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 – the project with him is here:

Tonight I worked through the 7 parts with my older son

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

His ideas involved the area of a triangle and the Pythagorean theorem

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

It took him a while to come up with something, but eventually he mentioned the quadratic formula, which seems like a great example:

(3) My gut tells me that this is true

Here he picked a postulate from Euclidean geometry – a single line passes through any two given points.

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

OMG OMG OMG OMG – I’m not even going to give it away. The best!!

(5) My gut tells me the statement is false

He had a really hard time coming up with an example here.

Eventually he came up with a really interesting example from the quadratic formula – the quadratic equation has integer roots.

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

He came up with a nice example here – a cube has integer sides and volume 7.

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

He came up with a simple example first -> 1 + 1 = 7. I told him that was too cheap and asked for a second example.

The second example was . He also gave a really nice explanation.

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