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An innovative way to teach multiplication tables

I recently tutored a student who was struggling with multiplication tables. He could do the product of two numbers so long as they were less than 6. However once it got to numbers bigger than 7 he had to use addition, which as one would guess would be time consuming. So It occurred to me since he did not struggle with multiples of 5, or 10, or for that matter numbers less than 6, I suggested trying the following time saving method. What is 12 x 15 = to. In order for him not to have to add 12 15 times in his head or using pencil or paper, this is what I suggested he do. First multiply 10 x 12 = 120 and add it to 5 x 12 = 60, the sum of the total being 12 x 15 = 180. The result was good. Before he would struggle with 8 x 7 and now he can do complex multiplications in his head. At any rate the time he saved not having to add helped him improve his test scores.