*By William McCallum*

In one of our professional development workshops, there is an activity in which the facilitator asks teachers to skip count by $\frac34$. The facilitator records the count, $\frac34$, $\frac64$, $\frac94$, . . . and then asks for patterns they notice in the recording. In a recent workshop, a group of grade 5 teachers noticed that the numerator increased by 3 each time but that the denominator remained unchanged. When the facilitator asked why, they could easily explain why the number of pieces was increasing in the numerator, but couldn’t really give an explanation for the denominator other than “it is just always out of 4.” The funny thing is, they weren’t saying “3 out of 4, 6 out of 4, 9 out of 4” when they skip counted. They were saying “3 fourths, 6 fourths, 9 fourths” and writing it in fraction notation. The key to understanding why the denominator stayed the same was hidden in plain sight, in the very language they were using to name the fractions. Continue reading “Say What You Mean and Mean What You Say”