As part of SL Math I have to teach Kinematics, last year I
sort of rushed through it. I was too easily convinced by the smiles and nods that learning was happening. In calculus, I've never felt like my students accomplished much more than simply learning a series of steps to get the right answer. Sure they can solve the problems and most of my kids got very good IB scores last year. But! I wanted more.
Too often in SL Math kinematics is window dressing and an excuse for context on a calculus problem and rarely more than that. As a physics guy I see kinematics as the driving motivation behind differential calculus. So this year I swore I'd actually walk the talk.
In come the robots!
My school, like any other, has its problems, but we are blessed with dreamers and an administration that are willingly to fund those dreams. 4000 euros later we have
lego robots coming out our ears. Our school already supports two
FTC teams, one middle and one high school team, so it wasn't a stretch to find more funding for robots.
The students were given about 40 minutes to create their "car" with the two stipulations that it had one motor and allowed for easy removal of the NXT brick (so other classes could use the brick).
And now for the calculus...
Part 1  Constant Velocity
I preprogrammed 7 functions for the students. The first 3 are constant velocity functions. Student's used Logger Pro's video capture and analysis features to create position and velocity graphs and equations for each function.
Students wrote each set of equations on the board so as a class we had more data from which to make conclusions. I proceeded to mathteacherninja them to see that the slope of the velocity equations was virtually zero when compared to the other parameters. Then the jump to see the similarity in the slope of the position and the constant value of the velocity was quick and easy. Leaving the students to conclude (written in my 2grade hand writing):

If s(t) is linear then v(t) is constant. Velocity is the slope of position. 
What more could a teacher ask for?
After these conclusions the students worked some
very simple problems. Working with equations, graphs and most importantly writing rules to go from linear position to constant velocity and vice versa. I dangled the idea of the integration constant in front of them, not looking for full understanding, but trying to raise awareness that information was lost or is missing when moving back and forth between position and velocity.
Next up: Linearly increasing velocity in Part 2. Coming soon...