Friday, March 1, 2013

Math arguments today in class

Organic development of definitions
Today felt like one of those lessons that went way better than I could have expected. We used a Venn Diagram comparing two shapes at a time to come up with similarities and differences between all squares, rectangles and rhombus. Of course there were the kids that spouted "a square is always a rectangle but a rectangle is not always a square" but they really had to then think about how that applied in the diagram. This was a good natural stopping point for creating our class definition of these three shapes. The conversations were passionate and on topic and it was fun to see their understanding of these shapes deepen as time went on. To conclude this portion of the lesson I had the circles represent rhombus and rectangles and asked what they had in common, trying to lead the conversation toward 'squares'.

Flow charts and modifications
Next we moved to creating a flow chart, given a parallelogram, that would help us identify each of these three shapes. I had an example set in which they had to name the shape that applied and then we started to mix it up. I gave them a shape and then had them determine the property questions and answers to choose that would get us there. Another modification was to give them the answers (yes then no for example) and they had to determine what questions would lead us to the given shape. Through this my classes were able to determine that having perpendicular diagonals is just another way to identify equilateral parallelograms and congruent diagonals is an alternate way to check for equiangular parallelograms.
Here is a Google Drawing of the final flow chart activity we did.

Introducing programming in math
A secondary reason for the flow chart portion of the lesson was to introduce a programming extension I'm hoping some will choose. Without actually having to do code I want students to create a stack of PowerPoint cards with yes or no questions that will correctly identify any quadrilateral by its properties. I was hoping to hook them with a taste of it in class and give them some familiarity before taking on the bigger challenge. As the year has gone on and in my own personal learning I believe that getting my math students more opportunities to think like programmers will help them learn valuable programming skills and a deeper understanding of the math they are applying within it.

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