Our newest block was the third area block. After this block, on Tues-Wed, April 3-4, we will be learning about surface area and parts of circles. The quiz will be Thurs-Fri, April 5-6, about 40 pts. There will be a review assignment.

Today in class we had three different pieces of learning:

1) Apply the regular polygon formula until you understand it (warm-up from pp 427-8: 3-6,12).

2) Learn (derive, apply) formulas for Pi, circumference, and area of circles.

3) Find areas in the coordinate plane formed by 3 or 4 graphed lines enclosing a region.

We also went over homework and warm-up thoroughly.

For #2 above, the key issue is to understand that Pi is just the ratio of circumference to diameter for every circle (measure around a round lid, measure across, divide). Circumference is Pi times the Diameter of any circle (just rearrange the definition of Pi. This also leads to C= 2 X Pi X r.

We derived the area of a circle by dissection: take a circle and cut into 16 "pizza slices" (sectors). More would be better, but 16 is enough. Rearrange into a rectangle with side lengths of r and Pi X r, so area = Pi X radius squared.

The bounded area activity and answers are attached. Do this activity on graph paper if you were absent. You can find graph paper online by googling "graph paper PDF" and printing something that you find in an image.

HW #3: pp 427-8: 7-8, 13, 15-16, p 435: 1-14.

Show work. When solving for a dimension, use algebra. On p 435, play attention to = vs. appr =. Approximate means to use the Pi key in the calculator.

Today in class we had three different pieces of learning:

1) Apply the regular polygon formula until you understand it (warm-up from pp 427-8: 3-6,12).

2) Learn (derive, apply) formulas for Pi, circumference, and area of circles.

3) Find areas in the coordinate plane formed by 3 or 4 graphed lines enclosing a region.

We also went over homework and warm-up thoroughly.

For #2 above, the key issue is to understand that Pi is just the ratio of circumference to diameter for every circle (measure around a round lid, measure across, divide). Circumference is Pi times the Diameter of any circle (just rearrange the definition of Pi. This also leads to C= 2 X Pi X r.

We derived the area of a circle by dissection: take a circle and cut into 16 "pizza slices" (sectors). More would be better, but 16 is enough. Rearrange into a rectangle with side lengths of r and Pi X r, so area = Pi X radius squared.

The bounded area activity and answers are attached. Do this activity on graph paper if you were absent. You can find graph paper online by googling "graph paper PDF" and printing something that you find in an image.

HW #3: pp 427-8: 7-8, 13, 15-16, p 435: 1-14.

Show work. When solving for a dimension, use algebra. On p 435, play attention to = vs. appr =. Approximate means to use the Pi key in the calculator.

pre-ap_geometry_2018_bounded_area_worksheet_and_answers.pdf |