Multiplication

Multiplication is just accelerated addition. 3 x 5 means "three lots of five". The number contained in three lots of five can be obtained by counting up all the items present in those 3 lots. Whereas that may be an option for small numbers like those in the example, it ceases to be a viable approach when one is trying to identify the number contained in 257 lots of 983. A shortcut is needed. To achieve this shortcut there is one absolutely essential element. The pupil has to learn their times tables. I once taught maths in a technical college, and one of the young adults was a South African man, whose maths education was practically non-existant. When asked to do the relatively straightforward multiplication 254 x 26 he could lay out the numbers in the proper order to do the calculation, and he would know that he now had to multiply the "4" and the "6". But when asked what 4 X 6 was, he would stop and say "Ah". He was stymied simply because he didn't know the fact that 4 x 6 is 24. Learning these facts are the key to doing mathematics, but having to do so puts children off mathematics. They think that there are too many of them to learn. It's boring having to chant them in class, and all the time they do so, they're concerned (of not in terror) of making a mistake; and although the teacher is unlikely to hear it, the pupil standing next to them will and may well use this knowledge in a disparaging way. I gave my adult student the Sands-Daniels Musical Times Tables to play on his stereo, with the instruction to sing along. He learnt the 45 facts contained in the times tables quickly and painlessly. This 20 year old man had put off learning these 45 facts because he retained the childish view that there were so many of them that doing so was an impossibility. Once he actually attempted to learn these facts, and did so in an environment that made doing so less boring, and which helped him get the answers right by providing him with musical prompts, he found that learning the times tables was easily accomplished. Puppet Maths uses the Sands-Daniels Musical Times Tables to teach these vital facts to our pupils. They can learn them without boredom and often seemingly without effort.