Counting digits

My younger son had a problem from his math club that was pretty fun:

Tough little challenge problem for my 4th grader – write the integers from 1 to 200. What is the 200th digit you write?

— Mike Lawler (@mikeandallie) September 19, 2015

For today’s project, we revisited that problem, made up our own version, and then finally solved one of the problems posted in response to the original problem:

What about the one from math team's state meeting last year, the 1,000,000th one? https://t.co/3R6iP0fn8J

— Antti Pihlajavesi (@Antti_Pih) September 19, 2015

Here’s my younger son’s solution to the problem I posted on twitter:

Next, I asked my older son to make up a similar problem and solve it. His problem was – if you write the integers from 1 to 805, what is the 805th digit that you write. Great! Here’s his solution to that problem:

Finally, we moved on to solving the 1,000,000th digit problem. This one took a little longer simply because the numbers involved were larger, but we managed to find our way to the solution of this one, too.

One bit that took a little time was the subtraction problem 1,000,000 – 488,889. The boys chose to evaluate this subtraction problem in sort of a strange way – which is totally fine – one of the nice things about these Family Math projects is sometimes getting in a little bit of arithmetic practice 🙂

So, a neat problem from my son’s math club gave us a chance to talk a little bit about counting techniques, arithmetic, and even a little bit about problem solving. Definitely made for a fun morning!