How exciting it was to watch as students actually constructed a method for efficiently calculating the area of a rectangle today!!!

After introducing the concept of area yesterday by having students use patterns blocks to cover the surface of the smallest and largest book cover from books in their literacy bins, we discovered that squares tend to cover surfaces more efficiently than the other shapes.

Hence, when we worked on the practice question today, students began by using colour tiles to measure the area of a piece of paper.

Many of the students covered the full sheet of paper, but sure enough, some of them discovered "shortcuts". For example, one group decided to fold the paper in half, and measure only half the sheet's surface, then double their measurement results to get the area of the whole sheet. Several other groups discovered that you merely needed to line up one row of square tiles, and then figure out the number of tiles in the "vertical row" (as some of them called it), to see how many rows would be needed to cover the whole sheet. In this way, they were able to calculate the area of the sheet of paper without actually covering the whole thing.

It was exciting to see the lightbulbs go on for some students as the "short-cutters" explained their thinking during the debrief.

After introducing the concept of area yesterday by having students use patterns blocks to cover the surface of the smallest and largest book cover from books in their literacy bins, we discovered that squares tend to cover surfaces more efficiently than the other shapes.

Hence, when we worked on the practice question today, students began by using colour tiles to measure the area of a piece of paper.

Many of the students covered the full sheet of paper, but sure enough, some of them discovered "shortcuts". For example, one group decided to fold the paper in half, and measure only half the sheet's surface, then double their measurement results to get the area of the whole sheet. Several other groups discovered that you merely needed to line up one row of square tiles, and then figure out the number of tiles in the "vertical row" (as some of them called it), to see how many rows would be needed to cover the whole sheet. In this way, they were able to calculate the area of the sheet of paper without actually covering the whole thing.

It was exciting to see the lightbulbs go on for some students as the "short-cutters" explained their thinking during the debrief.

I wonder if part of the reason the students were so quick to construct an understanding of more efficient methods of calculating area was because we had spent so much time during our geometry unit really digging into the different polygons and their characteristics... the kids really are comfortable with quadrilaterals now, in a way no previous class of mine has been, and perhaps this comfort is serving them well in other strands of math, too.

We'll further consolidate the learning about area with tomorrow's lesson, during which they'll explore shapes with the same area, but different perimeters, and calculate the area of a newpaper page that is taken up by advertisements vs. the area taken up by actual news articles.

We'll further consolidate the learning about area with tomorrow's lesson, during which they'll explore shapes with the same area, but different perimeters, and calculate the area of a newpaper page that is taken up by advertisements vs. the area taken up by actual news articles.