Students will investigate the relationship between the base of a rectangle with area of 35 or 36 and its perimeter.
Before the Activity
Prepare the Activity Center with the desired windows
During the Activity
Assign each pair of students one of the following numbers:
2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, or 18. Have them draw a rectangle with that number for a base and having an area of 35 or 36.(or provide a worksheet with rectangles already drawn).
Have the students calculate (or measure) the height of the rectangle and its perimeter. The students can either enter their base and perimeter as a point to contribute to TI-Navigator™, or the teacher can call on students to randomly to submit their points to an overhead calculator.
Do a scatter plot of the data.
Talk about calculating the height by dividing 36 by the base. Take the perimeter formula and substitute x for the length and 36/x for the width in P= 2(l + w) to get P=2(x + 36/x).
Show that when you enter y=2(x+36/x) the line hits all of the points.
After the Activity
Ask the students to look at the graph and tell the minimum value for the perimeter.
What value of the base gives this value?
What is special about this rectangle?