Fifth graders have a hard time understanding that 1 is not a prime number. It's not composite either. Does it have its own category? I haven't been able to find anything.
To institutrice, I was always told that 1 was a "special number." Of course, Three Dog Night told me that 1 was "the loneliest number that you'll ever do." I'm not helping you, am I?
the best way of teaching why 1 isn't prime is a lesson I got out of Teaching Children Mathematics. Get some colored cubes. Tell the children: red is 2, blue is 3, yellow is 5 (or whatever colors you want). I'm going to put some cubes in my pocket/bag/whatever, and I'll tell you that when you multiply those numbers together you get 12. Can you figure out what cubes are in my pocket (yes). Repeat for several other choices of cubes (what cubes could give you 10? 20? 90?). Every time, there's only one choice of what could be in your pocket.
Now pick another color and make it a composite number like 6 or 4. Now can they figure out what cubes you have if the product is 12 (not for sure--there are two possibilities). So that's why 6 and 4 aren't prime.
Now, throw out the composite numbers and go back to the 3 primes, but add a color that you say will be 1. Now can they figure out what you have when the product is 12? No--because you could have any number of ones--there's no way of knowing how many ones are in your pocket. That's why 1 isn't prime.
Prime numbers have as their most important job giving a unique way of factoring any whole number.
(BTW, the number 1 has two special terms associated with it. One is that it is the multiplicative identity; the other (which is more directly comparable to being prime or composite) is that it is a unit. It is a unit because it has a multiplicative inverse (that is also a whole number). That seems like a silly definition when all you ever do is whole numbers, but mathematicians like to play the same prime and composite games with things like matrices, and then there are a lot more things that are units.
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5552357?
Tsk, tsk
67*79*1049
Fifth graders have a hard time understanding that 1 is not a prime number. It's not composite either. Does it have its own category? I haven't been able to find anything.
Sadness! I totally wanted that shirt, but only when I thought it was correct.
I'm hoping a review of the school play comes soon!
To institutrice,
I was always told that 1 was a "special number."
Of course, Three Dog Night told me that 1 was "the loneliest number that you'll ever do."
I'm not helping you, am I?
I hate math...
To insitutrice,
the best way of teaching why 1 isn't prime is a lesson I got out of Teaching Children Mathematics. Get some colored cubes. Tell the children: red is 2, blue is 3, yellow is 5 (or whatever colors you want). I'm going to put some cubes in my pocket/bag/whatever, and I'll tell you that when you multiply those numbers together you get 12. Can you figure out what cubes are in my pocket (yes). Repeat for several other choices of cubes (what cubes could give you 10? 20? 90?). Every time, there's only one choice of what could be in your pocket.
Now pick another color and make it a composite number like 6 or 4. Now can they figure out what cubes you have if the product is 12 (not for sure--there are two possibilities). So that's why 6 and 4 aren't prime.
Now, throw out the composite numbers and go back to the 3 primes, but add a color that you say will be 1. Now can they figure out what you have when the product is 12? No--because you could have any number of ones--there's no way of knowing how many ones are in your pocket. That's why 1 isn't prime.
Prime numbers have as their most important job giving a unique way of factoring any whole number.
(BTW, the number 1 has two special terms associated with it. One is that it is the multiplicative identity; the other (which is more directly comparable to being prime or composite) is that it is a unit. It is a unit because it has a multiplicative inverse (that is also a whole number). That seems like a silly definition when all you ever do is whole numbers, but mathematicians like to play the same prime and composite games with things like matrices, and then there are a lot more things that are units.
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