Two sisters, two parents, two cousins, and four grandparents, all met up at the park (true story). During the car ride home, one of the sisters (lets call her Katie), exclaimed, “There were ten of us at the park.” The parents confirmed this statement.
Katie: Want to hear how I know?
Katie: I counted the people in each car, and four plus four plus two is ten.
Mom: How else can you make ten?
K: Well, Zoe was in grandparents’ car on the way there, so that’s three plus three plus four.
Dad: You can also get three, three, four by splitting into kids and adults and the adults into males and females.
K: And you can also do kids, parents, and grandparents which is four plus two plus four.
And so it went on for a bit – six, two, and two was obtained by splitting according to last name and also doing adults, little girls, and little boys. It was a lot of fun for Katie as well as her parents (the other sister, Zoe, fell asleep, but that’s what happens when you put an exhausted 2 year old in the car). I highly recommend playing variations of this game on long car rides and similar situations!
And an afterthought. I think a lot about mathematical conversations I can have with my kids, but I believe that the best ones come about naturally and are usually started by them. I just have to seize the opportunities and sometimes steer them in fun and productive directions.
And if each parent wants a quiet ride home, you could have 1, 1, 8.
There is some great stuff going on here. Thanks for sharing it!
I like your thinking there, but I’m afraid that 8 wouldn’t fit into one car. Perhaps almost as good would be for the parents to go in one car, and then have the two sets of grandparents divide the kids however they want 🙂
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Did you say, “Suppose we divide into groups by [something where she doesn’t know who’s what] and then add them. How many total people?”? I guess commutativity and associativity of multiplication and distributivity are close behind!