I’ve caught the crud. It is either from:

- My tiny toddler germ factory and/or her daycare
- My teenage student germ factory

Your guess is as good as mine, but I’m home with a 100 degree fever, and so is my kid. I’m thanking my lucky stars that I selected a primary care doctor in the same building as my kiddos pediatrician. Nothing says family bonding like getting a nasal swab at the same time as your kid. Good news: we’re flu free. More good news: my kids napping so I get to blog.

Now, to the math. Last week I did an activity in Geometry and I promised @**druinok** that I’d blog about it. I called it *Two Proofs and a Lie*, its based off the Two Truths and a Lie structure that I first saw on Jon Orr’s Blog (he’s done a new posting on it recently which re-reminded me how much I love it!). What I love most about this structure is that you need not waste a time explaining what to do–its in the title, it says, “hey student, I’ve given you something that contains two true things and one lie…figure out which is which.”

We were on our second day of quadrilateral proofs. Students had figured out that most of the proof center around finding a triangle that helps prove the thing we want, prove those triangles are congruent, then CPCTC (i.e. their favorite mathematical acronym). I wanted to push them a little. But a doable amount. So I gave them the handout (here) and told them they had 5 minutes of no writing brainstorming with their peers. They were to discuss *what* it is they are being asked to prove, *what* was given, and *how* they think they might find that information.

Students were then told they could use whiteboard markers to collect their brainstormings into a proof rough draft. My kiddos don’t like the #VNPS for some reason (probably because chalkboards aren’t as ‘cool’ as whiteboards), but they LOVE writing on the desks with markers…so I have #HNPS (horizontal non-perminant surfaces).

The thing I like about making them brainstorm twice is they actually have to say what they are thinking out loud. I do believe that there is an added benefit to verbalizing what you’re thinking when it comes to math, but in particular with proofs. The biggest hurdle I’ve noticed with my students is forgetting a step in a proof because “they know its true.” Well yeah, its true, you know it. I know it. But you’ve gotta say *how* you know its true in a proof. We ran out of class time here. Students took photos of their white boarding work and we picked up the next class.

The next day students then wrote up, as a group, the two proofs that were true and peer-edited them before turning them in. I gave groups feedback, and we then moved, in the following days, to more individual proofs.