Chapter 8 Review and Test

For the Chapter 8 Review I spent 2 days.

I thought I was clever to use questions 1-10 from the review section as a warm up. They were a set of matching questions where you match the area formula with the shape it works for.

After that we went over questions from 8.7, that used elements from the whole chapter.

On the second review day I used another set of questions from the review section to warm up, then gave a review assignment. So half of the review was in warm-up form, and the other half was classwork. I guess that was my attempt at being tricky.

On Tuesday I gave the test. I still have to grade it and will post my general feelings about that when I have some results to share.

8.7 Surface Area

Surface area was introduced through the context of cutting up a cube, or box, and laying it out and measuring the area of each piece.

I think that this is a massive section to cover in a day or two. In this chapter we are looking at:

• Prisms
• Pyramids
• Cones
• Cylinders

I think that this would be a good chapter to break up into a couple parts and look at with a little bit more detail then I was able to. I think things would go more smoothly if we looked at prisms and pyramids one day, then cylinders and cones the next day. This would allow for students to make a stronger connection from prism/pyramid formula to the cone/cylinder formula.

I think it is good to develop an intuition for looking at objects in 3-D. But rushing through this section doesn't do much to help build this intuition.

The vocabulary and 3-D intuition comes back into play in chapter 10 when looking at volumes of 3D objects.

Exploration: Geometric Probability II

This Exploration looks really interesting, but I didn't have time to do this with my class. I think that geometry is a great way to look at probability and I would like to try this with a class in the future.

8.6 Any Way You Slice It

This chapter looks at parts of circles.

My students found this very challenging. In this section we are looking at the area of 3 types of sections of a circle: a sector, an anulus, and a segment.




In the book they explain how to find the areas of these and I think that these were confusing to my students. As I think about this more I believe that the concept of how to find areas is more important then the formulas.

For the area of a sector a complicated formula is presented, and I think that the best way to think about this is by comparing fractions.

partial degrees / 360 = partial area / total area

This will help understand the idea of comparing proportional parts. The degrees are proportional to the area. This concept is very useful, and could be used for a wide variety of problems, I think this alone might deserve a full day in the future.

8.5 Areas of Circles

The chapter looks at Areas of circles.

There is an activity which I didn't do but I would like to do if I had time. Cut a circle up into a bunch of sectors and lay them out to form a rectangular-ish shape. The rectangle will have a length of ( C / 2) and a width of r. I would like to do an activity where students cut up a circular object, like a paper plate or a pizza and find the area, then derive an area formula.

One thing I like about cutting up a circle into pieces is that it is a good way to introduce the concept of infinity, and thinking about cutting something up into infinitely many pieces to find the area.

8.4 Areas of Regular Polygons

8.4 has a nice investigation where students break a regular polygon up into triangles, and find the area of each triangle, then multiply this area by the number of sides. Interesting how the number of triangles and the number of sides are the same, eh?

I started this by asking the students to try the Investigation as homework. It is my hope that some of them will notice the pattern on their own and better understand the formula. Only a few students seam to have made an attempt at the homework, but the people who have tried seamed to do well on it.

In class we looked at a regular polygon inscribed in a circle and looked at how as we add more sides to the polygon it is becoming more like a circle. I am trying to prepare students for tomorrow's area formula.

8.3 Area Problems

8.3 Brings together all the area formulas we have found so far. And it is bringing them together in word problems. I am used this lesson to go over how to approach word problems.

1: Read the problem carefully
2: Draw a picture and label the apropriate parts
3: Think of what equations might help with solving this problem
4: Fill the equations with the parts from the picture and solve

I would like to come up with a nice concise way of explaining word problems for my Geometry students. Any help would be appreciated.