Breaking the Rules – My Unplannned Math Lesson

Today, my Year 5 (Grade 4) and Year 6 (Grade 5) students were learning about the rules that dictate how odd and even numbers interact.  We used my Odd and Even Numbers Rules Lesson for our Interactive Math Notebooks.  My plan was for us to learn the rules and then work in pairs to prove that the rules were correct.  However, while reviewing the rules, I heard a student say that they could prove that the rules weren’t true.  This snide comment led me to side track my lesson.

I handed each student a piece of scrap paper and challenged them to find one example that broke one of the rules.  I offered my students “the ultimate prize” – no homework for the ENTIRE YEAR.  After a few minutes, many of my students were able to realize that this challenge was impossible.  Of course, there were quite a few who kept on trying, determined to beat the teacher and win the ultimate prize.  After about 10 minutes of working towards breaking the rule, I stopped the class and announced to my students that the task at hand was impossible, and that these rules had been proven by mathematicians throughout history (and I made a connection to all of the astronomer/mathematicians we are studying in science).  I had 3 students who still thought they could break the rule, so I told them to go ahead and keep trying at home and that the ultimate prize would stand for the entire school year.

At first, I was worried about these students who didn’t believe that it was impossible.  Then, I realized that my offer of  the ultimate prize might inspire these students to continue this work – proving to themselves that these rules are true, and practicing math computation in the process.  This is a time that inquiry learning truly worked in my classroom, and I’m jumping for joy.

This also got me to thinking – should we be asking students to try and break other math rules?  Before we teach a formula, perhaps we should give them two different formulas and let them “experiment” with numbers to figure out which one is the right formula for the topic.  How do you use inquiry based learning in math?