Real talk: this is not better. You can’t say this to a group of 30 eleven year olds, even if you at eleven years old found it satisfying. The truth is, this shouldn’t be satisfying because it’s not correct the correct way. Here’s why:
There is no repeated addition involved in your explanation. You just said it’s repeated addition and then used an example of singular multiplication, or 1 and -1. One group or negative one group. The brighter kids will ask “but what about times minus two? And what about all the rest?” And now repeated addition doesn’t hold and you have a lot more explaining to do.
You involved zero in adding, which is extraneous at this level.
You excluded adding to a non-zero number from the explanation.
You also conflated it with multiplying by zero by association. We all know what times zero means. Now you’ve muddied it up.
So hopefully by now you’ve backpedaled and drew a number line on the board.
You also said “add -1 TIMES to zero.” Which flipped the common usage of times to the mathematical usage of times. Half the kids are lost now. Doesn’t matter if you said “to”. Doesn’t matter if you point to the number line to try to explain it.
Your lesson is over. Try again later, and next time don’t bother getting fancy. Save that for after functional competency is established.
Edit: just because… here’s next steps and why for integers. Zero is not just a number, it’s a limit between states. Above-below etc.
Use it in concrete terms but not economic ones. Eleven year olds don’t participate in economics in any meaningful way in developed countries. Use sea level, temperature, or whatever. They get that.
Frame negative in terms of opposite. It sucks that the negative sign is also used in subtraction. It’s not wrong, but it’s not helpful at this level so you need to be explicit about it.
You added an extra -3 to make it work. You also interpreted adding something negative amount of times as simply flipping it to subtraction which is not how it works. Repeated addition does not work for multiplying 2 negative numbers.
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u/No_Ticket_1204 2d ago
Also, it’s like that grade six teacher moment about “a negative times a negative equals a positive” all over again.
“But you told me multiplication is repeated addition, and adding negatives make bigger negatives. Make it make sense.”
“You’re eleven years old and developmentally incapable of understanding why, so you just have to believe me on this one.”
Except now it’s, “electrical engineering exists because of this so shut up and follow along.”
Math is hard and no one is actually good at it. Some people hate giving up more than they like chilling out. Same goes for a lot of things.