Wednesday, 29 May 2013

Maximizing Area of a Rectangle

Catching Up - Part I

You know how it is.  We are approaching the end of the year and there is so much to do.  And somehow blogging takes a back seat, even though I know that I need to do it right away or I lose some of the detail.  Thankfully I take pictures so I can remember what I was going to blog about!

Last week we were looking at the dimensions that will produce the rectangle with  maximum area given a fixed perimeter.  Everyone has probably taught this at some point and I don't think that I'm doing anything particularly exciting but I am trying to put more of the learning in the kids' hands and do less "telling".  So, this is how I started:

They each had their own perimeter but they worked together.  They had Cuisenaire rods to build the different sized rectangles.  (As an aside, I would really have liked them to have had something flexible (pipe cleaners? to be able to make the rectangles as some didn't understand what I was talking about.)

This is what they came up with:

It was interesting to see that most chose even numbers.  There were lots of multiples of 4 which worked out nicely, but it was great to talk about the options for the perimeters which were not multiples of 4 and especially to talk about the one odd perimeter.

Task 2 took a little longer for them to figure out and again, so many even numbers!  

We went through what they came up with and then worked out the whole number possibilities for a perimeter of 20.  

Then we generalized - they seemed to feel good about being able to answer the question for some ridiculously large perimeter.

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