You need to have JavaScript enabled in order to access this site.

8.6 - Area

Introduction:

This is a set of guiding questions and materials for creating your own lesson plan that introduces 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 $\pi$ $\pi$ ?

The ratio of the circumference of a circle and its diameter.
$\pi=\frac{C}{d}$ $\pi=\frac{C}{d}$

What happens when we solve for $C$ ?

$C=\pi d=\pi\left(2r\right)=2\pi r$ $C=\pi d=\pi\left(2r\right)=2\pi r$

What is area?

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 $r$ ?

$A=\pi r^2$ $A=\pi r^2$
View the 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 Sources:

Additional Resource for Teachers:

If you wish to download the contents of this page as a printable pdf, click here: 8.6 Some Area Formulas.pdf Download 8.6 Some Area Formulas.pdf