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.