Number Expanders

• Description of number expanders
• Usefulness of number expanders
• Two electronic versions to try
• How to make a number expander (templates)
• How to use a number expander

Description of Number Expanders

A number expander is a simple aid made of paper which can show the many ways of renaming a number (both whole numbers and decimal numbers). Here are some examples:

Various expansions of 3.145

 

 

 

 

 

 

 

Various expansions of 3174682

 

 

 

 

 

Usefulness of number expanders

The ability to flexibly rename numbers is an essential skill which is used in many situations. For example:

• Using the addition algorithm for 478 + 351 requires renaming 12 tens as 1 hundred + 2 tens
• Using the (decomposition) algorithm for 829 − 351 requires renaming (decomposing) 1 hundred into 10 tens before subtracting 5 tens
• Explaining 0.4 ÷ 10 = 0.04 is easier if 4 tenths is firstly renamed as 40 hundredths, then these 40 objects are shared amongst 10 people, giving 4 objects to each person (i.e. 4 hundredths each or 0.04)

Two electronic versions to try

Number Expanders (http://extranet.edfac.unimelb.edu.au/DSME/decimals/SLIMversion/teaching/models/nexpand.shtml) - two electronic versions of a number expander can be accessed here. To use the number expanders, just click on the digits or the place value names to open and close at that point.

How to make a number expander (templates)

Number expanders are made by folding strips of paper. Here are various templates for printing so that students can have access to this useful device as they learn about more place values throughout their schooling. Choose one of the templates, print and copy as required, then slice horizontally into individual strips and give one to each student.

Templates for printing:

• Hundreds, tens and ones (PDF - 11Kb)
• Thousands, hundreds, tens and ones (PDF - 12Kb)
• Millions, hundred thousand, ten thousands, thousands, hundreds, tens and ones (PDF - 13Kb)
• Ones, tenths and hundredths (PDF - 11Kb)
• Ones, tenths, hundredths and thousandths (PDF - 12Kb)

 

How to use a number expander

Students will enjoy the challenge of folding them correctly - somewhat like a fan. Help them to fold (shaded rectangles are folded in half with a 'valley fold' and then a 'mountain fold' is used to put the shaded rectangle behind the white rectangle on its left). For example, in the photos below, the ‘ones’ rectangle is folded in half (with a valley fold) and then behind the digit 3 which is on its left.

The decimal number version works in the same way as for whole numbers but a decimal point made of Blu-Tak (or similar sticky material) must be used when the words are hidden. As shown in the photos above, this decimal point is removed when the words are shown (so 3.145 can be renamed as 3145 thousandths).

Students write their own numbers on the number expander, one digit per blank space. Open the number expander up in many ways to see the possibilities. Every combination is correct!

Here are some examples of expansions of the number 236.

 

	This is a ‘closed’ number expander showing 236
	The number 236 has been written in the blank place value columns. This shows 236 = 2 hundreds + 3 tens + 6 ones
	This shows 236 = 2 hundreds + 36 ones
	This shows 236 = 23 tens + 6 ones
	This shows 236 = 236 ones