Yesterday evening I spent half an hour with Stephanie, a graduate education student to help her develop her project which was to teach place value through reader's theatre. Since I believe math should always have an aesthetic component this seemed like a wonderful way of developing the fundamental concepts of place value in an artistic and motivating context.
We talked primarily about place value, how it is groups of tens of tens and how we have ten numerals with which to make every conceivable number possible. We also talked about the misconceptions caused by phrases such as "0 is a place holder" and how 0 really means "none of". For example, in 103 the 0 means there are no tens. We also talked about the reason for putting a comma every three digits to help us read large numbers. Most people remember being taught this but few people ever remember being taught why. If you think about a large number such as 21,487,439 the first 3 digits from the right, 439 refer to ones, the next 3 digits, 487, refer to thousands while the 21 refers to millions. Between each set of commas, from right to left are ones, tens and hundreds. 439 is ones, tens and hundreds of ones. 487 is ones, tens and hundreds of thousands and 21 is ones and tens of millions. This pattern of ones, tens and hundreds repeats itself between each comma for ever.