Some are just inherently interesting.
Ask a group of kids how long it would take to count to a billion and they go crazy...
After discussing how big a billion actually was (for the record, it's enough to buy every single person in our town a brand new ford Fiesta, and if you stacked a billion BK whoppers on top of each other they'd go 10 times further than Venus) I challenged the class to find out how long it would take to count to a billion.
They were off!
Almost every group started by simply timing how long it would take them to count to 10, then multiplying by 100,000,000 (getting around 300 million seconds as an answer)
They were pleased until we looked at it more deeply.
I asked "What numbers take longest to say?"
seven, eleven, seventeen all came back at me.
One chimed in that 7 was the kicker - the only 2 syllable single digit number.
I asked which number between 1 and a billion would take longest to say - the groups decided on 777,777,777 as it contains a whopping 23 syllables (i had said it contained 18, and the kids to me to the cleaners saying i'd forgotten we'd need to say the words million and hundred!)
We timed a few kids saying this number on its own and they ranged between 3 and 7 seconds.
One pointed out that it had taken longer to say this single number than it had taken her to count 10 separate numbers.
So what's my point? I asked.
We aren't taking a fair sample are we sir? was the spectacularly on the ball response.
This said, i asked the groups to get back together and think of away they could take a fair sample and get a more accurate estimate for the time it would take.
A couple of groups shared a great plan to keep their original time for 1-10 (3 seconds)
but also take another 2 samples - they timed
777,777,767 to 777,777,777 (which took a full minute)
and also took a sample between
222,222,222 to 222,222,231 (which took 40 seconds)
They took an average of their 3 times (short, medium, long) and decided the average block of 10 number would take about 34 seconds, estimating 3,400,000,000 seconds (or 66,666,666 minutes) to count to a billion.
Their comment was this was fairer as most bunches of number from 1 to 1 bn would have 9 digits, so to just take the first 10 and last 10 would skew their data. Delicious logic.
After taking a few different solutions from the class (our average guess was 3 bn seconds) we then though about whether this was possible or not.
That take years some kids said. I agreed!
In changing this value to years, we estimated that it would take 95 years to count from 1 to a billion.
Pointless, contextually irrelevant, but a fab investigation.
This was then followed with a discussion of freaks - namely freaks who can talk at ludicrous speeds.
As far as I'm aware, Fran Capo is GWR holder for words / minute (667) and we amused ourselves watching this clip (from about 1:40):
and deciding how many years she would take to get to a billion.
(we googled that the average person speaks at 120 wpm, so we think she'd only take 17 years!)
This intrigued us, so we watched a couple more vids that we found at this link and tried to see how fast these guys could get to a billion.
Nice, easy, accessible and fun lesson with aboslutely no motivation aside from playing with numbers.