There’s about a hundred different ways you could use the following artifacts to construct a lesson around Pythagorean’s Theorem. So I’ll just toss out all the artifacts and let you, esteemed teacher, take it from there. I’d love to get feedback and suggestions on how to implement these materials in the comments below.
Use any combination of the following.
This video from This Old House in which two small girls assist with the construction of a pint-sized soccer net: How to Build a Soccer Goal | Video | Family Projects | This Old House.
The screen shot of the girl holding up one of the 5 most beautiful right triangles I have ever seen. (note: before math geeks go berserk, I know it’s technically not a right triangle with the extra bit off to the side, but still.)
The cutting diagram given by This Old House.
- Can we do this?
- How much netting will they/we need?
- How much PVC Pipe would we need to make a goal of each size?
- What about those connectors, how many of those will we need, and which kind?
- What will the cost be?
You can pretty much tailor this exercise to whatever your class needs. Personally I like the simple netting question and perhaps extending it with the “goals of each size” question, which would involve ratios more than Pythagorean Theorem per se. So let’s tackle those.
Why not have the students build the soccer goals? Contact a local soccer club for various age groups and ask if they’d like a few PVC pipe soccer goals for their practice fields. Assign each student group a different age group goal requirements. Now you’ve got a rigorous math activity that will get the students engaged with hands-on construction and really impress your administrator for adding a sprinkling of community service.
For the U8 (under 8) age group, we know the following, although this might be a good time for some Socratic discussion on where the “6 1/2’ (height)” should go and if that “12’ (width)” should go anywhere. Some manipulation of objects would do well here.
At this point, you can either choose to keep it proportional to the This Old House goal or mandate the depth of the soccer net (for more of a Pythagorean approach). I’ll choose to keep it proportional to TOH, where they make a 3-4-5 right triangle.
To find the missing leg we can set up a proportion.
At this point you can either make it a Pythagorean Theorem problem or proportionalize it again. Let’s do Pythagorean Theorem.
This is for the U8 (and U9) goals, and similar methodology could be used to construct the other goals.
- Given the exhaustiveness of the This Old House episode and supplementary materials, you don’t really have to use Pythagorean’s Theorem for these problems. So they may need to be teacher “mangled” like this.or
- Even without Pythagorean’s Theorem you have to be able to use proportion. And had I answered the “how much netting?” question, that would take into account area.
- Here’s a fun one that always seems to trip up students: we increase the goal size by X%. Does that mean we would need to increase the netting by X%?
- [Commentary Alert!] The last two bullet points speaks to one of the main criticisms of Project Based Learning: that it’s hard to cover everything. While there’s merit to that statement, in this one project, we touched upon Pythagorean Theorem, Proportion, Proportional Area, Percentages, and Area. If you’re looking at five major topics covered in – what, a week and a half? – that’s pretty good coverage.
- The TOH website suggests it costs about $50 (and 2 hours) to construct their tyke-sized goal, but I wonder if that price could come down if we’re building multiple goals. The cement could be used multiple times for instance.
- The This Old House Family Projects portion of their website contains a wealth of potential projects. I’m sure we’ll be revisiting some of them on Emergent Math, but take a look around yourself. You might be inspired by some of the stuff on there. For your class and your home.