Anticipatory Set: We're going to tile an area outside of our classroom so we have a place to keep our muddy shoes in the spring. Objective and Purpose: Tell the students that the purpose of this lesson is to, "Calculate the area of squares and rectangles using a formula." Finding area is important so you can caluculate how much space is inside a given shape. Knowing this helps you order enough materials so you can cover that space.

Instructional Input and Modeling:
1) Open the Geoboard and make a square that measures one squared unit.


NLVM Geoboard

2) Use one geoband and make a rectangle. How can you use another geoband to illustrate the number of square units in your rectangle? How many ways can you illustrate 1/2 of a square or rectangle? Can you distinguish between vertical, horizontal, and diagonal lines on a geoboard?

3) Clear the geoboard and make a right triangle. How can you use another geoband to illustrate the number of square units in this shape?

4) The steps for finding the area of shapes that include a diagonal lines are:

a) count the number of diagonal lines in a polygon.
b) for each diagonal line, take a geoband.
c) use the ends of each diagonal as opposite corners of a square or rectangle.
d) after you surround each diagonal with a square or rectangle, count the total number of square units in the resulting shape.
e) from the total, subtract out the parts you do not need.
f) the remaining number of square units is the area of the polygon.
g) check your answer using the "measures" button.

Checking for Understanding and Guided Practice:
5) Make a shape on your geoboard and switch places with a partner. Have your partner use the diagonal line rule to determine the area of your shape. Do the same with your partner's shape.

Assessment:
What evidence should the teacher look for to determine that a student understands how to use the diagonal line rule to determine the area of any two-dimensional polygon?

a) student can apply the diagonal line rule and determine the area.
b) student can explain the process.
c) student can apply the rule in other situations.