Sunday, August 8, 2010

The Last of the Complex Diagrams

If you tried the previous problems for the past two posts, I have two more for you. I use both of these problems at some point in time in my classes. They are both excellent for stressing the importance of organizing thoughts and work. I also ask my students for a written explanation of their problem solving strategy.



The triangle question really forces one to be very organized in order to find all 28 triangles. This is a great problem to have students work together on.



The square problem allows one to analyze a pattern. When discussing this problem have students make up a list of the number of individual squares, of squares made up of four smaller squares, of squares made up of nine smaller squares, etc. The students should see a pattern occurring. This will allow you to move into examining patterns and finding rules.
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2 comments:

  1. Molly WhiteAugust 16, 2010 at 9:05 AM

    Jeannie,

    These problems are always so tough to figure out. Do you have any suggestions for solving these problems and to help organize student answers?

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  2. JeannieAugust 18, 2010 at 7:51 PM

    Molly,

    First, I have the students number the individual triangles or squares. Then we make a list of combined figures. For example, all triangles formed by combining two of the original ones. Then all triangles formed by combining three of the original ones, etc. I do encourage my students to constantly look for patterns. The square problems has a pattern.

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