People often ask me, "How do you teach math to both 4th and 5th graders? Do you split them up?" In many classrooms, it would be very difficult -- the texts for the fourth grade and fifth grade curriculum would necessitate completely different lessons. With time, I've learned how to craft explorations so that we can begin together and then students engage in the activity at the level that is appropriate for their current understanding.

We've been working with probability in the last week. We began with a few demonstrations of single event probability (6 sided die, tiles in a bag) and then looked at the classic bell curve of the probability of getting a certain sum when you roll two dice. We also considered experimental versus mathematical probability. With those concepts securely under our belt, I opened it up.

Students were asked to create a simple game with the dice we have (a nice variety of 4-20 sided). They were to explain how to play the game and then they were to list the different probability events in the game. Finally they needed to figure out the probability of those events.

Needless to say, "simple" to me and "simple" to the fourth and fifth grade mind are not the same thing. As students began to unpack the probability in their games, they realized just how much complexity many events held. Some modified their games to make the probability more manageable for them, others decided to they wanted to tackle it. One student had a game with two twelve sided dice. If one rolled a sum of less than 10, you lost your points. If you rolled more than 12, you gained points for that round. Of course, he had to figure out how many combinations were possible (144) and how many of those gave the desired outcomes. Students who were newer to probability stuck to one die. One game involved rolling the die once and then rolling it again to see if you got a multiple of your first roll.

By picking the complexity of their work based on their "comfort level", students learn to evaluate their current understanding of a concept. There is no stigma of "low math group" or "high math group" -- instead, students see themselves as new to an idea or more experienced with it. They push themselves accordingly and my job is simply to support them along their way.

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