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Mathline

Dr. Bill Whitmire, Mathematics Educator and House Builder

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Bill Whitmire Part of my life is teaching kids and working with math teachers, solving math problems and working with technology. That is good. But I also really like pounding nails, sawing wood, and trying to figure out the best way to solve a problem. That's what building stuff is: a lot of thinking to go along with the physical activity.

A construction project includes quite a bit of mathematics. It starts with figuring out how much of the materials you will need. Materials are a large chunk of the cost of a building. This includes the cement for the footings, the lumber( including studs, joists, beams, and sheeting), as well as nails, flashing, roofing, and insulation. You don't want a lot of waste, and you also want the materials you need to be there when you need them. This is one place where accuracy counts. This is a great opportunity to use a spreadsheet and your head!

When you start building, you have to be able to read the blueprints and figure out how (and where) to pour the foundation. You want things to be square and level. If you get off here, you make a lot of extra work for yourself later. I use 3-4-5 triangles to make sure my angles are square (right angles) and the lines are parallel. You also have to think about the slope of the land and how you are going to deal with water drainage. Water runs down hill, and you don't want your house at the bottom of a lake.

When it comes to framing the house, you need to take a lot of measurements. You want the walls to be plumb (straight up and down) and square. You also have to build in the rough openings for the windows and doors. Mathematics also comes into play when you build stairs. You want the rise and run (or slope) to be right so that the stairs come out perfect! No one likes to walk on stairs where one step is different than the rest. It just isn't right. So you have to do the math to make your stairs perfect.

Mathematically, one of the hardest things to do on a house is to cut rafters. Roofs need a certain pitch, or angle, so water will run off them correctly. Many houses have hip roofs that are made up of two large trapezoids along the long sides with triangles on the short sides. You want the ridges and the valleys to have the same angles. Making that work out requires some hard thinking and high school geometry.

Once you get the walls up and roof on and "dried in," there is still a lot of work. But this gives you the idea. You have to use your head and have knowledge of measurement, geometry, trigonometry, ratios and proportions, along with some algebra for figuring costs and paying the crew that help you.