Extending Place Value

Research reports that many children lack an understanding of the relative sizes of numbers greater than 100. 

(Fuson 2003; Payne & Huinker 1993)

One way to counter this is to have students to manipulate materials that model large quantities. This allows students to develop a visual conceptualization of large numbers. A number expander can be used alongside the materials to show that the same number can be represented in many ways. 

Number expanders can help develop a student’s number sense and they illustrate the importance of front-end or lead-digits. They also underscore the importance of zero.

What is a Number Expander?

A number expander is a piece of paper that we use to represent the same number in various ways. For example, the number 123 can be represented as:

• 1 hundred and 23 units
• 12 tens and 3 units
• 123 units
• And there’s more using other notation.

How to Make a Number Expander

If you don’t yet have a number expander, you can grab a set here, or just use any old piece of paper for now. We take a strip of paper and fold it to make visible how we can manipulate a number to show it in different ways. Children enjoy the challenge of folding the pieces of paper. Once it is made, write numbers on the blank spaces provided. Then expand and contract to check out all the possibilities.

Developing Number Sense Activities

The University of Melbourne has a few activities that you can use with the number expanders. These include:

• Expand, record and compare
• When do zeroes matter?
• Multiplication and division by 10

Number expanders are great to extend your learner’s number sense, to reinforce the importance of zeroes and to promote the base-10 system. 

References

Reys, R. E., Lindquist, M., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2014). Helping children learn mathematics. Queensland: John Wiley & Sons. ?: https://amzn.to/2NeCL6l

https://extranet.education.unimelb.edu.au/SME/TNMY/Decimals/Decimals/teaching/models/nexpand.htm