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 jeanmarie's Message: I have them begin with tracing various shapes on cm graph paper and then count and number the squares contained within the drawing. When I am sure they understand what we mean by area, rather than perimeter, then we can explore how formulas are used to save us time. I have also had students draw a shape, and then use a ruler to draw a cm grid over the top and then count the squares. When we count the squares, we number them and record it right inside that square. We have to put smaller pieces together as best we can to make complete squares. They really do get pretty good at it. When they have had to count all of the cm squares in a fairly large square or rectangle, using the formula becomes a helpful and time-saving tool. I also have them create triangles by cutting rectangles and squares in half so they see how the area of a triangle is half of its rectangle. I think my students who truly understand that area is the number of little squares retain it better. I have seen them divide a shape into 1 cm squares and then count them if they couldn't figure the area of some strange polygon by using a formula. They get it almost perfectly although it takes a lot longer and they have to use a ruler to draw straight lines. I've used geoboards, but it's hard to keep track of all of the squares contained within the shape without writing on them so I prefer graph paper. Hope this helps.

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