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.

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