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.

Saw this today & was crushed. For the record…this is NOT modeling with mathematics. pic.twitter.com/orr91zRWei

— Graham Fletcher (@gfletchy) December 3, 2015

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!

.@gfletchy challenging us to start with the hard problems.

I just broke my neck from nodding so vigorously. #NCTMregionals

— Geoff "Ned the Head" Krall (@geoffkrall) November 19, 2015

This is interesting and engaging! Can this be applicable to students outside of 3rd grade? or is it targeted only towards 3rd grade? How can it be modified to fit younger or older grade levels?

Great question Maritza. I think you could extend this task to 2nd grade students for sure. The big piece is to make sure that students understand the context of the problem which isn’t really an issue I’ve encountered when using 3-Act tasks. Although I wouldn’t expect 2nd grade students to dive right into division, I would expect many to perform some kind of repeated subtraction.

You have me intrigued now. If you do give this a try in 2nd or 1st please report back and let us know how it goes.

Thanks for pushing my thinking on this one.

I think you could try this specific task with 2nd grade and up. But I think if you reduced the quantities in the story to less than 20 for Kindergarten and 100 for 1st grade you would be fine.

In terms of the idea of starting a unit with a 3-Act task, this is definitely something that’s applicable to every grade level.

I love this. Thanks for providing such a clear example of how a topic could be introduced and more sense could be made by using a challenging task.