Activity Overview
In this activity, students use the Geoboard to determine the perimeter of polygons. They learn to picture square roots visually as the side length of a square.
Before the Activity
Start the Geoboard App and format it
See the attached PDF file for detailed instructions for this activity
Print pages 65 - 72 from the attached PDF file for your class
During the Activity
Distribute the page to the class.
Follow the Activity procedures:
Construct a decagon whose sides are vertical or horizontal and find its perimeter by counting the number of unit line segments
Use the calculator to find the perimeter of the decagon and check the answer
Note it is easy to count units when the sides are vertical and horizontal lines, however diagonal lines, are not easy to measure as they are sometimes irrational numbers and must be estimated
Construct a diagonal segment
Build a square with the diagonal as a side and find its area by counting squares and half-squares, by using a surrounding rectangle, or dissection methods
Note that the exact length of the side of the square is the square root of the area of the square
Use the calculator to measure the length of the diagonal
Observe that this is an approximation as the length of this side squared does not give the exact area
For each given line segment, find the exact length by building squares and the approximate length by using the Geoboard application
Find different ways in which a rectangle can be divided to form three shapes that are equal in area
After the Activity
Students complete the Activity sheet and answer questions.
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary