My Algebra Honors students have been learning how to solve systems of equations. We learned 3 methods: graphing, substitution, and elimination. While each method will always work, there usually is one method that is easier to use based on the two equations given.
In groups of 3 I assigned my students one method to solve. I then gave the class a system of equations. I gave each group a few minutes to discuss why the method they were given was the best method to solve that system, even if it may not be their preferred method. Each group then shared out with the class why their method was the best. Groups could then engage in a friendly debate on which method was the best method to solve that specific system. It was wonderful to hear the reasons students came up with for each method and how they tried to sell their method to the class. The students got excited and were really advocating for their method. After we debated which method was best students then had to solve the system of equations by all 3 methods, starting with their method first. After everyone solved the system of equations we circled back to our debate and asked if anyone’s opinions were changed based on solving the systems. We were able to repeat this process 4 times with students getting assigned a different method each time.
This lesson reinforced that no matter what method you use to solve the system of equations you should end up with the same answer. I hope it also got students to think about the benefits of each method so they can decide which method to use when presented with the equations. I loved how it got students talking about math as well which is a skill we are working to develop in our department.