Our New Math Unit in 301
This week in 301 we’ve started a new math unit. It’s exciting for me because it’s the start of our work with equal groups, which will take up much of the rest of the year. We started today by looking at some photos of equal groups that we might encounter in life, such as egg cartons, boxes of markers, or spiders with a full set of 8 legs. I introduced the convention we use for naming these sets of equal groups: 2 cartons with 12 eggs each, or 2 groups of 12; 3 spiders with 8 legs each, or 3 groups of 8. We had an interesting conversation about a particular photo of a chocolate box, because it could be described both as 1 box of 8 chocolates, or as 2 (smaller) boxes with 4 chocolates each, if you were looking at the plastic cups nestled inside the larger cardboard box. You can help your child by seeing how many equal groups you can notice and name around your house, or as you walk down the street – for example, my next door neighbors have 7 windows with 8 panes in each window, or 7 groups of 8.
We start with naming equal groups because we want our mathematicians to be able to visualize what’s happening once they start putting equal groups together. It’s important for multiplication to be a part of real life for them, not just numbers and equations on the page. And yes, it matters whether it’s 4 groups of 2 or 2 groups of 4. If I have 4 ice cream cones with 2 scoops each, I will have four happy children! If I have 2 cones with 4 scoops each, I will have 2 ecstatic children and 2 who stomp off muttering darkly about unfairness. It’s true that both situations would use 8 scoops of ice cream, but that’s not the only aspect that’s important.
We will soon be switching over to the mathematical symbol for “groups of,” which is of course “x” – but even after we start writing that, we will still be saying “groups of” as we write the “x.” This is a really important way to ingrain in the students’ memories that “5×4” means 5 groups of 4, or 5 plates with 4 cookies each (or whatever it is that we’re talking about). After all, as I tell the children, “times” is a silly word to use – it doesn’t have anything to do with telling time! If you’re looking at your children’s math homework with them, you can support us in this by saying “groups of” rather than “times” as you talk about equal groups.