Visited a 3rd grade class today, and the teacher was teaching a lesson on how to model division. Gotta give kudos for his animated teaching style and enthusiasm. Back to math...
The day before, he had read The Doorbell Rang by Pat Hutchins as an engaging way to introduce division. Today, he started by having the kids use manipulatives to show how the cookies from the story were divided equally among the children. He had the students draw circles to represent the children in the story, and then they "handed out" the cookies (manipulatives) to the children (circles). Great concrete learning!
After practicing with the manipulatives using different numbers of children, he showed the students how to draw a model to represent the division (see picture below).
First, he had them draw small circles to represent the cookies and larger circles to represent the children. As they "handed out" the cookies to the children, they crossed them off. When he asked the class if this reminded them of a different kind of math, several students actually connected it to subtraction. Good point! Division is really repeated subtraction.
To make a good lesson even better, he brought fact families into the equation. He asked, "What if the mean mom decided to take all the cookies back after giving them to the children? What math would that be?" The students realized it was multiplication, and the teacher wrote the fact family as the students gave him the number sentences.
After giving the students several practice problems to model and write the fact families for, he let the kids come up with their own division stories. They had some really fun ideas! All the elements of CRA instruction were in this one lesson--concrete (manipulatives), representational (drawing the pictures), and abstract (the fact families).
You can download a file with the model shown below and a blank template to use by clicking on the picture.