This activity is adapted from one of the TI books. Students measure lengths and widths of rectangles and record for the class to see. Each group's rectangle has the same perimeter, but different areas. After a discussion, students make predictions, a scatterplot, and quadratic regression. An extension is available for maximization when given a set length for only three sides of a rectangle.
Before the Activity
It is important to have the rectangles already cut out with lengths and widths marked as l and w. This is because one rectangle may have a length of 5 and a width of 7, whereas another may have a length of 7 and a length of 5.
Another option is to give the students directions, but no figure. The directions give them perimeter and length instead of making them measure. While I prefer measurement, this would save a little time. I have provided an attachment if this is preferred.
Also, make sure the chart for recording data is on the board. A representative from each group must come and record the group's data for the class.
During the Activity
The teacher basically serves as facilitator. Unless the class is advanced and accustomed to working in groups, I would expect some questions in regard to calculator functions.
I have tried to make the student document as thorough, yet user friendly, as possible. After the initial sharing of data, the groups should be ready to proceed with teacher facilitation.
After the Activity
After the activity, discuss the results. You may assign the extension at the end of the student document for homework.
I have found it is very good for students to focus on explaining how they answered the extension. It allows for an opportunity to review material from the day before via communication from students' to the class.