Then umm take it up with Eureka math because their answer key was putting only equations adding a number to a 5 in the mentally visualized 5 group.
They could have taken the opportunity to teach p-adic numbers. To negate a p-adic number, you don’t just stick a minus sign in front. You take the complement of each digit (with respect to the base-1) and then add 1. So:
…00000043 becomes:
…99999956 which becomes:
…99999957
Now we just add normally:
…00000567
…99999957
…00000524
Of course, once we get to the nines, we end up carrying a ones digit forever, so we have to recognize this and stop early. Easy, and a nice prep for two’s-complement representation, which is how basically every computer stores integers.
Well, that’s certainly dumb terminology for a sound concept.
I never heard this term before and illustrates the tendency to focus on obscure words rather than concepts. In the new math, first iteration, they spent a lot of time teaching words like commutative and associative. The words themselves are obscure and come into focus only when you find natural examples of non-commutative or non-associative systems.
To me, the 5-group is subgroup of symmetries of a regular pentagon consisting of the rotations, of which there are 5 (including the one by 0 degrees).
I prefer to think of that group as the integers mod 5.
Yes, tally marks occurred to me too. Look at it this way: If you’re an adult who already understands tally marks, then five-groups are pretty much the same thing but shown in a different way.
That’s true. You can guess the right answer without having a clue about how to do the problem and that doesn’t mean you should get points for learning math.
TEACHER: What’s eight plus seven?
STUDENT: twelve! twenty! fifteen!
TEACHER: Yes you got it right; the answer is fifteen. Okay, moving on…
Of course, accuracy should count too. And, to a certain degree, over analyzing the problem can become counterproductive. But there’s a balance to be struck there. Current consensus is that we should expect the students to understand that eight plus seven is the same as five plus three plus five plus two, which is the same as five plus five plus three plus two, which is the same as ten plus five. But we won’t ask them to do it that way all through the other grades. It’s a stepping stone.
Here’s some 5 group cards, aka dot cards.
You can see cards for 6,7, 9 and 15, without having to log in .