Fractions Are Not Shapes

Fractions are numbers, and we need to make sure that we are not creating misconceptions in the primary grades that will interfere with this understanding.

On the math word wall in many second grade classrooms that I visit, I see similar definitions for fractions. Numerator: The number on top, the number of boxes shaded. Denominator: The number on the bottom. The total number of boxes.

How does that connect to a fraction as a number? It doesn't connect. The emphasis as students initially learn about fractions needs to be on equal shares. This understanding in second grade builds to the understanding in third grade that a fraction represents equal shares on the number line. This progression is important for students to build understanding. Fractions are not pizzas or rectangles divided into squares. Fractions are numbers that can be used to represent equal shares of shapes.