The grades that I am most familiar with are K-3, so that is what I am going to concentrate on for this paper. Once of the sources I used was my mother. She is a recently retired 2nd grade teacher, and when I asked her what I should teach children about infinity, she said that little kids are much smarter than we think sometimes, she told me that she used very basic ideas, and simply enough, she told them that infinity is something that goes on forever, and doesn't stop. So I had an idea, I thought it might be a good idea to introduce infinity to them, by showing them a globe, and asking them to "walk" around the globe, until the globe stopped, (they fell off). I would use one of the children, and either cut out a paper person, or have them use to fingers, and I would spin the globe, while they "walked" on it. I would ask the other children to tell me what was happening.
Next, I would have all the children go back to their seats, and I would ask them to raise their hands and tell me the biggest number they could think of. Every time they give me one, I will write it down, and then when I have enough numbers, I will explain to them that if I add 1 to all of those numbers, the number will be bigger. (mathforum.org) Then I will explain to them that infinity is NOT a number, and show them the symbol for it. I will also explain to them, that you can never really count to infinity, because every time you think you get there, you could just add one more, and it would be a greater number. I would also explain to them, that there is no such thing as the "highest" number.
The next concept I would bring to their attention, (and they would not learn this all in one day, it would be more like a week long unit) is one-to-one correspondence. Before class that day, I will take out all of the desks and chairs that do not have a person that sits in them, and if anyone is absent, I will leave their desk in the classroom.
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