When: after dinner and before brushing teeth

Where: bedroom

I've talked before about Peter Liljedahl's Numeracy Tasks as explorations in fair sharing. Tonight, J1 and I briefly discussed the cookie question and the cupcake conundrum.

# Sharing Cookies

Six cookies, 3 friends (J1, Ji-Ping and Tanya), sharing is easy peasy, right? Well, one mom insists that her child (Ji-Ping) can eat only one cookie, so what do you do?J1 responding quick: Ji-Ping gets one, Tanya and I each get 2 and a half

J0: Is that fair?

J1: Its fair because he gets to eat as much as he is allowed and then Tanya and I get the same amount.

J0: How will Ji feel if you get so much more?

J1: Well, his mother probably only wants him to eat one because he is going to get more treats at home, like birthday cake, so that's fair. (By chance, today is Ji's sister's birthday!)

J0: Are there any other ways to split?

J1: We could all have one today and save the others for tomorrow. We could ask Ji-Ping's mom to let him have more.

J0: Maybe you could share with other friends?

J1: yeah, and then in the future, they might share with us. At first, I thought you were going to say that the snack was yo-yo bear <laughs>

J0: What if it was yo-yo-bear, how would that change the situation? Each pack has two strands, but what if Ji-Ping was only allowed to eat one?

J1: <thinking> I guess it wouldn't change it.

J0: So, what about your first idea with the cookies?

J1: Oh, Ji-Ping would get one loop and the treasure card, Tanya and I would each get a treasure card and 2 and a half loops.

J0: how does that feel compared to the cookie split?

J1: it seems pretty fair

# Sharing cupcakes

Again, we've got three friends and six treats, but this time 4 cupcakes have delicious chocolate frosting and two do not. This time, J1 had a clear sense that the right answer was to cut in equal portions.J1: well, we each get 2/3rds of a cupcake with no frosting. And we get two with frosting. Wait, how many had frosting?

J0: 4

J1: I thought it was 6 <laughing>. Hmm, then we get .... 1.5.....no......1 and 1/3rd with frosting.

J0: any other ideas about how to split them/

J1: Well, this is fair, we all get the same treats and we don't have any left over so that's got to be best.

# A bedtime math confession

Recently, we've been talking about the "fun nightly math" activities on Bedtime Math. Both J1 and J2 enjoy the scenarios and they have fun calculating to answer the questions. Frankly, I'm not in love with the questions as they usually seem a bit artificial to the story and are often just a single arithmetic calculation. However, it is a very handy resource to easily add a couple minutes of number thinking to the end of a day.Tonight, the 1000-year Rose led to some good diagrams and a fun discussion about very long times (hundreds of years). J1 made a number line to answer the "sky's the limit" question and a labelled array to answer the big kids bonus question.

Hardly a thrilling photo, but some evidence I'm not making all of this up |

So, I hereby officially give you permission, nay encouragement, to open bedtimemath.org the next evening when you don't have time or energy to have a more extensive TMWYK conversation.

I talked about the sharing questions with J2 tonight. He had a very different take on each question:

ReplyDelete6 cookiesI posed this version in the form: "your teacher has brought cookies for you, there are 6 for you and two friends."

His first idea: each friend gets one and the teacher keeps 3. "She should get to keep them because she bought them."

His second idea, they should get different amounts of cookies based on size. By chance, the friend who was told she could only have 1 is the smallest, so he organized it as: constrained friend/smallest gets 1, he gets 2, the other friend/largest gets 3.

CupcakesFor the cupcakes, he had two ideas: First, cut the cupcakes into thirds so everyone got equal amounts of equally frosted cupcakes. Second, he proposed dividing the frosting from the 4 frosted cupcakes amongst all 6 so that the cupcakes were all the same.