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

Geogebra: The Unit Circle and the Reference Angle.

A couple of colleagues of mine have been showing me things in Geogebra.  I tried it this week with a unit circle problem.  It turned out great.  I had each student/pair with a computer in front of them.  We went over the Unit Circle and the students used the laptop or iPad to maneuver around the GeogebraTube post that I had made.  My colleague called this COMPANION Technology.  (They used it with their learning) Many of the students started out using the digital Unit Circle and manipulating it.  However, as time went on, many stopped using the digital technology and just did the work in their head or on paper. There was a homework assignment that involved the digital Unit Circle that I had made in Geogebra.  About half of the students ended up needing it.  The next day the unit circle questions and discussions were amazing.  They really had a conceptual grasp of it.
Here is the link to the http://geogebratube.com/student/m69795  to see the unit circle geogebra worksheet.  Please note the questions at the bottom of the page.

Steps I took to get this up and running.
1.  Download Geogebra to your desktop.  http://www.geogebra.org/cms/en/download/
2.  Make an interactive Geogebra File.  (see intro to geogebra youtube:  http://www.youtube.com/watch?v=OwNru3Znsfk  I used this video to help me:  http://www.youtube.com/watch?v=GG0F49XBJO0
3.  Save the file to a place where you can remember to retrieve it.
4.  Go to Geogebratube.org  http://geogebratube.org/  You will need to login.
5.  Upload your file to Geogebratube and fill in all needed information.
6.  Get the link of your upload and distribute it to your students.

I hope you can give Geogebra a try,
Dave

Will Froggy get to the other side of the Lake? Solving Trig Equations.

WILL FROGGY GET ACROSS THE LAKE?

Froggy is a mechanical toy Frog.  He follows a sine wave path surfacing every 12 feet.  He dives down 7 feet from the surface along his path.  He is trying to get across Lake Tad which is 120 feet wide..  There is one problem, actually two.  There are two shallow places in the lake that if Froggy hits will break.  That's right.  Froggy will not make it if he hits those shallow spots.   The first low spot is 24 feet from the starting spot.  The second low spot is 51.5 feet from the ending spot.  The video actually will tell you a possible way of solving and the answer.  This is definitely not the only way to solve this question.
Click Here to get the Frogger Worksheet

This activity helps students put a few skills and concepts together.  They need to know how to build a trig equation.  They need to know how to graph a trig equation.  They need to recognize the periodic nature of the trig equation to spot the answer farther out on the graph.  

I had my students make a video of their answer.  I checked out the iPad cart for the day and had students make their videos on the app called DOCERI.  We then uploaded them to our content management system called CANVAS.  At the bottom of this blog, I am giving you an example of one of the solutions.

STUDENT SOLUTION

All the best,
Dave