Equal Shmequal

A few days ago, Katie came home from a party with 3 Oreo cookies.   In the evening, she asked to have one of them with her milk.  Permission was granted.  As she was finishing up her munching, Katie asked me the following question:

“Are two Oreos equal to a Kind Bar?”

I was both confused and amused by the question, but ultimately thought that I knew where she was going with this.  I started comparing the nutritional qualities of each, saying how a Kind Bar had fiber and protein whereas an Oreo is pretty much all sugar.  Meanwhile, Katie was giving me one of her “What are you even talking about?” looks.  Finally, she interrupted me and said:

“No, mom, I mean are they equal or is one bigger?”

Now it was my turn to have a dumbfounded look.  However, I quickly regained my composure and seized the opportunity to have some math chat.

“I don’t know, how can we find out?”  I asked while taking out a Kind Bar and the two remaining oreos (how fortunate that we started out with three!).  First we put the two oreos on top of the Kind Bar:

and noticed that the bar was longer.

“But the oreos are bigger this way!” said Katie, using her hands to refer to the fact that the oreos were wider.  “What if we cut them up and put them back together,” she continued.  “Would they be equal to the Kind Bar?”

And this is where I realized that Katie was talking about volume!  Unfortunately, we did not have the skill or time to do the experiment properly (did you ever succeed at cutting up an oreo into neat pieces?).  But I definitely hope to have follow-up discussions and experiments in the future.  Also, our conversation reminded me of the book Equal Shmequal (hence the post title), which is a cute story about some animals discussing the various meanings of equality (mathematical, not social).  I should reread it to her.

When I was putting Katie to bed later that evening, I couldn’t stop myself from asking her for the reason behind her question.  “Did you want a second Oreo?” I inquired.  She gave me a “You would think that” look and said, “Nope, I just wanted to know whether they were equal!”