I’ve recently spent a lot of time visiting 3rd grade classrooms as they begin to dive into division. Here’s what I encountered on one of my first visits which was a crippler for everyone involved.

 

As bad as this is, I don’t think it’s much worse then what the majority of us encountered in elementary school. So instead of walking students down the garden path and showing them how to divide, I shared a different approach by introducing division using the Orange 3-Act Task.

The question students came up with: How many cubes will it take to balance the scale?

In Act-2, students wanted to know the weight of the orange and the weight of a single cube.

 

And with that… they were good to go with little to no explanation.  Too ofter we’ll tell students what to do and how to do it, and then expect them to genuinely engage in some “authentic task”.

Some students went for base-10 blocks…

Some strategies were tedious and inefficient however they’re super important for students to work through as they begin take ownership for their own learning.

Some students thought multiplicatively about the “division” problem which was awesome to see.  In 3rd grade, students need to “understand properties of multiplication and the relationship between multiplication and division”.  Far too often, multiplication and division are kept in isolation of one another and we need to change that.

 

The student below intrigued me but I missed the mark on asking him better questions.  I wish I would have gone back and talked to him some more.

 

There were also some really good disagreements which helped engage students in SMP #3: Construct Viable Arguments and Critique the Reasoning of Others.  

This conversation was echoed at multiple tables.  Students weren’t sure what value to assign the cubes. We eventually got to a place where most students understood that the value depended on how they solved the problem.

My takeaways:

• We could have spent 2-3 lesson talking about division and what it means but we would have robbed students of this learning experience.
• Sure the task had a dividend greater than 100 but I’m ok with that. The numbers were accessible to students and everyone was able to work through the task.  If I would have given the students 15 counters and said, “How many groups of 5 can we make?”, we would have been done in 5 minutes which would have allowed us the opportunity to do 30 more questions just like that one…NOT!
• Beginning a unit with a 3-Act Task tells us so much more about what students know and what they can do.  The proof is in the images and videos.
• The word divide or division wasn’t brought up the entire class period and there’s something to be said for that.
• As a rule of thumb, I’ll try to begin every unit with a 3-Act task and implement 1-2 more of them throughout the unit.  I shared this idea of swinging for fence on day one at NCTM Regionals and apparently Geoff Krall agreed. I hope he’s ok!