Week 44: Conics, Orbits, and Projectile Motion

You don’t have to be in high school math to play with conics, orbits, and projectile motion. This week (or month) learners can play with projectile motion, orbits, and conics sections with the activities below:

1.) Slicing cones

• Learners can mold cones with clay and slice to see the possible shapes. This will give circles, ellipses, parabolas, and hyperbolas.
• Create a cone sculpture with an intersecting plane using paper, string, pipe cleaners, or other mediums.
• Try John Sharp’s sliceform template.
• Check out this Conics Geogebra tool by Irina Boyadzhiev.

2.) Observe parabolas through projectiles

• Create a straw rocket (don’t aim it at someone) and take slow motion videos of their flight and observe the curve that is created. For a template and activity, go to NASA’s website here. Look at various launch angles and analyze the differences and similarities in curves.
• Create a water balloon launcher with PVC pipes (or other parent/teacher approved apparatuses). Record their launches and analyze. (Water rockets are also fun.)
• Play with a garden hose and the curves created by shooting water up into the air.
• Play with the PhET simulator.

3.) Play with ellipses and circles through gravity

• Use tacks and string to create ellipses (2 tacks) and circles (1 tack or compass). Create an abstract work of art with these tools.
• Play with this gravity simulator by the NSTMF (really fun!)
• Universe Sandbox is a program that costs money, but is excellent for playing with orbits and answering a lot of learners’ “what-if’s.” I love, love, love this tool!
• JPL learning activities are here.
• Use a large piece of elastic cloth and place weights in it. See if you can create orbits with marbles. We have found that a hula hoop works with swimsuit material. Here is a video as well.
• Take time to get outside and observe the planets, comets, and astronomy that is with us every day.

There are so many other ways to play with these curves, so experiment, draw/paint, and enjoy.

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Week 12: Galileo and Gravity

This week we are going to take a look at applied math. Learners will be given a ramp (this can be a ruler), a ball that fits on the ramp, measurement device (ruler) and a timer. With these instruments learners can investigate the relationship between distance and time as the ball rolls down the ramp. I encourage teachers and facilitators not to give too much procedure here and let students come up with the way they will execute an experiment and record their data. I usually go with a 10-15 minute “sweat-it-out” period before I give them any hints.

This exercise is a great intro into calculus concepts like “instantaneous velocity” and derivatives of functions that model falling bodies. I think this is fun to do with middle schoolers and up. You can plot your functions and then draw the tangents to the curve and find slopes (this is fun in groups).

If students are stuck, hints may look like this:

• Have you set up an experiment that you can repeat to get multiple samples?
• What time intervals are you going to try to record? how far has the ball rolled with zero seconds? 1 second? 2 seconds?
• Once you have your data, can you plot it to see if there is a relationship? Is it a direct variation?
• If you plot the relationship, what type of curve is it? Can you create a function for that curve?

Here is a sheet I had for a class that students received after completing their experiments: