Math talk at Elementary School

A friend's 7 year old son has a rather difficult assignment from the teacher, and that is to invite a speaker to the classroom. The speaker can talk about any topic. Some kids brought in skiing expert and other fun stuff.

I was invited to talk an interesting topic in math!

I am DELIGHTED to do such talk.

After all, I almost became a teacher. I backed out of teaching for a variety of reasons: low pay, guns in school, little respect. The most important reason why I backed out is that I don't think I have what it takes to teach the kids to be honorable, respectable individuals. I'd love to make a living teaching math. But it is more than teaching the subject when you become a teacher. It gets especially hard when kids reach the high school age. I have no interest to teach kids the four basic operations and elementary school stuff. I'd like to teach at least high school level where I can let the students think past beyond calculations...

So I went to Graham elementary school. I haven't been in an elementary school for gosh so long. The 2nd grade kids were adorable! They sit on the floor instead of at chairs like I expected.

So what can I talk to the 2nd grader kids about? in 15 minutes?

Finally, I settled with Gauss's famous homework problem: adding 1+2+3+4...+100.

I asked"Do you know how to add?"
The kids: "Yes!"
I asked "What is 1+2?"
The kids: "THREE!"
"What about 1+2+3?"
The kids: "SIX!"
How about "1+2+3...+97+98+99+100?"

That stumbled the kids for a while. Finally one kid says "400"!

"How did you get 400?"
"1+99=100, 2+98=100+3+97=100, plus that 100 = 400"

This (smart) kid did not understand the "..." notation. But she saw the pattern!

Then I explained the dot-dot-dot notation, she stumbled for a while.
Finally I told her that she is on the right track. The pattern here is 1+100=101, 2+99=101, for each pair of numbers.

"How many pairs?"
One kid said "50".

"Multiply it out what do you get?"
"5000"
"Almost"
Then a bunch of kids raised their hands to guess: 6000? 10000? 4500? The kids simply pull numbers out of thin air.
Finally, one kid says "5050".

He got it! I gave him a gift calculator that I got at a dollar store. I told the kids that sometimes we have to look for patterns in solving math problems.