This document is an activity sheet that asks students to use a rope to form different sized rectangles, measure their dimensions, calculate their areas, and look for patterns between the rectangle sizes and their areas. Students are asked to record their results in a table, write equations to represent the areas, and identify the maximum and minimum areas. They are also prompted to look for patterns and write a general rule for maximizing rectangle area.

1. © 2011 National Council of Teachers of Mathematics
http://illuminations.nctm.org
Princess Dido and the Ox Skin NAME_________________________
1. What is the length of your assigned rope? _______________
2. Use your rope to form many different rectangles until you recognize
a pattern. Measure the length and width of each rectangle, and
record them below. Make sure that the two longer sides have the
same measure and that the two shorter sides have the same measure.
Attempt to use whole-number dimensions wherever possible. Then
calculate areas to complete the table. Use the back of this sheet for
more room.
RECTANGLE
LENGTH OF
RECTANGLE (l)
WIDTH OF
RECTANGLE (w)
AREA OF
RECTANGLE
(A = l × w)
1
2
3
4
3. Write equations for the areas of your rectangles. What were the maximum and minimum
areas?
4. Did you notice a pattern between the size of the rectangles and areas of the rectangles?
Explain. Compare your answer with another group that had a different length of rope.
5. After comparing, write a general rule for maximizing the area of a rectangle.