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Movies in Math. Math in Movies.

18 Nov

Here is a website with a compilation of short movie clips on math and physics that you can freely download.

http://www.math.harvard.edu/~knill/mathmovies/index.html

I use the Shrek clip as the introduction to inverses and contrapositives in Geometry.(This one was also on YouTube.) The PowerPoint I used is in the Box widget.

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M&M Catapult

2 Jun

I’ve been eye-ing this for awhile now so I was so excited to run this!! SO excited! I first read about this from Sweeney Math and seriously fell in love with it because the math in it is not forced. I really dislike those forced math projects, though I must admit, I use them sometimes anyways for engagement purposes.

Student’s Goal: To build a consistently-shooting M&M Catapult and find the equation of the M&M’s trajectory when shooting from the floor. Using that equation, calculate where the M&M will land when shooting from on top of a table.

Teacher’s Goal: Again, this was for my post-Calculus students so I really wanted them to understand some of the physics behind what we were doing. I created a few pre-questions to prime them a bit. I really wanted them to be able to see the integration between all the different maths over the past several years. (Pictures of problems below)

Copy of my modified lesson plan is to the right in the Box.net widget. As a note to that copy, I gave them one front-back page at a time. In other words, they had to get pgs 1-2 completed before they getting pgs 3-4 and they had to finish pgs 3-4 before getting pgs 5-6.

Materials Needed:

  • box of fat popsicle sticks
  • one clothespin per group
  • multiple glue guns
  • a wooden board to attach the catapult to (I asked the woodshop teacher who had a bunch of cut up desks available)
  • 2-3 bags of M&Ms (they crack with every launch so students kept wanting new ones)
  • tape measure
  • masking tape to hold M&M. I didn’t have any so we cut small Dixie cups I had laying around for geometry.
  • timer(s). I used my Flip because each launch lasted around one second and I can be accurate to within 1/30th of a second with it.

Overview of Project

  1. Build a catapult that shoots consistently to the exact same spot.
  2. Time how long the M&M is in the air for and measure the horizontal distance the M&M shoots
  3. Use a bit of physics and the vertex form to figure out the equation of the M&M’s trajectory
  4. Give students the height of the desk they will launch from. They calculate where they need to place the bull’s eye if they were to shoot if off that desk!

Tips and Hints

  • I gave my students freedom to build the catapults as they saw fit. I just gave them the hint that it should launch to the exact same place every time AND that they should know at which angle it launches if their M&Ms were flying crooked.
  • Doubling up the “diving board” makes each launch a bit more consistent b/c it gets rid of the bend.
  • Try to run this outside or in the gym. It was raining and windy in sunny So-Cal the days we were doing the trials so we had to limit the launches to within the classroom. This makes the launches limited to the height of the room, making the times shorter than I had wanted.
  • Try to avoid using the stopwatch the shorter the launches are.
  • Make the target fit into about 1 square feet. I’d say the bull’s eye was about 2 in radius. I had several groups get a bull’s eye on their first shot!

… the rest is in the file “MM catapult” to the right.