In this Computer Algebra System (CAS) activity, students use 'landscape' paper and fold the top left corner of the page so that it just
touches the bottom of the page. They calculate the area of the triangle formed by the bottom left corner and find the distance that forms a triangle with maximum area.

Before the Activity

Install TI Connect™ using the TI connectivity cable

See the attached PDF file for detailed instructions for this activity

Print pages 1 - 2 from the attached PDF file for the class

During the Activity

Distribute the pages to the class.

Follow the Activity procedures:

Fold the top left corner of the landscape paper so that it just
touches the bottom of the page

Measure the sides of the resultant triangle and determine its area

Fold the paper using the outlined method for different values

Record the corresponding values for the base and for the area of the triangle

Determine the value which gives the maximum area of the triangle

Draw a scatter plot of the increment value against the area

Use the graph to estimate the value which gives the maximum area of the triangle

Determine an expression for the hypotenuse of the triangle

Find the expression for the area of the triangle

Calculate the derivative of the expression for the area

Equate the derivative to zero and find the maximum area

Generalize the solution

After the Activity

Students answer questions on the Activity sheet.

Review student results:

As a class, discuss questions that appeared to be more challenging