Arcs and Sector Areas

Currently in Geometry, the students are working on area, circumference, arcs, area of sectors, etc.  They are struggling to relate the topics and try to look at each topic as a separate topic.  I want to find ways that might help them learn to flow from one topic to the next.

I found this 39 page Pdf which contains a whole unit on arcs and area of sectors. It has everything from the pre-assessment to the lesson plan to the activities and the post assessment.  This is great in that it introduces radians so it would be perfect between circles and the trigonometric ratios.  I wish I'd found this about two weeks ago when I was starting this.  That being said, I could easily use parts of this to help my students learn the material better through the use of activities rather than relying on worksheets.  It is labeled as a concept development packet.

This site has a great pdf of cards with real life problems for finding circumference, area, radius, and other interesting things.  For instance one card has you calculate a sheet of gold to cut coins from but the sheet has to be of the smallest size so there is less waste.  I like the variety of problems since the problems are not all circumference, or area, or diameter.

This slide share shows where circles are found in real life from theater to car tires, to the earth, to manhole covers.  It has some good information and would be a great introduction to the card activity.

The Department of Education in Virginia has a great 5 page lesson plan and activities for arc length.  There are two activities included.  One finds the length between two ends which are actually arcs and requires use of the Pythagorean Theorem while the other is an activity that requires students to cut a 10 inch cake into 12 pieces.  The questions require thought so it will take them a while to complete.

This activity has students working to figure out the area of a large cookie that is at least 8 inches in diameter.  They end up calculating area and circumference of the cookie, the area of their slice and the length of the edge (arc) of the cookie.  When done they can eat it.

Finally, this power point presentation has some great practice problems for students that are done in such as way as to have a friendlier feel than most worksheets.  There are instructional slides scattered through out the problems.  I like the way its organized.

Have fun checking it out.