We began our lesson on fractions, and I prepared to say the words I read in the manual the day before. “*The numerator is the number above the fraction line. The denominator is the number underneath the fraction line. They represent parts being taken or the total number of parts in the whole, respectively.*” As I considered these words, I realized how abstract these ideas are. My lesson could be much more effective with a practical activity in my students’ hands.

After my first year of teaching math in 4^{th} grade, I learned some valuable lessons about good teaching. Most adults can comprehend abstract concepts, but grammar-aged students need support with concrete practice, often in the form of manipulatives. So, our fractions lesson began very differently this year. I handed out long slips of paper. We called it one whole. Then we folded it into two equal parts. We talked about the value of each part. We identified the parts and the whole. The numerator and denominator. Then we discovered what they mean.

After we had seen two equal parts, we folded each side in half again. We wrote the fraction on each part. This is what it looked like.

Then, we took the same fraction and drew a number line on our white boards. Same concept. New concrete image to support understanding. It looked like this.

One last image. This time we baked a class pie. Students decided it should be a pumpkin pie. Yum. So, I passed out a circular piece of paper. Students had to fold it into four equal parts and label each one.

To cement our understanding, we practiced the concept by filling out shaded fractions in squares, circles, and rectangles as well as number lines. Students were prepared for this challenge because they had manipulated the concept in several personal and concrete ways. They were not overrun cognitively, trying to reach into the lofty math universe. Rather, the concept came down to them, practically, and with colored paper, which is an easy way to delight a 4^{th} grade student.