Today’s lesson focused mainly on understanding slope and how it pertains to topographic maps and contour lines. If you wanted to go rock climbing, would you want to go to a place on the map where contour lines are very close together, or very far apart? What about if you wanted to go for a hike with your grandmother? Learning about slope and how it is related to topographic maps is a real life application in which linear algebra can be visualized. We discussed how slope is measured by the change in elevation over the change in distance (rise over run) using the example of a skier going down a black diamond (steep slope) versus a bunny hill (gradual slope). We learned how to calculate slope using the equation: m= ▵y/▵x.
To demonstrate slope, we made our own topographic maps using playdoh mountains to create contour lines. We first constructed a playdoh mountain, then using fishing line we cut that mountain into slabs of equal thickness and traced them onto paper which created contour lines to create a 2-D representation of our mountain. Our second activity involved an opposite process, constructing a 3-D model using a 2-D topographic map. We traced the contour lines of Hawaiian island onto cardboard and then cut them out and pasted them to create a 3-D model of the islands topography.
So, the next time you and your child are driving on the hills of San Francisco or going for a leisurely walk in the park, ask them what the contour lines might look like if you were to draw it on a topography map!