Geometric Applications of Exponents
Introduction:
When you hear the word "GEOMETRY," probably one of the first people you think about is Pythagoras. Most adults you ask, whether they were good in math or not, remember the infamous Pythagorean Theorem. In this module, we'll explore how Pythagorean's Theorem works and how we can use it to solve for missing lengths of right triangles. While this is the most common way that we think of using Pythagorean's Theorem, we can also use it to find the distance between two points. As we study this fundamental geometric theorem, we'll also take a look at its proof. In other words, we'll see why it always works! Finally, we'll wrap up this module by learning the formulas for finding the volume of the three dimensional shapes of cones, cylinders, and spheres. We'll use practical applications to interact with the idea of what volume really means and how it changes when looking at, not only three dimensional shapes, but three dimensional shapes with curvature. It's going to be a ball!
Essential Questions:
- How do we use the Pythagorean Theorem to solve for unknown side lengths of triangles?
- How do we use the Pythagorean Theorem to find the distance between two points?
- What are the formulas for finding the volume of the three dimensional shapes of cones, cylinders, and spheres and how do we use them to solve real-world problems?
Module Minute:
In this module, we investigated what could be the most famous of all fundamental geometric concepts, the Pythagorean Theorem. We discovered, by looking at Pythagoras' proof, that in any right triangle the sum of the squared legs is equal to the hypotenuse squared. In reviewing the proof, we can see that if we actually draw squares of the appropriate number of units how and why this theorem works. We also solved problems to find the missing side of a triangle. To do this, we used the formula a2 + b2 = c2,where a and b are the lengths of the legs and c is the hypotenuse. Furthermore, we learned that we can take this knowledge and apply it to finding the distance between two points by drawing a right triangle, labeling our legs, and solving for our unknown.
We also observed the formulas for several three dimensional shapes. The cone, cylinder, and sphere are all three dimensional shapes with curvature. We discovered that because these shapes all have curvature, or bases that are circles, that each of their formulas contains Pi in their calculations. This is what sets them apart from their all straight-edged counterparts.
What to Expect:
- Homework 1 and 2
- Quizzes 1 and 2
- Discussion
- Project
- Geometric Applications of Exponents Unit/Module Test
Key Terms:
|
Click 'Show' to see the hidden portion. |
|
This content requires JavaScript enabled.
|
|
