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# Slipping and Sliding with Waterpark Math

Updated: Mar 15

Looking for a way to apply some math and engage students? Look no further than amusement parks, and specifically waterparks, since today is National Waterpark Day. These are great real-world experiences many students are probably enjoying right now, that provide a fun way to show them where the math comes into play. There is so much you can do - i.e. the angle of elevations, the amount of speed needed to do a loop-de-loop, the height of a roller coaster or a water slide, what's the maximum drop or the maximum angle you can safely construct a slide or roller coaster. Geometry, physics, algebra, science, engineering - talk about your STEM application!

I found a fascinating article on the physics of waterslides, The Physics Behind Waterslides (Kramer, 2013), that describes inertia, radius-curves, depth of water, etc. It mentions one of the world's tallest waterslides, Disney' waterslide, Summit Plummet, in Florida, which happens to be mentioned in the activity I am sharing in this post. It's a 120 foot high slide (YIKES!!) that many people change their mind about after they climb to the top (I wouldn't even make the climb!!). If you look at the two images above and to the right, you can see why.

The very first waterpark was Wet-n-Wild in Orlando, FL, opened in 1977. This park closed in 2016, but no worries, there are over 2,000 waterparks worldwide, so probably some right near where you live. I know as a child, my first water park was when my parents took us to Disney World in Florida, and we camped on the grounds at River Country (which I don't believe exists anymore). It was amazing! When we lived in Richmond, VA and Virginia Beach, we use to go to Kings Dominion's Waterpark with the kids or Water Country USA in Williamsburg, VA. I know there were a couple slides that were frightening to go on for various reasons - i.e. height, darkness (so sliding in a tube/tunnel), fear of falling over the sides, speed, etc. But overall, super fun and scaring and cool on a hot summer day. If you have not been to a waterpark, definitely worth the experience! Here are some links about waterparks (where to find them, data comparing different slides around the country, etc.)

There is so much math and science that you can do when looking at waterparks and water slides, so here's where student interest might guide what direction your students go in. It could be a great way for them to research information, make comparisons in several ways using different technology (so tables, graphs, images, geometric applications, etc.) You could look at heights vs. speeds or angles....so many directions. For example, the world's tallest water slide, Kilmanjaro in Rio de Janeiro, Brazil, is 163.7 feet high (49.9m) and you travel at speeds up to 57 mph (man...that's gotta hurt!!). So how much does an increase in height impact the speed you go could be a question to explore. Or how many stairs do you have to climb to get to the top? What's the angle of elevation or angle of decline?

In the spirit of waterparks and water slides, I wanted to share an activity that uses a real-world image of a water slide to let students explore one way to apply mathematics, in this case the Pythagorean theorem, and triangles as a method for determining height and length of a slide based on an image. Students then use this understanding to look at real water slides (i.e. Summit Plummet) to get an understanding. This is a relatively simple activity using the fx-CG50 Prizm and it's ability to insert images as background and do graphing/geometry on top of these images. Here is the activity in PDF form, and then I did a quick little lesson overview video to walk through things. The great thing about the PDF is that it includes calculator how-to's, student questions/worksheets, and then sample solutions to support the discovery.

Here's the activity support video:

Have fun slipping and sliding, and stay cool!