Students create a family of similar rectangles and then write the equation of the curve that will connect the upper-right vertex of each rectangle. Students will then create a family of rectangles that have the same area and will write the equation of the curve that connects the upper-right vertices of each rectangle. Students will make comparisons of both sets of data.
Before the Activity
This activity is appropriate for an Algebra 1, Algebra 2, or Geometry class. Before beginning the activity, students should review the definitions of rectangle and similar. They should also review identifying direct and inverse variations. Students should also be able to write a quadratic equation to fit a set of data.
During the Activity
Teachers should put the students in groups for this activity. This is a student-centered activity. The teacher should circulate among them offering assistance as needed. The activity is written in for students to record their answers on the handheld although they can be instructed to record their answers on a separate sheet of paper.
After the Activity
After the activity has been completed, have the students present their families of rectangles to the whole class along with the equations that they wrote. Have students compare their results to their classmates.