Before we jump into adding and subtracting negative decimals I thought we should spend some time defining what estimation is and is not. That way students would be able to determine if their answer was reasonable. It took about a period and a half to clear up misconceptions but I think it was time well spent.
The basic structure of the lesson was 15 minutes of group work using giant whiteboards, followed by a 10 minute a gallery walk for feedback, then the remainder of the period to refine their definitions and examples.
I posted the following directions: Create your “bestest” definition of estimation and provide one example and non-example.
Here are the first drafts of student work from one of my classes:
Some groups were on the right track, but their definitions and examples could be more explicit. When it came time for the gallery walk the groups examined each others’ work, commenting on two things: one thing they like about the work and one thing that needs clarification. Groups struggling with the definition or example/non-example really benefited from seeing others’ work. The post it feedback also helped them to refine thinking.
At the end of the period I asked students to use their iPads to take a photo of their work and the next day we debriefed. The definition of estimation being an educated guess was lacking for me, so I added the phrase, “by using a strategy.” I think that condition to the definition will allow us to continue our estimation conversation when we talk about scaling up or down with proportional reasoning.
Having students create their own version helped them participate in the final draft. We talked about where rounding occurs in estimation so we could identify the characteristics. One student thought it helpful to include arrows to clarify what is being rounded, and I threw in my caveat about using a strategy as part of the definition.
While it took a lot of time the students ended up owning the definition more than if I had told them what to write in their notes. The collaboration and post it feedback also helped those students who may have had some trouble getting started on their own.