When students are able to make connections for themselves I find it truly exciting. I think moments when students turn the corner and begin to reason, become more human and less like a robot a celebration should occur. This past Friday a group of students made the connection between the area model and factoring and simplifying expressions. It’s a connection the task they worked on earlier last was promoting but I’ll tell you not every student did so.

Someone once told me, that kids don’t naturally make conclusions or summarized math concepts without teachers making it plain for them.

Picture above is the sequence of thoughts these students had in regards to factoring and simplifying expressions. The thought begins on the right and travels left. I was the scribe and facilitator through the process but NONE of the thoughts on the board are mind. The most beautiful part was right at the end when students were given the expression 5x + 20 and asked “what would you do with this?” Several of the students jumped describe the how they would create a large rectangle, split it and label the areas 5x and 20. They went on to reason that 5 had to be the width of the entire rectangle because the first area of 5x and if x were the width, the other area would contain an x. With enthusiasm they explain why the length was x and 4. From that, they wrote the factored expression. When given a factored expression, with even more excitement they explained their strategy of using a rectangle to help simplify.

I had not thought them this strategy, they made that connection from engaging in task from the GA math frameworks. More on that later…