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What Do You Notice? Squares and More Squares


Primary students (K-2): shapes

Intermediate students (3-5): shapes, area, fractions

Mathematical Background

This was designed around fractions. It's one of the very open-ended posters that offers very little direction. Using the graph paper as part of the design, the large square is made up of 8 x 8 smaller squares. The placement of the 5 x 5 dots resembles a geoboard; the lines would represent the geobands. Each one of the 4 shapes has the same area - 16 small grid squares (or 4 geoboard squares). I deliberately made different shapes with the same area because sometimes students will think that because the shape is different the area must be different, as well. This is not the case and we need to give our students plenty of practice with these types of problems.

Sample Student Responses

"There is a square."

"There are 64 little squares and 16 squares of four each."

"Each shape has the same number of squares."

"A small square in a big square."