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I am currently working on source material for a math-related software project with my mother, who has a PhD in Elementary Education and specializes in math education. While she has quite a strong fundamental understanding of the current techniques and topics taught to children at an early grade school level, I am relatively unfamiliar with the subject area. Lately, I've been looking for sources of inspiration and information, such as Conrad Wolfram's TED talk "Teaching kids real math with computers".

Remembering that the Stack Exchange family now has this excellent math site, I figured I would ask this question here:

What are some interesting concepts in math that can be taught to elementary school children, that aren't traditionally taught? This can be because the topics aren't considered suitable, or perhaps because no one's thought to do it yet. For example, at the end of his talk, Wolfram describes a technique to visualize calculus using limits and shapes inscribed in a circle.

(While I realize this question is slightly unusual compared to other questions I see on the front page -- in other words, university-level math questions -- I think it is appropriate given what the FAQ mentions as appropriate topics for this site.)

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    I think you might get more useful answers if you provided more specific information. First, if you are talking about American students, please be explicit about this: a lot of the readers of this site come from other educational cultures. Also, to me "elementary school" means students aged 6-11: is that accurate for you? This still leaves quite a range: are you looking for activities which would be appropriate across this range or would it be okay to have some activities which are better geared towards older (or younger?) students?2012-12-29
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    Finally, are you looking to devise materials for particularly bright / gifted / motivated students, or materials that would capture the attention of a wide range of elementary school students? There is a very small percentage of children who are ready for truly advanced mathematics at a very young age; however the majority of students are not.2012-12-29

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