Math strategies

The instructions on Jordan's math homework today were simply, "Number Stories.  Show your work."  The first problem read:  "Tucker had 12 silly bands.  His mom bought him a pack of 5.  Now how many silly bands does Tucker have?"  (Silly bands, in case you don't know, are rubber bands in the shapes of things, and they are the hot thing in elementary schools right now.)  Jordan thought, and did some silent counting on his fingers, and said, "Seventeen!"  I said, "Okay, now it says to show your work, so draw how you got that answer?"  He drew this:

and explained that he had counted up from 12, and had kept track of how many he counted up on his hand, until he was holding up 5 fingers on his hand and that was 17 in his counting.

This knocked me out.  I was expecting your basic picture of 12 silly bands, then 5 more silly bands, and counting the whole group to get 17.  This was much more interesting.  The next one read, "Hannah brought 20 cupcakes to school and 12 people ate one.  How many cupcakes did she have left over?"  For this, Jordan made a more typical 20 tally marks and then erased 12 of them, then counted the remaining 8.  But, more fun: he also drew himself holding the paper that he used to solve the problem.

Last but by no means least, we had this problem:  "Shannon has 8 gummy bears.  Her friend gave her 8 more.  Now how many gummy bears does Shannon have?"  Jordan instantly said "Sixteen!"  I said, "Wow, you knew that right away!" and he said, "Because of the inchworm song, Mommy.  Eight and eight are sixteen."  Then he drew the inchworm.

I was loving this, for sure, but I was a little worried that Jordan's unconventional representations would go unappreciated by his teacher.  So at the dropoff this morning, I chatted Miss Wodrich up about what a good time Jordan and I were having with his different ways of showing his work.  To my delight, she said, "Yes, that's what we do in class with our mini white boards; everyone has their own board, they show their own way of doing a math problem, and then they share their way and we talk about all the different approaches."  How great!

Speaking of the inchworm song:  I'm not sure I had ever seen the Danny Kaye movie or heard the song in that context - I think I only ever heard it on Sesame Street.  I am startled to learn that in context, the song is not extolling the fun of arithmetic at all; if anything the Danny Kaye category is pitying the children learning rote lessons in school, while the truant appreciates the wonders of nature (the inchworm on the marigolds).  YouTube, how did we ever live without you?