Naming Equal Groups
In class we’ve started exploring equal groups, starting with the mathematical conventions for naming them.
In Ariel’s picture, we see 5 U.F.O.s with 3 aliens each, 5 groups of 3, or to use the mathematical shorthand, 5×3.
The picture below (drawn by Jerry) shows us 3 ninjas with 5 swords each: 3 groups of 5, or 3×5.
Yes, of course 3×5 = 5×3 = 15. Understanding the commutative property is important for children, and we’ll be doing a lot in class that helps them develop that understanding, so they’ll never have to remember it as an arbitrary rule. But when we’re dealing with word problems, or real life situations, it’s important to remember that there can be a big difference between three groups of five and five groups of three. The mathematical convention that we’re teaching the children is that the quantity of the group always comes first (5 U.F.O.s) followed by the number in each group (with 3 aliens each). And for the time being in class, when we write the ‘x’ sign, we say “groups of” instead of “times,” just to reinforce that awareness.