Quick Reads: Another Good Idea: A Yin and Yang Approach to Area and Irregular Shapes
The Measurement Standard for grades 6–8 in NCTM's Principles and Standards for School Mathematics (2000) emphasizes that students should develop formulas to find the areas of triangles, parallelograms, and trapezoids and develop strategies to find the areas of more complex shapes. “Developing formulas” often involves doubling or cutting and translating pieces of basic shapes, such as triangles, parallelograms, and trapezoids. Strategies for working with more complex shapes often include partitioning them into triangles, rectangles, or parallelograms. The yin and yang activity offers an irregular shape to investigate and extends and reinforces these strategies. Behind the name and the objects in the activity is the yin and yang story, which gives students the opportunity to reflect on different cultures and may help them remember the doubling strategy for finding area. This activity has been successfully implemented with students in China by Zhou Jinyan and with students in the United States by David Yopp.