Students’ age range: 12-14

Topic: Sum of interior angles in n-sided polygons

 

Description: 1. Issue each group with the compass point for them to discuss among themselves and identify and record what they need to know about angles in a polygon as well as what excites them, what worries them and what current stance or ideas they have on the topic.

2. Each group will be issued with a polygon. Two groups will be given pentagons, two will be given hexagon, two groups will be given heptagon and one group will be given an octagon. Each group will try to give the name of their polygon and a reason for its name. Teacher will correct and clarify as necessary.

3. Students will be asked to suggest ways that we can figure out the sum of the interior angles of their polygon without the use of a protractor. After taking suggestions, groups will then be instructed to see how many triangles can be formed by connecting one vertex to each of the other vertices using straight line segments. These line segments are called diagonals.

4. Each group will share and the results placed in a table. The sum of interior angles column will be left blank.

Name of polygon Number of sides Number of triangles Sum of Interior angles.
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon

5. From the table students will see if they can see any pattern in the number of sides on a polygon and the number of triangles formed. Students should note that in each case the number of triangles is two less than the number of sides.

6. Teacher will ask students if this information about the number of triangles can be useful in finding out the sum of the interior angles in the polygon and if yes, how?

7. Teacher will explain that since interior angles in the triangle add up to 180 degrees, the number of triangles can be multiplied by 180 to get the sum of interior angles in the given polygon.

8. The stop sign and the school road signs will be displayed for students to state the name of the polygon. Teacher will ask if by their estimation each angle in the polygons are equal. From this, students will see that some polygons are regular while others are irregular. Regular polygons have all their angles equal while irregular ones don’t.