## Standard Notation to Expanded Notation to Standard Notation

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 Manipulative

On 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.