The more I teach, the more I find I get stuck in a particular method of problem solving or diagraming I think works best. Over the course of the last two years with Modeling Instruction, I have found that as I steer kids to particular methods less and less, they come up with creative and elegant solutions more and more. Today was no exception.
We were solving a problem where a projectile is launched from a cliff and lands below the launch height, find the time of flight. My typical solution would be to find the time of flight via the quadratic formula from
A student brought up: Why don’t you just solve for in and plug the solution into ? So we tried it, result below. Despite that it is using two equations, it’s actually easier than using the quadratic formula symbolically. I love my job.
I love doing projectile motion after both kinematics and forces for a couple reasons; 1) There’s a very good reason g=9.8 m/s/s 2) After doing forces, I love the opportunity to go back and review kinematics in a slightly new context. These two groups squared off about which velocity graph was correct for a dropped object, assuming the position graph was correct. After that I asked the class to draw a new position graph assuming the left velocity graph was correct, and we had a discussion about coordinate systems and the importance of defining it (and that it doesn’t matter how you define it).
Today I took another page from Kelly and used Dan Meyer’s Basketball Shot for a visual representation that a projectile exhibits constant velocity in the horizontal direction and constant acceleration (or at least acceleration) in the vertical direction. Interestingly enough, I had one student who said, “I really need to know if it goes in.” I told her to use math to find out.
Today I finalized my Projectile Motion Packet, once again with heavy borrowing from Kelly. I realized after reading her post about model building that I was able to cut a bunch of fluff from the unit, which is awesome because I’m more than a week behind compared to last year and this allows me to catch up while offering my students what I think is a better, more concise model building experience.