the same. Importantly, this concept (posh name: the commutative law) can be used to our advantage.
- Familiarity with arrays is essential when you move on to recording, and the grid (or area) method is recommended. However, you need to support your learner using counters or squared paper first, as this will ensure the child fully understands where the numbers in the grid come from.
- Always have in mind the next steps for the learner, as we will want – ultimately – to use standard long multiplication. When recording with the grid method, to make the transition to long multiplication smooth, place the larger number to be multiplied in the horizontal part and the smaller number in the vertical part of the grid. Ensure you then total each section horizontally before you make your final vertical addition. This will transfer directly into a standard long multiplication algorithm.
- When the main learning objective is the recording process, consider giving the learners a tables square, otherwise they will lose fluency. Don’t complicate matters for them if your main objective is not developing instant recall – there is a time and a place for everything!
- As always, ensure you move between the concrete, the symbolic and the oral forms of a calculation, (the translation element of Catch Up). Remember, though, that the concrete could be pictorial; it could, in fact, be a squared paper array.
I think this is enough to consider for this blog, but next time we will think about tables, the scourge of many a poor kiddiewink!