How far away is he from the hole?
What information would be useful to figure this out?
The students need to know the dimensions of whatever triangle the announcer used to make his calculation. However, instead of immediately giving two sides and an unknown, I think it would be neat to allow the kids to use a little reasoning. Therefore, I’d put this image in front of them first.
This is the same image from the Act 1 video. My vision is for the students to try to figure out where the announcer formed his triangle. I want the kids to visualize possible shapes and talk about why some may or may not work. This could lead to a good discussion. For example, why doesn’t this one work…
What do you think about this one…
It looks pretty close, but how can we figure out if it’s an acceptable triangle? You could ask again what information could be useful to analyze this triangle and use this Desmos graph to find that information.
After the side lengths are determined, the kids can do calculations to prove whether or not it’s truly a right triangle. The students can also form other triangles in Desmos as well to test their initial reasoning. Overall, the discussion can help reinforce the fact that a right triangle is necessary for the Pythagorean Theorem to work, and it also allows the students to play with the math for a bit before jumping into the given triangle and dimensions.
Next, I’d show this image and have the class estimate the missing sides.
Again, I’m trying to allow for as much reason and wonder as possible (Michael Fenton may enjoy that phrase). Before giving the class all of the dimensions, it would be great for the kids to make an even more precise estimate to compare with their eventual calculation.
At this point, we’re ready for the final image.
Let the Pythagorean Theorem begin.
Draw a different triangle where the shot length is the hypotenuse. What are some possible dimensions?
How can you prove that your new triangle is a right triangle?
Official Lesson Page:
- Common Core
8.G.B.7 – Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
- TEKS (2015-2016)
- 8.7(C) – Use the Pythagorean theorem and its converse to solve problems
How can this task be improved? I’d like to hear your thoughts.