Last week I had a couple of posts dealing with coordinate geometry. Those can be found here and here. There were some get suggestions in the comments, which are worth reading. One of my good friends Austin, a fellow teacher in my district wrote the following:

*You should definitely look at the pooltastic problem that was developed from Howard County public schools. The problem is right up your alley for the objectives you are looking to cover. I used it for slopes, perpendicularity, and parallel lines. I made it a group worked problem and we spent time talking about the mathematical practices. We had one day to share how each group attacked the problem and then they needed to individually reflect on other groups’ methods. Check it out:*

*https://commoncoregeometry.wikispaces.hcpss.org/Unit+1*

I checked it out and it really did align to almost all the objectives I wanted to cover in Day 65. The website is also a good place for resources, I haven’t dug around it much through… it is on my to do list.

I find it kind of hard to get excited about the context of building a pool for your parents so I modified it and took out the fluff. Here is the handout I gave students.

Have a look at their work

It was fun to watch students work and discuss how they wanted to show that the shape they chose was a rectangle.

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JoshuaWith an eye toward whether you could have left anything out of your handout, I wonder if you would consider first giving them a diagram of the lot without a coordinate grid drawn? Since your current emphasis is coordinate geometry, it would seem obvious that they would start by adding coordinates, but I wonder what would happen. And, would this be a helpful reminder of some reasons why coordinates are helpful in the first place (but you’ve already had those discussions)?

Also, read the original outline of the problem and have to admit those follow-up questions aren’t the ones that naturally occur to me when thinking about pool design. I’d be tempted to pursue things along the lines:

– why would the regulations stipulate a perimeter restriction (instead of surface area or volume)?

– what are other reasonable pool shapes? What are the pros and cons of each?

– Given the perimeter constraint, how much surface area are we giving up by starting with the given side length instead of going for the largest area rectangle/shape with that perimeter?

– Are there important sunlight considerations around the lay-out of the pool? I can imagine considerations around heating, sun reflecting off the pool to the house (and vice versa) and unfair advantages for one side in a pool volleyball game.

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danburfPost authorThese questions are great. I will admit that students were not interested at all in the follow up. We did a little gallery walk which was good but after that point student engagement/interest was low.

It’s a shame I only teach one section of geometry, I will file these questions away on the template for next year!

Thanks

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