Act 1
How many houses are in the development?
Write down a guess.
Act 2
3. What information would be useful to figure this out?
4. Write down some questions you have in your head right now.
Check out this Desmos graph to give the students an opportunity to play with the angles in the circle. Two radii and an equation are setup to calculate the angle as the students move the radii. From there, the kids can find sector areas.
Finally, here is some real estate information on Trulia. The students can figure out an average square footage by using the average listing price and average price per square foot.
Act 3
Sequel
5. How much money would be needed to build and develop this community?
In order to extend the task, I like the idea of putting the students in the shoes of the community developer. They could brainstorm the information needed in order to figure this out. How much does each lot cost? Material cost? Zoning permits and restrictions? Wildlife preservation issues? There are numerous possibilities.
It’s also interesting to note that the original developer sold the property due to financial issues. As a final report, the students could write a letter to the developer in order to provide a guide to financial planning.
Standards
Common Core
HSG.C.B - Find arc lengths and areas of sectors of circles
TEKS
G.12(C) - apply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems