Squaring a rectangle Introduction In order to properly locate the footings for the shade structure, students will have to create a system of “batter boards”. This is a layout method that creates a perfect rectangle of string which students can use to verify their excavation measurements to insure that the posts for the structure will be correctly spaced and at proper depth.  The Lesson We created a small-scale simulation of this process that uses rubber bands, tacks, and a cardboard “site”. The students had to create a series of perfect rectangles of different dimension. Index cards were handed out to use as a “check” for the first rectangles. Students had to check the last rectangles using only a ruler. After these group activities were complete, the class would be brought together for a description of the issues that came up.   The Essential Question What methods can you use to check whether your shape is a rectangle? The Math According to the NCTM, instructional programs through grade 12 should enable all students to- • Analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships. • Specify locations and describe spatial relationships using coordinate geometry and other representational systems. • Represent and analyze mathematical situations and structures using algebraic symbols. (Principles and Standards for School Mathematics, 2003) These ideas are imbedded in the lesson: 1. Students will conduct a comparison of the attributes of rectangles and parallelograms. These shapes have specific qualities in common: two pairs of congruent sides and parallelism of opposite sides. The length of their diagonals is what makes them different. Rectangles have equal diagonals. Parallelograms do not. By identifying these traits, students will be able to classify the shapes they have created, and make appropriate modifications. 2. Rectangles also have four angles that measure 90 degrees. Students can use the properties of right triangles to create right angles on their shapes.  3. The Pythagorean Theorem describes the relationship between the side lengths of a right triangle and its hypotenuse. By “breaking” their shape into triangles, students can predict the ideal length of the diagonal, and construct the shape appropriately. 4. They can also use benchmark Pythagorean triples to check their angles, i.e. the ubiquitous 3-4-5 right triangle. On Site Students created full-scale versions of their rectangles later that day on site. Their strategies and ideas from class were put to the test while laying out the shade structure, platform, and patio. This led to further questions about acceptable error and accuracy.  home projects the program about us donate sample activities math literacy