If you have 5 egg cartons with 0 eggs in each carton, how many eggs do you have?
Or, if there are 12 eggs in each carton and you have 0 cartons, how many eggs do you have?
If you have 5 egg cartons with 0 eggs in each carton, how many eggs do you have?
Or, if there are 12 eggs in each carton and you have 0 cartons, how many eggs do you have?
Maybe Billy Preston can help.
yerwot, mate?
That I not only have no frisbees currently, but also owe you one. So if I get another frisbee, I have to give it to you and still have no frisbees.
This is where things are going off the rails for you. You don’t “start” with a frisbee when you’re multiplying - you “start” with a frisbee when you are adding (or subtracting).
Thudlow_Boink has the right approach a few posts above with the eggs.
Let’s say you’re cleaning out your garage. You really like to sort things into piles of 5. You sort out the tennis balls into three piles of 5 - that’s 3x5 for 15 tennis balls. You sort out all your hammers into two piles of five. That’s 2x5 for 10 hammers. Now you want to sort out all your frisbees. You look around but don’t find any. That is zero piles of five - or 0x5 for 0 frisbees.
Wouldn’t burning the frisbee in a blast furnace be the physical equivalent of multiplying it by 0?
There is nothing wrong with your brain. You were just poorly taught.
Mmmm…fried frisbee!
Or refused to learn.
But for a basic concept like multiplication, that’s taught at a very early age so that’s on the teacher yeah.
Here’s how I would explain it:
Here is 3 * 1 drawn, expressed as how many individual 1’s: 1 1 1
Here is 2 * 1 drawn out: 1 1
Here is 1 * 1 drawn out: 1
Here is 0 * 1 drawn out:
That last one, which is nothing, can also be expressed mathematically as 0.
Living things can multiply. Numbers can be multiplied. If you have one or zero Frisbees you can do anything you want to them but you won’t get any more Frisbees. Even if you divide one you just end up with multiple non-Frisbees.
You can multiply the number of Frisbees you have, but that just gives a different number (unless you multiply by one), but you don’t end up with any more or any less Frisbees. And multiplying any number by zero results in the number zero, that’s just the way it’s defined.
I wouldn’t necessarily say that. I’ve never heard someone describe mutliplication in the way the OP does. Stoid’s teachers may not have been able to address the misconceptions if they weren’t aware of them.
I remember some things that confused me when I was a kid. There were ideas that I wasn’t able to articulate. It was years later that I realized what diffferent assumptions I was making, but I couldn’t really blame other people for not reading my mind at the time.
I would hesitate with this one because multiplicative identity is 1 meaning if we are multiplying or dividing, blank spots are filled in with a 1 (think of no coefficient means a coefficient of 1)
If instead you wrote it as
Here is 3 * 1 drawn, expressed as how many individual 1’s: 1 + 1 + 1
Here is 2 * 1 drawn out: 1 + 1
Here is 1 * 1 drawn out: 1
Here is 0 * 1 drawn out:
And point out additive identity is 0, then your analogy works out.
ISTM part of stoid’s issue issue is that it is accepted by society, parents, students and many (not all) elementary teachers that it is OK to be bad at math. So when stoid had problems with misunderstanding basic concepts everyone said, “Math is hard. Let’s forget about it and move on to reading.”
Maybe it will help to think about slowly multiplying that one frisbee by smaller and smaller numbers that approach zero.
As you can see, as the multiple becomes smaller, you are left with smaller and smaller amounts of the frisbee. From that sequence, you should be able to predict that a frisbee multiplied by 0 should be 0 of a frisbee.
By the way, you’re not alone in being confused about zero. Zero is weird. You can think of it both as a number and as a concept. It took mathematicians a long time to come up with zero. It was a concept not known to many societies. I saw this Nova episode about concepts of zero and infinity:
It was really interesting, but it may leave you with more questions than answers. It’s hard to wrap your mind around these kinds of things.
I teach this stuff for a living, so I’m gonna tell you some true stories. If you were here, I’d show you; but you can model it yourself.
In front of me I have two containers. Each container has 1 pencil in it. These are equal groups (groups with the same number of items in each one), so I can express the total number of pencils with multiplication:
Whoops! I just put a couple more pencils in each bowl. Now each bowl has three pencils. Check it out!
Forget one of those groups. It’s gone. Now I just have one bowl with three pencils in it.
Now for the clincher: I take all the pencils out of the bowl.
Alternatively: I know that if you find a Snickers wrapper at the store on the shelf, there’s likely to be one Snickers bar inside. One container has one item in it. I look on my desk, and see zero Snickers wrappers. How many Snickers bars to I have?
Again, this probably works better with objects. Were you in my classroom, I’d break out some math manipulatives to demonstrate it.
It’s also a helpful way to demonstrate division by zero. Give kids six pencils, and ask them to put all of them into six groups so that each group has the same number. Then put them into three groups. Then into two groups. Then into one group. When they’ve done that, and you’ve written the corresponding equations, ask them to put all six pencils into zero groups such that there are no pencils left over and each group has the same number of pencils.
I agree that many elementary teachers are poor at teaching math, but as a math teacher it is offensive that you IMMEDIATELY assume it is the teacher’s fault.
Nope–and this is an important point. If you can’t describe what you’re doing without math, you can’t describe it with math (so the OP doesn’t make sense–what does it mean to “multiply a frisbee by zero”?) But ALSO not everything you describe without math is translatable to multiplication.
In your example, by translating the frisbee into ash and smoke, you’re essentially subtracting one frisbee from the world. One frisbee minus one frisbee equals zero frisbees.
If you treat the furnace as a group, you could do a different equation: you have one furnace, and each furnace has a frisbee in it. 1x1=1 frisbee total. Turn the furnace on, though, and now it’s 1 furnace with zero frisbees in it: 1x0=0.
Re: the OP and Frisbees.
Start with one Frisbee, multiply by 2 you now have 2. If you had multiplied by 3, 4, 5, … you would instead have 3, 4, 5, … .
Why is multiply by 0 and have 0 so puzzling?
Note that multiplication seems to have it’s origins in calculating area (e.g., of a parcel of land).
A 2 by 3 parcel has 6 units of land. A 1 by 7 parcel has 7 units of land. A 0 by 53 parcel has 0 units of land.
Remembering back to 3rd grade our teacher introduced us to multiplication by stating:
5 x 3 means count to 5 three times.
3 x 5 means count to 3 five times.
This always kind of stuck with me and makes sense for multiplying by zero.
1 x 1 means count to 1 one time.
1 x 0 means count to 1 zero times.
So it would follow that if you counted to any number “zero times” you would just not count anything.