I put together my packet for the Central Force Particle Model (CFPM) today. Per usual, I stole most of it from Kelly, but I wanted a worksheet to directly address the fact that in some situations force direction depends on the speed of the object when going in a circle, so I wrote Practice 2 for that purpose (gdoc version of the packet here).
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 like to mix it up. So today when students were working in groups on problem solving, I decided to do a modified whiteboard face off by simply having two groups next to each other compare and share their solutions. The difference between this and Kelly’s version is I had every group find a partner group, so I had 5 face offs going on at once. I already do whiteboard speed dating a lot to expose kids to a variety of methods and ideas about a problem, and I will be adding this to the repertoire for that purpose as well.
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.
Over break I thought a bit about how to get more kids engaged in discussions, particularly when everyone did the same problem (I do that a lot as we progress in a model, particularly with harder problems). I tried splitting the class into two different board meetings (where students form a circle and ask questions of each others’ boards), and I love it for two main reasons; 1) It takes class sizes of around 25 and makes the circle smaller, so more kids can be involved. 2) More importantly, I can’t be in the circle. Not once did they look to me for an answer. Not once did I feel the need to interject because of silence. I was an observer rather than a participant. I heard much more discussion from more people. Another benefit is that you can try to manipulate the groups a bit to put students who are more hesitant in the same group with folks who encourage discussion. It’s a keeper.