1. How long will it take for the lava to cover the field?
2. Write down a guess.
First, this task is a complete copy of Dan Meyer’s volcano lesson (this whole blog is inspired by him, so no surprise here!). However, I decided to make this despite the similarity because it sets up perfectly for what we’re learning in class next week (sector areas).
Second, this image is from Daily Overview. Here’s the description from the site:
Pivot irrigation fields surround a lava field known as The Cinders, in Millard County, Utah. Along with farming, one of the elements of Millard County’s economy is fossil digging as Trilobite fossils are relatively common in the region west of Delta.
3. What information would be useful to figure this out?
4. Write down some questions you have in your head right now.
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
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
Daily Overview / Satellite imagery courtesy of Digital Globe / Benjamin Grant