Day 69: Pooltastic

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

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

Day 65: Revisiting a Problem

In case you missed it I gave my Geometry class this at the end of the period on Monday.

Day63.1It didn’t go over very well and that piece has been bothering me for the last couple days.

I am not expecting to come up with the magical fix to making this sorta question great. However, I want to use this post to look at what I was trying to get at in this problem and where it went wrong.

Let’s start by looking at the objectives I had in mind with this thing

  1. Position a figure in a coordinate plane.
  2. Prove a geometric concept by using coordinate proof.

To proves this students need to know one or more of the following

  • Definition of a rectangle
  • Distance Formula
  • Slope

A majority of the struggle probably came from the definition of a rectangle. When thinking about this I immediately jumped to proving lines perpendicular and congruent distances. A lot of my students were still stuck in the two column proof mindset.

There isn’t really anything groundbreaking in proving a shape is a rectangle. For some reason I was expecting this problem to challenge student’s thinking and encourage them never to just jump to conclusions about a shape.

What I am really interested in though is how to re-vamp this problem to meet the same objectives but approach them from a different angle.

The first type of problem that comes to my mind appears in my Fence Problem Part II post.

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I am still working on how exactly this problem could be modified into a rectangle… But hey, it doesn’t necessarily have to be a rectangle.

Feel free to share your suggestions/comments, I would love some input!

Day 63: Class Goals

Coming off of Thanksgiving break I feel ready to go. In Algebra, we are just starting to work with slope. I am excited for tomorrow’s lesson… stay tuned for that.

I graded Geometry’s concept tests over the break, and a majority of the class bombed Triangle Congruency… Hard.

The fact that 7/8 of the classes scores didn’t raise tells me I messed up somewhere along the way. We spent about 40 of the 49 minutes in the period reviewing different problems on whiteboards. I think it helped them quite a bit.

For the last 9 minutes I threw this up on the board:

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They were giggling and having a great time. I thought it was interesting that none of my 20 students tried to make the side at a slant… Taking the easy way out I guess.

After about two minutes I revealed the bottom of the slide:

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It is really interesting to me that after about 3 seconds, most of the class decided it would be too much work and checked out.

Did I ask the wrong question? Were students not perplexed by this? Is there a lower entry point into coordinate geometry that would have been more effective? Was a bad idea to give this problem with 7 minutes left?

Maybe.

I don’t regret asking students to find a place to start on this for homework. I set the bar high… Students should see that I want them to struggle and be challenged.

This summer I went to one of Dan’s workshops. One idea that stuck with me was you can always add to a problem, but you can never take away. I believe that if I led students through a coordinate geometry problem before hand, it would take away from the magic and struggle that makes math so great. Working at a problem for a longggg time then finally getting it, ya know?

I had parent teacher conferences a few weeks back, the only talking point I had planned was to project my class goals up on the board for parents to see. These were on my syllabus this year and I refer to them constantly to make sure I am excited and passionate about what I am teaching…

Here they are:

  • Encourage the development of mathematical reasoning by:
    1. Incorporating multimedia into lessons.
    2. Presenting students with low entry and high exit problems.
    3. Focusing on student work.
  • Develop patient problem solving skills.
  • Make math social.
  • Provide the appropriate level of mathematical rigor for each student.

I believe there is an appropriate place for guided examples, notes and repetition; after the struggle. After students discover and apply the mathematical tools that make their lives easier.

Tomorrow I am planning on having students talk about the problem for a few minutes, creating a plan of attack with their groups, then trying it again. I will work in examples along the way according to where they are at in the solution process.