My kids wrote a page about one math problem...

...just because I said "prove it" instead of "tell me why."  My directions were that simple, and they took 10 minutes to really dig in and do a great job. 

Yesterday, I used a matching activity from Flamingo Math to have students match piecewise functions and their graphs.  I left off the domain and range aspect because I haven't taught interval notation and I wasn't ready to focus on that aspect quite yet.  The kids worked in partners to sort out the cards.  I didn't make them record anything.  When time was up, we discusses particular graphs or equations that gave them trouble.  (One note: if you go download the activity, which you should, card E1 has the incorrect inequality symbols in the domain constraints of the function, so change them prior to making your copies.) 

Today, their first independent activity was to go back to the pile of cards and select one match.  They were to glue the cards to their notebook paper and I asked them to, "prove to me that you are correct."

I was so impressed by my kids' hard work on this assignment.  Most of them ended up filling all of the blank space on the front and many of them continued onto the back.  Some of them wrote paragraphs.  Others used lots of labels and arrows to make their point.  I'm counting it as a quiz grade; they did so well after struggling with the concept a day or two earlier.

This student wrote so much...

That she used about 1/3 of the back, too.

Clearly a different approach in doing proof from the text-heavy examples above.

One thing I need to clarify: since we've been learning about parabolas and absolute value functions most recently, they're interchanging the terms "slope" and "a-value."  Sometimes, the terms do serve the same purpose, however they've never before used "a-value" for linear functions.  We use y=mx+b.  The connection they're making is great; their terminology needs some refining. 

Have you ever had a lesson or assignment that had kids doing awesome work beyond your wildest dreams?

Mathematically yours,
Miss B