Pakora Math [#tmwyk]

My kid LOVES the vegetable pakora appetizer at a local Indian restaurant. Yesterday she had some serious dental work done and I sweetened the stressful day with an offer of pakoras for dinner.

Our plan was to get one serving of pakoras to eat there and one to take home to share with the papa. We talked on the way to the restaurant that we needed to find a way to split the two orders evenly between three people.

Our in-house plate of pakoras came first; there were eight of them.

"So," I said, "How many should we start with?"

9yo: Two for me and two for you.

[Eating commences. Yum!]

Me: So we have four left. What should we do now? If we take one more each, there'll be two left on the plate and...Oh wait, I just realized we don't know how many pakoras there will be in the take out box!

9yo: Probably eight.

Me: So how could we split 16 Pakoras evenly between three people?

9yo: [Turning slightly and looking to her left for a couple seconds] Five and one third.

Me: I wonder how you got that?

9yo: Well, 5 times 3 is 15 and then you split the last one into three pieces.

Me: But what if there are only 6 pakoras in the take out box? How will we split 14 pakoras so it will be fair for all three of us?

9yo: Well, 4 times 3 is 12...

Me: But that leaves two. How would you share those last two pakoras between three people?

9yo: Well you could cut them in half and each person gets a half.

Me: What would you do with the last half?

9yo: Give it to me? <sly grin>

Me: Well...but what could you do to share that last half fairly?

9yo: Hmmm. Cut it into thirds?

Me: Cut the last half into thirds? That would make what, exactly?

9yo: Um....really tiny pieces?

Me: It would make sixths!

[Take out order arrives!]

Me: Let's see how many are in this box! There are EIGHT!  Great, what do we do now? We've each had three, let's take two more each ... Okay, now Papa has his five in the box, and there is one left. Wanna cut it into thirds?

9yo: Sure! ... well they're not really equal ... I'll take the biggest piece!
............................

I love how we ended up talking about two ways to share between three people. First, many pieces into three shares. Second, only two pieces into much smaller shares. Both fractions, but of slightly different natures I think. In my mind "fractions" refer to really small pieces. But that's obviously not the case with my share of five whole pakoras!

During the entire conversation I felt really proud of myself! Helped by projects such as Talking Math with Your Kids and also a recent video showing two boys figuring out how to share sausages, the whole pakora conversation just flowed. Good modeling is definitely the key to learning how to 'talk' math.

And, as we were waiting for our check we also got a bonus #dswyk (Doing Science with Your Kids)!

Me: What do you think is happening there? 
9yo: There's a rainbow on my hand! Lol.

Sidewalk Math: Circle Fractions, Division and Multiples

Okay, so we've walked past these two covers about a million times but today I saw them in a completely different light.

This winter/spring we've been doing a LOT with number multiples and conceptualizing multiplication and division.  Last week my mind moved toward the inevitable: fractions.  Although shivers go down my spine every time I think about fractions I'm still resolved to figure it all out for the sake of my seven year old, if not myself.  It's been sitting in the back of my mind so I guess that's why this cover caught my eye and brought me to a dead stop.

Can you see it?  Fractions and multiples!

And, a little further on, this beauty: an 8-star and some fractions!

What I really want to know is who designs these?  I want that job.  To see some other cool round things we found on a walk last spring, go read my post Channeling Tana Hoban: Juxtaposition Edition.   Now that was one amazing day for circles!