The third lesson in this chapter addresses area of a circle and is differentiated for process, product, student interest and readiness. The lesson has a menu of seven activities to give students a variety of experiences in finding the area of a circle. Each menu item is a different strategy for determining an approximate area of a circle, with the objective being that students understand the concept of area of the circle as well as the formula. Students were paired with another student, based on interests, strengths, learning styles, personality, and readiness. All students completed menu item number 7, and then each partnership was assigned 2 other menu items. If they completed these, they could complete as many of the other items as they had time for. The menu items/strategies were:
1) Count squares
2) Inscribe and circumscribe squares
3) The octagonal/Egyptian strategy
4) The simulated parallelogram – Kepler’s derivation
5) Find area by weighing
6) Measuring area with beans
7) Measuring area with radius squares (**all students did this one)
There were a variety of materials provided to complete these explorations: centimeter gird paper, colored pencils, straight edges, scissors, Post-it glue, balance scales, cardboard circle and rectangular weights, linoleum circle and rectangular weights, beans, paper cups, and drawing compasses.
In the launch part of the lesson, students were given a 7-cm radius circle on grid paper. They worked with their partners to estimate the area, and then the class shared their estimates and strategies. The menu strategies were then explained.
For the exploration part of the lesson, students had 2 class periods to complete their assigned choices, as well as any other strategies they had time for.
For the summary, students posted their area data on a class chart, and the class compared the different methods used. Students then chose their favorite strategy and explained why it was the favorite.
Additional thoughts about menus – they can be tiered or can offer the opportunity for choice. Menu items can be completed over a few days. Students may have a choice of the sequence in which they complete the items, or be required to only choose a certain number of items to complete. Menus are great for practicing procedures, reinforcing skills, reviewing, providing extension or preparing for assessments.
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