Unitizing Your Vitamins

For about two years I have been reading Christopher Danielson’s (@Trianglemancsd) blog Overthinking My Teaching and greatly enjoying the frequency with which he writes about the mathematical conversations he has with his two kids.  While I greatly enjoyed his presentation at NCTM, I was more excited to realize that he’s Tabitha and Griffin’s dad.  Unfortunately I realized this after returning to Berkeley, so I never actually talked to him about this.

Hopefully he won’t mind me utilizing  his style to write from time to time about the developing mathematical thinking of my own son Egan.

This morning after finishing breakfast, Egan, four years old, asked for his vitamins.  He gets 4 of them: two multi, a probiotic and an Omega-3.  He quickly ate two of them.

E: ” I am saving the other two to have with dinner.”

Me: “Oh, so you are saving 1/2 of them?”

E: “No mom.  You can’t break vitamins in half, they are too hard to break.”

Me: “So the only way to get half of something is to break it into two pieces?”

E: ” Of course.”

Me: (holding out 2 hands): “On one of my hands, put out fingers for how many vitamins you just ate and on my other hand put out fingers for the number of vitamins you are saving for dinner.”

He does this with ease.

Me: “Now cut my fingers in half.”

Egan chops his hand between my 4 fingers.

Me: “Hmmm..I thought to take half of something you had to break it into two pieces.  But you didn’t chop up my fingers.”

E: “But I did cut your fingers in half.  I put two on each side.”


Me: “So eating your vitamins today will look something like this.”

E: “That’s cool!”

I was struck by Egan’s ability to refine his understanding of one whole within the course of our conversation.  His initial understanding of 1/2 was when you take something and break it into two pieces.  I am not quite sure he understands the importance of equal pieces, but I know he knows that you get 2 pieces when you break something in half as that idea has come up before with sharing food.  This may have been the first time he was faced with unitizing, the idea that 1 whole can be made up of many pieces.  I think we’ll see where these finger games go at breakfast tomorrow.


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