Fourth Graders were working on developing strategies and the rectangle model for solving d x dd problems. So we gave them the MARS task, Waste Wise, to see which strategies and models they would use. Student responses to 31 x 25 were most interesting. Students tried to stretch the model or the algorithms they had developed for d x dd to dd x dd but most were unsuccessful. Errors revealed that students were having trouble keeping track of the products and with the distributive property.
To re-engage students, we showed them the problem again and asked them to work with a partner to solve the problem again on a white sheet of paper. We also directed them to record their thinking so someone else could clearly understand. Students eagerly got to work, even without seeing their work from the previous day.
Check out their student work here. To further engage students in their thinking, groups traded papers, and each group prepared feedback for the work they reviewed. These questions guided their feedback: What questions do you have? Do you agree with their response? How is this students thinking like your thinking?
The conversations were fruitful because students were activated as resources. Students invented their own ways to extend the models and understandings they had already developed. They challenged each other’s misconceptions and discovered the errors in their own thinking, and the class revealed the varied ways they are thinking about multiplication.