On Tuesday I gave geometry the following opener.
I let them think about it for 5 minutes or so. After I asked them for smaller cases. We looked at 2^8 vs 8^2 since some were claiming whichever number had the larger base would have the larger value.
After a few more minutes of discussion they plugged them into their calculators and checked their claims as to which was larger. The issue was the answers were all in scientific notation, sure it says a lot about how much larger one is than other, but students were not able to see how larger the numbers actually were.
So I pulled up Wolfram Alpha.
What students found most interesting was the number name. I had no idea these existed… We tried to find where a google would be….
This turned out to be a fun opener!