Number Discovery

In retrospect, this amazing discovery started with parental neglect and erroneous math.  I freely admit I was at fault, but it all worked out amazingly well in the end.

It was all precipitated by an innocent question, yelled from another room: "Mama, what is half of 38?"

I did a little mental math: "Sixteen!" I yelled back.  In my defense I was in the middle of something very important.  That's why I didn't insist she figure it out herself, you see. 

When we were finally in the same room it took me a minute.  I was actually fairly impressed with her thinking.  Even though it was all wrong, she still had logic and structure to her reasoning.  Can you figure out what her 'rule' was?

[And, yes, at six she still writes many things backward; sometimes, as is the case here, she even writes from left to right.  Ah, the growing brain!]

Luckily, I had my wits about me and simply said, "Cool, look at that!  Hey, let's check your work with the Cuisenaire rods!"  This was a brave move since, prior to this moment, we have done absolutely nothing with 'taking away' or 'difference' in any formal way let alone using the rods.  Fortunately, the taking away part was so wonderfully obvious in this visual/tactile realm that I had no problem explaining it and the girl got it right away.  During this process I also noticed that in the intervening couple months between our first major experience with Cuisenaire rods and today, her ability to visualize and attribute amounts to the rods has become second nature.

Here the total number was 31, take away nine.  It was so very satisfying to physically take away a number and literally see the difference. 

Sorry this is so blurry, but hopefully you can see that we started with 37 and took away 15.  I'm not completely sure why we didn't start with the original number in question, 38, but like I said, it all worked out in the end.  Just look at it!  It's beautiful, don't you think?  By the fourth equation I asked her if she could figure out what would come next.  She guessed right for the last five equations, but wanted to check her work with the rods each time anyhow.

Today I am basking in the joy of unexpected discoveries and a growing mind.