A machine learning approach to teaching math to an 8 year old

Over the weekend, I came across a bunch of "mathletes" question papers that my son had used over the years. He is now in high school. My daughter is in 2nd grade and I thought I'd pick age appropriate problems for her to think about. There were some concepts that she had not heard about so instead of teaching them the regular way, I thought I'd give her a few examples and see if she can learn the algorithm. She knows place values, addition, subtraction, multiplication and can do division graphically, by distributing the dividend sequentially into the divisor.

Average

I showed her the table below and asked her what "average" means:

Numbers	Average
3,5	4
4,4	4
6, 6, 6	6
4,6	5
3,4,5	4

She said the average was somewhere in the middle but couldn't come up with a formula to find it. I then asked her to add the numbers and see if the sum was related to the average. At that point, she figured out that the sum was double that of the average. For the rows with 3 numbers, I asked her to write the times table of the average and see if she could figure it out. At that point she lit up and said we need to count the numbers. After that, she put all the steps in words, very nicely.

Rounding

The question was "round 10424 to the nearest hundred," so I started with some examples.

Number	Round to 10
9	10
11	10
17	20
23	20
29	30

This was particularly pleasing, because she not only worked out the operation by herself, she also asked how would "5s" be handled. And I explained that all the mathematicians in the world had gathered together and shook each others' hands and agreed to always round it up.

I then gave her a few round up to 100 examples, which she understood quickly. Then she could answer the question correctly, after making one mistake in which she rounded up to 10.

Remainder

The question was, what is the remainder when dividing 124 by 8. The picture below shows the 3 columns that were initially given to her as examples - Dividend, Divisor, Remainder. All artwork is her own :).

This one, she hasn't completed yet. She got pretty close with the circled examples dividing 7 and 8 by 3, but hasn't formulated the algorithm just yet. Will update the blog once we do that.

Have a nice day  - and don't worry about #ftcqcom.
Kuntal.