Geometry lesson plan: Spreadsheet of interior angles in polygons

Purpose:

To learn the relationship between the number of sides in a regular polygon and to measure the interior angles.

Objective:

We will create a spreadsheet in order to determine the relationship between the number of sides in a regular polygon and to measure the interior angles.

Motivation:

Draw a circle with a compass on the board.

Anticipatory set:

Discuss how many degrees are around the center point where the compass was sitting. There are 360 degrees in a circle, which does not have any sides.

Development:

1. Discuss how many total degrees are in other polygons based on the circle.
2. Think about how those degrees might be divided up between the sides in polygons with more sides. There is a formula for this that we can use today. Divide 360 degrees by the number of sides in the polygon.
3. Create a spreadsheet, titled interior angles in cell A1. In cell A2, type in the heading of polygon. Continue titling B2: Number of sides, C2: Total degrees, D2: Interior angle. In cells A3-A10 (more or less depending on the students), type the names of progressively larger polygons: triangles, quadrilaterals, pentagons,  For the cells in column B, type in the number of sides in each polygon. In cells C3-C10, use the fill down function to set the total degrees to 360. Fill in the rest of the information using formulas or as individual cells. Calculate column d (interior angles) using 360/number of sides.
4. Look at column D. Do the interior angle values increase or decrease? Why do you think this happens? Think, pair, and share these thoughts.
5. Write about our discussion in math journals. Remember to include the formula we used and why it worked.

Summary:

Review math journal entries by sharing and discussing a few.

Evaluation:

The spreadsheet and math journal entries will serve as the evaluation of participation and what has been understood from the lesson.

Follow up:

Exterior angles will be examined and the relationships between the number of sides, interior angles, and exterior angles will be discovered.

Extension:

Students may predict the interior angles for other larger polygons with more sides. Another more advanced option is to start thinking about how to find exterior angles and how that relationship may work.

Materials:

Large chalkboard compass

Computer Lab with spreadsheet program installed

Math journal

Time frame:

approximately 40 minutes

Grades:

4 and up

Integration strategies used:

• Integration to make learning efficient for highly motivated students
• Integration to remove logistical hurdles
• Integration to facilitate self-analysis and reflection
• Integration to increase transfer of knowledge to problem solving
• Integration to allow for multiple and distributed intelligence
• Integration to develop technological and visual literacy
• Combination of directed and constructivist approaches.