Measuring in the Field by Casey Murrow “

them to students from fourth to eighth grades. Using paper and pencil to find, draw, and label angles and dimensions has been part of the study of geometry for many years.

D Pythagoras Outdoors

But what if we create triangles on a larger scale, outdoors, pinning rope or inexpensive survey tape onto the playground or athletic field? On a paved area, students could create other versions of the triangles with sidewalk chalk. If we make that initial angle a true 90° and sides AB and AC are each ten feet, how long do you think BC will be? We can instruct our students to estimate; compute what is on the

ground; or use an algebraic formula to compute the length of BC. The answers from these different methods will vary, and that variation offers opportunities for all sorts of discussion, data collection, and further exploration of triangles. Part of my work is as a consultant for Synergy Learning, a profes-

sional development organization specializing in elementary science, math, and tech- nology. A group of sixth graders I was working with in Springfield, Vermont, recently made huge right triangles in a grassy area. They then worked through several conven- tional Pythagorean theorem problems from a textbook. We enlarged the dimensions, changed the units of measurement, and in the process of solving the problems, created a very large display of shapes. Then we climbed a slope and photographed our handiwork. Is this off-task foolishness, replacing work that could be done much faster at a desk

or table? After engaging in these activities, the teacher of these students reported to me that based on formative assessments, the students showed greater comprehension of concepts related to triangles than she had seen previously. The outdoor approach was memorable and students could recall the lessons months later. We essentially used text- book problems and worked with the geometry on a huge scale. A study such as this can include an exciting next step: seeking real-world examples of triangles either in nature (such as stem structures in some plants) or in the built environment (in bridges, build- ings, or smaller structures).

Using School Grounds

If your school is near a football or soccer field or a tennis court, consider all those par- allel lines. Or at least they should be parallel. There is a way to check them with right triangles, but you may want a measuring tape that is longer than the width of the field. Looked at in a different way, students might want to check those right angles them- selves. Is one side truly perpendicular to the other? Measuring dimensions on an athletic field presents a variety of large-scale problems that can involve parallels, angles, and

©synergy learning • 800-769-6199 • May/June 2011 Connect • Page 23

raw a right triangle on your paper. If side AB is five feet . . .” We have all heard such instructions, in fact, many of us have given

Field-based teaching takes planning. Here a group of teachers develop plans for integrated science and math units.

casey murrow