Slope in Context.

  As we know most of the mathematics taught in school is done in isolation with no connection to the real world.  We even teach things like two step equations as totally separate from a point on line.

If we could spend more time relating the math taught to the real world.  For instance if we could show how easy it is to calculate the orbital velocity of the space station.  Would that capture our student's interest.

Unfortunately, most of the time when we teach math, the "real world" problems used in most textbooks have an artificial feel to them even if they are based on reality because they seem rather isolated.  Providing context that feels real is important because it helps students answer the question of "When will I ever need this."

For instance, when we teach slope, we can make it so much more than just teaching the slope formula just to have students calculate slope based on two points shown on a coordinate plane.  This is not an authentic task.  It really provides no connection to situations in real life,  especially since slope in real life appears in many different forms.

Most students can tell you there is slope associated with roofs but they don't know much more than that.  They are unaware slope of a roof is called pitch and refers to the "rise" of the roof over the "run" based on a foot or 12 inches.  They don't know that most roofs have pitches of between 4/12 or goes up 4 inches for every 12 inches horizontally and 9/12 or rises 9 inches every 12 inches.

Furthermore, the pitch of a roof determines or eliminates the type of roofing material that could be used.  For instance, if the pitch is only 2/12, you don't want to use asphalt shingles because its  easier for the water to seep in but you wouldn't want to use rubber membranes on the normal pitched roofs.  On the other hand, a roof with a pitch of 2/12 is not going to be used in an area of heavy snow because the snow could build up so the weight causes the roof to cave in.  If the roof is too steep, the snow could slide off and hurt someone below.

Another use of slope is when building a house.  If you build a house on the side of a hill as many do in California, you'd use a different technique than if the land is much flatter.  One way to get a better idea of the contours of the land is to create a cross-section based on the elevations from a map.

A cross-section gives a wonderful visual representation of the information on a map and allows students to "see" what it looks like, even if they've never been there.  In addition, students have a chance to learn how a geologist might use this information versus an architect, versus someone planning a road versus planning a ski resort.

If you are a land developer, you are not going to build your gated community at the bottom of a steep hill because the water would rush down and possibly flood the area. If you do, you have to consider how you are going to keep that from happening.

So the next time we teach slope, maybe we could take time to do a couple of activities which would expose students to these real world situations so they see the use for learning about mathematical slope.

Let me know what you think, I'd love to hear.  Have a great day.