Put on Your Math Goggles! Exploring Measurement Using Josef Albers’ Squares

Fifth graders at All Saints’ Episcopal School recently donned their math goggles and engaged in a hands-on exploration of measurement using the visual arts as a lens.

In order to challenge fifth graders’ proportional reasoning skills, students learned about the German-born American artist, Josef Albers (1888-1976), and were introduced to images of his influential series entitled, Homage to the Square. These works by Albers, which are numbered in the hundreds, feature a series of three or four nested squares in varying colors, as Albers was fascinated with chromatic interactions.

Students created their own Albers-inspired art by selecting three different sized squares (measuring 2”, 3”, and 6” on a side) of varying color. Then, the students put their math goggles on and were challenged to explore how area and perimeter are impacted when a shape doubles or triples in size.

Using area and perimeter formulas as well as their artwork as visual aids, students came to the conclusion that when a square doubles in size (from 3” to 6”), its perimeter doubles, but its area quadruples. Similarly, when a square triples in size (from 2” to 6”), its perimeter triples, but its area becomes nine times bigger.

Students were surprised by this mathematical conundrum, but their square artwork was the key in helping them proportionally reason through this.

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