Introduction

Do we live in a regular or irregular world? Wouldn't it be nice and neat if all polygons in our world were regular with all of their sides and angles congruent? Did you know that most of our formulas for finding area and volume were written for regular polygons?

In this lesson, we will look at ways to find surface area and volume of irregular shapes. Remember that you can also use similar figures or divide your figures into more "regular" parts to calculate measurement.

Lesson Objectives

Following successful completion of this lesson, students will be able to...

  • Calculate area and volume from dimensions for a project.
  • Calculate appropriate materials to use for an application.
  • Calculate estimates for construction or repair projects.

Essential Questions

  • How are geometric principles used to define physical objects?
  • How can geometric principles be used to identify characteristics of objects?
  • How can geometric principles be used to generate measurements of objects?
  • How can ratios and proportions generate accurate measurements?
  • What is the relationship between dimensions length, width, and/or height) in two- and three-dimensional objects?
  • How does a change in one dimension affect the other dimension(s)?
  • How can technology be used to compare mathematical solutions?
  • What math is used to guide personal finances?
  • How is math used to analyze and model personal finances and everyday-life activities?
  • How is math used to guide decisions made in different businesses/industries?
  • How can technology be used to solve math problems and to compare mathematical processes or procedures?

Enduring Understandings

  • Geometric and measurement principles can be used to define and explain our physical world.
  • Geometric concepts are used to create three-dimensional products from two-dimensional concepts.
  • Mathematics can be used to analyze trends and to optimize products or performance.
  • Mathematical problem solvers apply various skills and strategies to make decisions about everyday-life activities and to solve real-world problems.

The above objectives correspond with the Alabama Course of Study: Career Math standards: 2c, 9b, 10a.