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As I write, the thump of sledgehammers and the whir of buzz saws can be heard outside my kitchen window. In my small community of houses, we all have white picket fences in our front yards. It was actually part of the charm that sold me on the house. The fences, however, are now 15 years old and starting to show the wear and tear of the years. The past few months have seen many of my neighbors replacing their fences. As each new fence goes in, I find it impossible not to scrutinize the workmanship. In my mind, a picket fence requires precision, and small inconsistencies like uneven pickets or cuts really stand out to me. Last week, the perfect picket fence went up and went up quickly in a neighbor’s yard! Each day on my twice-daily walks I looked for imperfections, but I just could not find one. I contacted my neighbor to get the contractor’s number, and today my new fence is going in.

We often think about real-world math as a way to engage students in problem-solving. But this situation got me thinking about how essential math skills are in operating a successful small business. Stop for just a minute and think about all of the math that took place between yesterday when the contractor provided me a quote through the completion of the project and how that impacts the success or failure of this businessman.

How could you turn this into a problem for your students? Let them work in groups and take on the role of the fencing company owner.

• What information would they need to generate a quote for a customer? (cost of materials, cost of labor, desired profit margin, length of fencing, etc.)
• What other considerations are involved in developing a quote? (quote must be comparable to other companies doing business in the same area, ability to schedule and carry out the work, etc.)
• What math skills are involved in building the fence? (very precise measurement, leveling of the fence, spacing of posts, etc.)

Sure, we could generate a lot of word problems for students to solve related to this situation, but giving them an open-ended challenge such as the one above immerses them in the math in a way that solving word problems can’t. Will every group think of every way that math is used? No, but when the teams all present their findings, I’ll bet you’ll have most of the bases covered. And if there is something important that none of the teams think of, a few well-placed questions from you can coax out additional ideas.

I would love to read comments about how you might use, or have used, a problem like this in your classroom. Drop a comment below or post one on Twitter! Be sure to tag me! @MathCoachCorner