Great Classroom Action

Tracy Zager illustrates a key feature of some of my favorite math tasks: their constraints are simple, but they create paths for complex thinking and ever more interesting questions:

I think my name is worth $239. Beat me? Haven’t figured out my $100 strategy yet.

Lisa Bejarano is a recipient of our nation’s highest honor for math teachers, so when she admits “I have no idea what I am doing” and starts sketching out a blueprint for great classrooms, I tune in:

Now, beginning with the first day of school, I intentionally work at building a unique relationship with each student. I make sure to find reasons to genuinely value each of them. This starts with weekly “How is it going?” type questions on their warm up sheets and continues by using their mistakes on “Find the flub Friday” and through feedback quizzes. I also share a lot of myself with them. When we understand each other, my classes are more productive. I still make plans, but I allow flexibility to meet my students where they are.

David Cox describes “a difficult thing for students to believe”:

Once students begin to believe that the way they see something is the currency, then our job is to simply help them refine their communication so their audience can understand them. Only then does the syntax of mathematics matter.

“Help me understand you.”

“Help me see what you see.”

Kevin Hall thoughtfully deconstructs his attempts to teach linear function for meaning, and includes this gem:

Once you introduce the slope formula, slope becomes that formula. It barely even matters if today’s lesson created a nice footpath in students’ brains between “slope” and the change in one quantity per unit of change in another. Once that formula comes out, your measly footpath is no competition for the 8-lane highway that’s opened up between “slope” and (y2—y1)/(x2­-x1).

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I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. I have used this in a similar way when talking about the qualities that determine success in what people do. Going with percentages rather than $ and aiming for 100%, the students are always surprised with the totals of three qualities of ‘Hard Work, Knowledge and Attitude’. I also stress that anything over 100% doesn’t count!

  2. I think this is a great activity for an ice-breaker or first days of school. I think it will set the tone of the classroom really nicely to show that math can be fun! My middle school students will love this and it will definitely become a competition amongst each other such as students can compete to see who can come up with one word with the largest total denomination.