I thought it would be fun to talk through the list with each of my kids and ask the for examples of each on of the statements. My younger son was home this afternoon so he went first:

(1) The statement is true, here is a proof:

He said that he knew how to prove that the square root of 2 is irrational, and got most of the way through the proof!

(2) I believe the statement is true, here’s why

For this one he picked the Collatz Conjecture:

(3) My gut tells me that this is true

He picked some of the infinite series stuff we’ve been talking about lately!! I couldn’t believe that this was his example for something that he thought was true – yay1!

(4) I have no opinion as to whether or not the statement is true or false

Here he picked the question about whether or not the number of twin primes is infinite.

(5) My gut tells me the statement is false

He had a hard time with this and I ended up breaking the video into two pieces because once he came up with a question relating to the Gosper Island, I had to go get them!

What his gut tells him is false is that the perimeter of the Gosper island is finite.

(6) I believe the statement is false – here’s why

Here he picked a really neat example, and one that his class is working on in school. The game is to make integers using only 4 fours. So, for example, 17 = 4*4 + (4/4).

He does not believe that you can make all of the integers using just 4 fours, and he has a nice reason.

(7) The statement is false – here is a counter example.

He didn’t quite understand the statement, but still came up neat idea. He made the statement “you can’t express all integers using binary” and (sort of) showed why that statement is false.

So, a really fun project – I’d love to see lots and lots of kids come up with examples for each of Matt’s 7 statements.