The Pythagorean Theorem, Distance, Surface Area, and Volume
The Pythagorean Theorem, Distance, Surface Area, and Volume
Objectives
Students will develop a general understanding of geometric formulas including the Pythagorean theorem and formulas for the surface area and volume of solids. Students will:
- use the Pythagorean theorem to find the lengths of sides of right triangles.
- use the Pythagorean theorem to prove that triangles are right triangles given the side lengths.
- find the distance between points on the coordinate plane.
- apply problem-solving tools to find surface area and volume.
Essential Questions
- How can recognizing repetition or regularity assist in solving problems more efficiently?
- How are spatial relationships, including shapes and dimension, used to draw, construct, model, and represent real situations or solve problems?
- How can the application of the attributes of geometry shapes support mathematical reasoning and problem solving?
- How can geometric properties and theorems be used to describe, model, and analyze situations?
Related Unit and Lesson Plans
Related Materials & Resources
The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.
- http://www.cut-the-knot.org/pythagoras/index.shtml
- http://mathworld.wolfram.com/PythagoreanTheorem.html
- http://jwilson.coe.uga.edu/emt668/emat6680.folders/brooks/6690stuff/righttriangle/pythagconv.html
- http://math.about.com/od/formulas/ss/surfaceareavol.htm
- http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/
Formative Assessment
Final 04/26/13