The goal is to be able to see a standard notation expression of a number and its matching expanded notation expressions as different but equivalent expressions. This paper-folding manipulative idea is not mine, but, I've used it for so long, I don't know where I got it. Usually, I just make a large copy and use it as a model, but, it is also useful to have members of the entire class make their own manipulatives. Make the Concrete ManipulativeOn a strip of paper write a whole number in expanded form. Here the number 5,432 is written as 5(10)^{3} + 4(10)^{2} + 3(10)^{1} + 2(10)^{0}. For another group of students, one might use the number 5,432 expanded as 5000 + 400 + 30 + 2. Just before each of the standard form digits, fold the strip. More folding is now needed. Here, the 4 in the hundreds place is folded just to the right of the 5 in the thousands place hiding the "(10)^{3} +". Next, the 3 in the tens place is folded just to the right of the 4 in the hundreds place hiding the "(10)^{2} +". Next, the 2 in the ones place is folded just to the right of the 3 in the tens place hiding the "(10)^{1} +" and the remaining "(10)^{0}" is folded UNDER the 2. |
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