Technology for Learning
a Math Trail in your Community
by BOB COULTER
I’ve often found that math becomes much more real for kids when they have a chance to use what they are learning out in the community. One of the most powerful tools to do that is to develop a math trail, a project idea that I first encountered through Ron Lancaster, a friend who teaches at the University of Toronto. Basically, a math trail involves walking through your community to see the many ways in which math is used “in the real world.” In this space I’ll share a few examples from my home town to spark your imagination. While examples from your community will be different, the ideas should work wherever you are. For each of the trail stops here, there are a number of technology extensions you can use in the field or back in the classroom to enhance your students’ experiences.
Symmetry in Buildings
Many buildings exhibit a symmetrical design. How many lines of symmetry can they see? For example, in the church photograph, if you were to draw a line directly through the center of the sanctuary portion of the building, it would appear to split the building exactly in two. In fact, the sidewalk seems to invite this view, with the centerline running directly into the middle of the building. Can your students define a portion of the steeple that exhibits symmetry? Digital photography can provide a useful exten-
sion to this activity in that students can use a vari- ety of software tools to mark up the photographs, drawing in the lines of symmetry. Given how ubiquitous digital cameras are these days (includ- ing those in smart phones) you can challenge your students in a homework assignment to submit pictures showing other examples of building sym- metry in the community.
Size and Scale in Sculptures
The fountain sculpture in the photograph provides the starting point for several interesting mathematical adventures. As a beginning, ask the students to measure the radius of each of the three bowls. From there, can they calculate the surface area at the top of each level? Or, for those looking for a greater challenge, can they calculate how much water each level can hold? Extrapolating from this beginning, ask students to extend the pattern they see.
If there is a pattern in bowl radius moving from small to medium to large, how large would the next one be? Would it still fit in the rectangular base of the sculp- ture? How many layers could be added before the sculpture would no longer fit in the alley? How tall would the sculpture be at that point? Note that one small question can mushroom into a range of mathematical investigations. Back in the classroom, students can use data software to graph the relation-
ship between these variables. What is the shape of a graph with the radius of each bowl on one axis and the corresponding surface area on the other? How does
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