I had a great team of 2 boys this week who were the first to build a LEGO NXT Dragster. I usually instruct kids to build a 10 foot course and time the car. Well, I noticed they were setting up a measuring course their own way so I was curious to see what they would do without specific directions.
I watched trying to determine the velocity of their car and was initially confused because the were not using a stop watch but a timer. So they measured the distance (in feet) the car went in 1 second rather than the time to go 10 feet. In the latter case, the velocity is 10/t. The way the boys measured, it is much easier to calculate. The velocity is simply the distance because it is over 1 second. I thought that showed a really good understanding of velocity and possibly ratio. Also, it showed what teachers can learn when the give kids more space to come up with their own solutions.
By the way, their car went 4 ft/sec using 2 gears and they immediately set out to improve the speed using 3 gears.