Wiscasset Elementary School’s third graders explored the properties of square numbers by creating visual representations of arrays with like factors, such as 3 x 3 = 9, 4 x 4 = 16, and 5 x 5 = 25.  As with doubles facts in addition, multiplication square facts tend to be easier to remember and act as a launch pad for a series of multiplication basic fact strategy mini-lessons to come.

Students worked in teams to align equal factors with arrays while sharing different strategies to determine products.  Some chose to skip count by columns or rows, others multiplied rows and columns (L x W), and a few built upon their knowledge of similar, yet familiar facts.

Many unique patterns were discovered among square facts while comparing and contrasting arrays.  Observations, such as “Each array has the same number of rows and columns,” “They [arrays with like factors] always make squares,” and “Bigger factors make bigger squares, and smaller factors make smaller squares” yielded insights that further fueled some great mathematical discourse:  Is 0 x 0 a perfect square?

These young mathematicians are an impressive group of thinkers who not only seek to understand, but understand to seek! Hats off to you, third grade mathematicians!