# Perimeter and Area Investigations

So to kick off our investigations surrounding perimeter and area, we had a great discussion on how to measure “shapes”.  After a while, we came to the conclusion that there are lots of “dimensions” to measure.  We talked about words like “length” and “width” and “height” (and even talked about spelling those words…and how “long” relates to “length” and “wide” to “width” and “high” to “height”.  This was an epiphany to some.  Who knew?)  We finally came to the conclusion that we can measure OUTSIDE shapes (which we identified as “perimeter” and INSIDE shapes (which we identified as “area”).  I can’t lie…I also try to help my students remember by calling them “square-ea” to remember that area uses square units and “fence-imeter” to remember that perimeter is like a fence around a shape.  Will it work?  We shall see.
After we did some review of our rectangle discussion and looked at how we would measure the inside and the outside, I put my students in pairs and asked them to do a few explorations.
First, I asked them to use 12 one inch tiles to find all the possible rectangles they could and to record the area and perimeter of each.  I LOVE the “a ha” moments when each group realizes that the area is 12.
HEHE
As students finished, I let them try rectangles with a fixed area of 36…by this point, some of them were asking if they HAD to build them or if they could just fill in their charts.  Once they could explain in clear mathematical language why they could do it without tiles, they were on their way.
If they finished this investigation, they were on their way to see if they could find a pattern or a rule related to what types of rectangles have the biggest perimeters and which have the smallest.  There was some GREAT discussion!
Stop back a few more times this week to see what happened when we REALLY dug in to our area and perimeter studies!  There was some GREAT mathematical thinking going on!