Math is Messy!

Today I filled in for a teacher who had to be out suddenly. It was so exciting! I’ve been coaching now for several months and I was anxious to slip back into teacher mode.

These were fourth graders who had been introduced to the distributive property the day before. The teacher was looking for something to both review and solidify their knowledge. I decided to try to connect their past experiences with multiplication to their new thinking from the day before. I wanted it to be a little messy!

The learning target:

I can solve multiplication sentences in more than one way.

I had the students rate themselves based on this success criteria:

0: “What is multiplication?”
1: “I’ve heard the word multiplication before but I do not have any strategies to solve it without help.”
2: “I can memorize facts, but I still don’t know what multiplication really looks like.”
3:  “I have more than one strategy to solve a multiplication sentence like 6 x 8: number lines, equal groups, repeated addition, etc.”
4:  “I can apply what I know for strategies to harder problems, like 16 x 8.”

Then, I put them in groups to solve the following two facts as many ways as they could on giant paper…6×8 and 17×5. The results were remarkable, AND messy!


Math is messy!


One student wanted a new paper, but I explained that mistakes feel kind of awesome. We should expect to make mistakes and try again, it is all about perseverance.

This messiness reflected the thinking of the students. I had to suppress the urge to organize their thinking into my own pretty little anchor chart. I had to remind myself that this wasn’t about an anchor chart, it was about letting the students know that math is messy and that they could learn from each other’s thinking.

After giving them about 10 minutes, it was time to share. We rated ourselves against the success criteria to see where each group was. Then, I asked them to think about which strategy was most efficient on their poster.  They laughed pretty hard about the inefficiency of drawing 85 circles/tallies.

Here were some of the favorite efficient strategies that students shared:


A nice notation of the distributive property, where the student broke the 17 into 10 and 7.


Classic repeated addition (bottom), and another way to note the distributive property on the top.


This person used the distributive property, but broke the 17 into 8 and 9! Very cool. I also appreciated how they showed their thinking below the number sentence.

My personal favorite was this one:


He broke the 10 into two fives! That is someone who really understands what he is doing.

It was wonderful to get them talking and sharing.  The person doing the talking is the person doing the learning!



2 thoughts on “Math is Messy!

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