Bridge Work (and Play)
By Lynn Hughes, sixth grade teacher
Imagine that a child’s experience with language arts consists only of handwriting and keyboarding practice, vocabulary lessons, spelling lists, grammar rules, and phonics instruction. How boring and empty that would be! But all of that becomes an invisible and essential skill set for some of the wonderful things we experience in life — writing a story, following a recipe, or curling up with a good book. It’s the same for mathematics. It comes to life when it’s integrated into something real and purposeful. At Miquon, math can be found embedded in many different kinds of projects, from the nursery group through the sixth grade. One example is our popular and engaging bridge study.
Every two years or so, my group engages in a multi-week, cross-curricular project that focuses on bridges. (This year, our sixth graders did it as a joint project with Diane and Jeri’s fifth grade group, and it was made richer through the involvement of more students and teachers.) Mathematics, history, geography, economics, literature, architecture, research skills, engineering, and more combine as students select and learn about a bridge somewhere in the world, consider bridges in a metaphorical sense through poetry and songs, and build their own bridges out of toothpicks.
As students start researching the real bridge they have selected, math comes into the work almost immediately as they gather statistics. We look for ways to make those abstract numbers meaningful.
- The Ben Franklin Bridge is 128 feet wide. How does that compare to the width of our classroom? Let’s get out the yardsticks and find out. It’s 9,650 feet long. Is that more than a mile? Close to two miles? If you walk at a rate of about three miles an hour, how long would it take to walk across that bridge?
- The bridge was opened in 1926. How many years ago is that? Do you know anyone who was alive when the bridge was opened?
- It cost about $37 million to build. What is that in today’s money? Well, $1.00 in 1926 is roughly equivalent to $13.00 today.
- As students work, they ask and find answers to a lot of these questions spontaneously. Their curiosity leads them to create and solve their own “word” problems.
Building bridges out of toothpicks is another big part of this study, and math is omnipresent. Students work in pairs to draw plans for a truss-type bridge, create a building site on a piece of foam core, and construct a bridge from toothpicks and white glue that will support a 2-kilogram weight. Students immediately want to know how heavy that is and ask to hold that much weight in their hands.
Precise measurement is required as they struggle to comply with the building specifications they are given. For example, the squares in which the bridge legs must be located have to be truly square, so they use protractors to create 90-degree angles. The squares must be five cm on each side and placed 20 cm apart. Errors as small as a millimeter are sent back to the drawing board.
Students must buy their toothpicks and glue from a limited budget. They learn to write checks and keep a balance sheet.
The plans consist of three views: front, side, and top. The scale is 1:1, and the plan sheet will be used as a template when building starts. We do preliminary lessons using Cuisenaire rods that help students learn to create 2D drawings of a 3D structure. We spend some time learning about triangles and their attributes, including the stability they give to any structure. The teams approach testing day with optimism and trepidation.
How is the math in a project such as this one different from traditional math instruction? One difference is the mixture of math skills that is required. Instead of assuming that all of the math in the current chapter will involve division, students need to think about their goal and select the right tools from all of their math knowledge – especially geometry, measurement, and arithmetic. Another difference is that most of the math questions are posed by the students, not the teacher or a worksheet. They ask them because they need to know. A third difference is that the math is deeply integrated with other subject areas, just as it is in our adult lives, rather than being something that is the sole focus of their attention for 45 minutes in class. As they read poems, analyze quotations, and hear songs about real and metaphorical bridges, they deepen their own language with new vocabulary and phrases, some of which are also a part of mathematics and engineering.
The entire project is (at least most of the time) a lot of fun. The amazingly varied and often beautiful assortment of the real bridges that they research has children calling classmates over to “look at this one.” The fantasy element of forming and naming a bridge building company, the satisfaction of designing and constructing something that first seemed impossible, and the excitement of testing day all combine to take mathematics beyond the idea that you are learning something because you will need it later in life. A project such as this means you need it right now.