## Monday, April 18, 2016

### Circumference and Area, How I Love Thee, Let Me Count The Ways.

It started off as a normal Monday in Geometry.  My students could not remember the work they did Friday.  They could not remember how to find the circumference or the area which they need for the arc length or area of a sector.  As part of the warm-up, they had to find the arc length of a circle, the area of a sector, and the volume of a cone.

So I started out the lesson telling them that the circumference formula and area formulas are their best friend.  If they know them, they know how to find arc length and area of sectors. One of the best way's I've found is for the students to use a fraction of 360 degrees time either the formula for the circumference or the area.

Most of the material I've seen for teaching these topics use radians.  I realize that radians are the usual choice but for my ELL students I'm finding they have too much trouble relating to it at the moment.  When I use radians, they often get confused so I have them use the fraction of 360 which is much easier for them to use because they "see" where it comes from.  In addition, most of the problems in the math book are in degrees an not radians.

Once I have students comfortable using degrees, I plan to introduce the concept of radians.  This is actually the perfect spot to introduce radians as it gives them something to relate the new concept to.  They have established prior knowledge I can build upon.

My first step will be to have them draw circles that can be divided in to 4, 6 or 8 parts.  This provides a visualization for radians and the circle being 2 pi. They can create their own unit circle for degrees and radians.  Once they see that the radians are a fractional part of the circle, I think they might find it easier to calculate arc length using radians.

I like using a hands on activity to help introduce the material.  CPalms has a nice introductory activity for radians using pipe cleaners. This lesson comes with the plans, the worksheets, the resources, everything you need to conduct the activity.  Better Lesson also has a complete lesson ready to go. This lesson is part one of a two part lesson on radians and includes a bit of history which is nice.  I like having a couple activities to choose from when I introduce radians to the students.  I'm set for tomorrow.