One of the requirements of middle school math in the International Baccalaureate program is that students must investigate patterns, describe them as general rules and either prove, or verify and justify, that they are true.
Because the proof, verification and justification (i.e. how you show your rule will work in any situation) depends on the situation, my students often struggle with this part of the task. I find it equally difficult to explain to them what is expected without giving them the answer.
A while ago, I used a Google Form to have students consider various statements about the properties of straight lines. I had done activities like this before as a way to assess prior knowledge and initiate discussion, but this time I required that students give a reason for their answer.
Once all students had submitted their answers, and a reason supporting each choice they made, I used the “Summary of Responses” tool, to show the class the results and the variety of reasons students had given.
The pie charts helped me to identify where opinions varied and where to focus the discussion; however, the best part is that all the reasons were visible and anonymous. As a class, we could talk about which reasons were the most convincing. In fact, after reading their classmates’ responses, many students changed their minds.
Having given reasons for a simple rule (i.e. the statement is true or the statement is false), students had a better understanding of what they had to do when it was time to prove, verify or justify the rules that they discovered through investigation.
You can view the original form and responses here. To make your own copy that you can edit and use with your class, select “Make a Copy” in the “File” menu. You can read about this specific activity in more detail here.