## Thursday, January 29, 2015

### Math is always better when you do more than just WATCH

It is easy to think that when students watch us do problems that they get it.  They are usually concentrating and thinking about what we are saying, but it often does not sink in.  I am trying to get my students to DO MORE themselves.  This time it has to do with making a Ferris Wheel and using it to help solve Trigonometry problems.   Yes, it does take time out of class to do this.  I think it is well worth it to invest the time now, so that they can recall it later.

This unit we are covering the beginnings of Trigonometry.  Working with the Trig fundamentals is tricky.  Students often get confused.  So a few years ago we introduced the unit called "High Dive" where a fictitious scenario of a person being released from a Ferris Wheel into a moving tub of water.  (Key Curriculum Press)  Most importantly it gives the students a visual handle on the basic Trig ideas.  This year I extended this to include a physical handle on Trig.  We made Ferris Wheels out of pipe cleaners.  It turned out really well.  Seeing the test scores from this year, I'm confident that the students did even better than last year.  Here is what we did.

There is a Ferris Wheel whose center is 65 feet off the ground.  The Ferris Wheel has a radius of 50 feet.  The Ferris Wheel is moving at a rate of 1 revolution per 40 seconds. The diver is on the Ferris Wheel which always moves in a clockwise direction and will start from the 3 o'clock position. Here are some questions we explored.
1.  When will the Diver be at the highest position?  What is that height?
2.  What is the angular speed of the diver?  What is the linear speed of the diver?
3.  Map the divers height for 1 revolution of the Ferris Wheel.
4.  What height will the Diver be after 14 seconds?
5.  If there was a 30 fence hiding the front of the Ferris Wheel, what percent of the time is the Diver ABOVE the fence?
6.  How long does it take to go from the 3 o'clock position to the 8 o'clock position?

So with our Ferris Wheels IN OUR HANDS, we went through many of these questions while moving the wheel to match our questions.  The students made the Ferris Wheel with their own hands.  It was a homework assignment.  I gave them 8 pipe cleaners and 2 Popsicle sticks and they had to make a working Ferris Wheel.  They also had to make a place where the diver was on the Ferris Wheel.  Kind of like a marker.

Here is one of my students talking about her experience with the Ferris Wheel.

One Student made an unbelievable Ferris Wheel.  He got his own piper cleaners.

I know I learn better when I can touch it, feel it, manipulate it and visualize it.

Best,
Dave