…ooooaaaaalllll!

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.

**Artifacts**

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.

This list of regulation soccer goal heights (from http://www.usyouthsoccer.org).

This Lowes price for 1”x10’ PVC pipe. ($2.72) Optional: PVC pipe connectors (Ts and Ls)

**Guiding Questions**

- 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.

**Suggested Activities**

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**.

**Solutions**

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.

**Comments:**

- 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.

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This is great. In fact, I think I’m going to do it with my classes this year, using our new Maker Space at our school. We will create toddler-sized goals and donate them, as you suggested. Thanks for the idea! Once I’ve got a more detailed version with actual tasks and plans made I’ll send it to you.

Very cool David! Would love to see pictures and/or plans!

Here goes nothing: http://approximatingnormality.blogspot.com/2015/02/huge-soccer-project-about-to-take-off.html