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I should be able to gauge this, but I have no idea if this is going to be too easy, or too hard, or just right for my geometry class as a warm up tomorrow.

It’s not that it’s a bad problem – it’s that I can’t get the level of challenge right. I’m not sure why, either.

Oh, the joys of the first year of teaching a particular curriculum. At least now, I think, after the 5th different variety of reteaching, they’ve finally got a handle on triangle congruency rules.

Addendum (on edit):

My geometry class, which has been working with areas of compound shapes, struggled with this. I also showed it to my 2nd & 4th period Algebra classes, who immediately decided that the areas were the same. Sometimes it seems that all I’m doing is making them think too much.

{ 5 } Comments

  1. Richard H | February 11, 2009 at 12:09 am | Permalink

    This is a good question, although I don’t understand how your kids can be motivated enough to actually attempt this problem…

    I’m not a teacher yet, but plan to attend a credential program this coming Fall. I’m working with kids right now and it seems like one of the toughest things is getting them to TRY and ATTEMPT things…

    Nice blog btw— lots of interesting things to read, esp since I’m planning on teaching mathematics.

  2. Mr. K | February 11, 2009 at 6:17 am | Permalink

    This is an 8th grade geometry class – to get into this class requires a lot of work. The kids are very motivated on their own. It’s a rarity at this school. Plus, they’ve had a bit of practice with finding areas of compound shapes, including circles and parts of circles.

    The problem is that their whole math education has been of the “You show me, and I mimic” variety. We just started exploring proportional areas yesterday, so there’s an easy way to get the answer, and a hard way. Hopefully, if they brute force it, they’ll clue into the more elegant answer.

  3. Kate | February 11, 2009 at 1:57 pm | Permalink

    I think my students would struggle because there are no dimensions labeled. I know that’s part of the challenge, but they might not have the tools yet to be able to start. Maybe you could just label the radius of the large circle “r” for them, or something, if you don’t want to provide any numbers to work with.

    (Also, my students would try to just bullshit it. Some people would say “pink” and some “orange” and they would just yell “pink” and “orange” back and forth, louder and louder, with absolutely nothing to back up their conjecture. It’s Fox News math.)

  4. Courtney | February 11, 2009 at 6:09 pm | Permalink

    Personally, I think it would be a great warmup, the point is to get them thinking conceptually, right? I love problems where the students are able to make a realistic hypothesis from what they see and then support or disprove it using their math skills. Labeling the radius of one of the smaller circles may give them a good place to begin, but you could always hint at this to the students who seem to need the help.

  5. Shanna | February 12, 2009 at 10:57 am | Permalink

    What a great warm-up! With my higher level 7th grade Algebra students, several would begin working on this with very little thought. This is particularly true for those in the MathCounts program. For the rest,(including my lower-level students) solving this might require some prompting and maybe some prior practice on working with area and perimeter without using any actual values. The students’ first inclination is always to look at the picture and shout out the answer. Although, by this time of year my students understand that answers cannot be discerned from merely looking at a picture. I am embarrassed to say they come to this conclusion by looking at my drawings.