In all honesty, I have probably always liked this project a little more than the kids, but over the past few years I've improved the delivery so that they definitely get into it. My biggest mistake the first year with this was not giving the students an overview of what they were going to do and trying to let the packet speak for itself. That failed... miserably. Now I give an general overview complete with pictures and a discussion of why the lesson is important beforehand and they seem to enjoy and understand it a lot better.
I think one of the reasons I like this project so much is that it actually works. When the kids are consistent and do their calculations correctly, they will hit the center of the target with ease. It's one of the all too rare opportunities that students get to see that the math they did directly affected something in real life.
Some tips for the teacher:
- I generally work the stopwatch for them. I've found myself wincing at how much the kids think the timing is "fine" when they do it on their own. I'll start a countdown out loud, and if I feel like my button presses weren't as good as humanly possible, I'll tell them not to count the trial. Letting them do it on their own (poorly) could I supposed be a "lesson learned" but I feel like after all the calculations they do, they won't realize what exactly went wrong or take such a lesson to heart. It would probably be worthwhile to let your kids try it on their own first, but keep a close eye on the timing aspect.
- Strongly encourage the students to make sure they are shooting consistently before they do official trials, and to start over if their official trials aren't close together. You'd think the bold, caps, and underlining in the description would be enough, but my kids tended to be a bit overconfident and tried to rush through without frequent reminders.
- This project takes me ~2 40 minute classes based on class size and skill level. I'm sure it could be done faster with more space and more student independence.
- Having some backup Skittles might be a good idea in case of allergies or dislikes. (I mean, what fun would it be if they couldn't eat some leftovers?)
I realize that there is a bit of hand holding, some of which could be removed to get kids thinking more on their own (especially if you were to give this to an honors class), but it's mostly to get it to fit within time constraints. As with any lesson or project on here, I encourage you to use and edit this to meet your own needs. Let me know what you come up with or if anything is unclear.
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wow - this catapult thing is such a great & simple idea! i am going to TOTALLY use this.
ReplyDeletei love it when i find new blogs to add to my reader! welcome!
Hey, thanks for the comment, Sam. I'd say that I'd add you to my reader, but you're already there!
ReplyDeleteHey - If you have the information handy, what are reasonable numbers for a,h, and k in the floor equation?
ReplyDeletea is usually a messy decimal. I just now got -0.009377 for a in a quick test run. This can vary, but with my catapults, there has generally been two leading zeros. My h's and k's are usually somewhat close to each other. This also will vary pretty significantly, but I got h as 114.3cm and k as 122.5cm from the ground. For us, the candy is usually in the air for about 1 second.
ReplyDeleteI actually used small clothespins for mine, and angled them a little forward so that they go farther(5-7 feet). So if you've made your catapult already, my numbers might be very different.
Terry Kaminski (transformededucator.blogspot.com) did this recently. So if your catapults came out like his, he might have closer numbers.
I'm confused as to why you need the vertex version of the quadratic equation. I haven't done this myself yet, but I would think that the first times you try it, your equation will look like:
ReplyDeletey = 1/2gt^2 + vt + 0, where g = -980 cm/s/s and v is the initial upwards velocity. Granted, you don't know what v is yet, but with the collected data for how long it takes to land (ie. plugging in a nonzero t), you will be able to figure out what v is.
Then, when you launch from desk, the equation gets modified to y = 1/2gt^2 + vt + h, where v is the value you calculated from before and h is the height of the desk. With this, you can quickly find out how long it takes to land, and then using some simple proportional reasoning you can find out how far away it would land.
Am I missing something here? Is your math simpler / more accurate than the one I am thinking of doing with my kids?
Thanks for the feedback! (And for the design.) :)
Oh, BTW we did the project using the math I described; I verified beforehand that it yields the same result as your method! The results were pretty good; the kids' M&M's on their own self-built catapults all landed fairly close to (or right on) their targets. Yes! Thanks for sharing your lesson and design. :)
ReplyDeleteHelp. I'm totally stuck on how you got a. Your h was 114.3 and k was 122.5. You got a as -0.009377. Can you show me the math you did to get a. I'm blanking on this step.
ReplyDeleteEvan, you plug in 0 for x and y into vertex for and the vertex in for h and k, so y = a(0 - 114.5)^2 + 122.5 Then solve for a. It's always going to end up be -k/(h^2) for this since you use (0,0) as the extra point. Hope this helps!
ReplyDeleteCan you explain how the equation changes when you account for the height of the desk? My equation is y = -0.07x^2 + 5.866x The height of the desk is 77 cm.
ReplyDeleteOh wait, maybe I understand now. Will the value of k (the y value of the vertex) just increase by the height of the desk. In my case, the vertex would be k+77cm. Is that right?
ReplyDeleteYea, you've got it now, that is exactly right!
ReplyDeleteUmm i dont get Question 1 n page 8! is says we have to put our numbers in the previous pages into standard form. but WHAT standard form?
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ReplyDeleteHello, I am wondering if you have ever done this by getting 3 points and doing a quadratic regression in the TI calculator? That is how I planned to do it until I say your worksheet
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