8.6 Area
This is a set of guiding questions and materials for creating your own lesson plan on the
introducing the concept of area, along with some area formulas.
Common Core State Standards: G-GMD.1, G-GMD.3
Learning Objectives
 To understand the concept of area.
 To learn the definition of pi.
 To understand an informal argument for the formula for the circumference of a circle.
 To understand an informal argument for the formula for the area of a circle.
 To apply the formulas mentioned above.
Guiding Questions
 What is the circumference of a circle?
 What is  ?
o The ratio of the circumference of a circle and its diameter.
o

C
d
What happens when we solve for C?
o C   d   (2r )  2 r
 What is area?
o Area is the measurement of a surface. Traditionally we measure area in square
units; that is, we divide the surface into squares of the same size.
 What is the area of a circle of radius r?
o A   r2
o What video below for a derivation of this formula.
Optional Questions
 How many faces does a cube have?
 How can we find the surface area of a cube of side s?
 How can we find the surface area of a sphere?

Notes for Teachers
 I have indented some suggestions in the questions above.
Video of the Day
 Two videos have been included under Online Resources.
Exercises and Problems
 Successful Mathematics: North Carolina Common Core Math 1 Item Bank, Nagy-Lup, p.
92, problems 1-5.
Online Resources
 Derivation of the formula for the area of a circle
 Surface area of a sphere