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Broadbent Maths - creative primary maths

Modelling and representing Place Value

Friday, 2 October 2015
The way place value is modelled and represented is the key to getting a good understanding of how our number system works. So what resources will support an understanding of place value?
It is too easy to take our number system for granted, so try to teach it with a sense of awe and wonder that all our numbers can be made with just nine digits and a zero!

When I started teaching we taught place value as a concept by using different base systems - so Base 5 was shown by bundling sticks in groups of 5 and also using 'multibase' equipment like the Dienes material. I'm not necessarily advocating it as a method, but it made us really consider the way our number system can be represented in different ways to help make sense of it all.
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A Roman abacus or calculi, you will notice a pebble above the bar represents 5 - probably saved carrying so many pebbles!
When teaching place value, it is worth considering those six elements from my previous article and the models that are useful to make sense of it all. 

PV models

What resources will support an understanding of place value?

 
Base 10 apparatus, such as Dienes, is still the most useful concrete representation of a number. The physical manipulation of each part of a number helps understand our number system, and I find that using arrow cards alongside these at the same time gives a useful step towards the abstract, showing, for example, 482 as 400+80+2, or 480+2 or 400+82.
 
Place value counters do a similar thing to arrow cards, bridging the gap between the base 10 apparatus and the actual numbers and are particularly useful for showing exchange for calculations. However, I still find I get more ‘Aha!’ moments with arrow cards if you want children to understand place value.
 
An abacus isn’t used as much here as in many countries, but, again, it is a good step into the abstract, with each digit value represented by a bead. It certainly gives children a feel of the columns for hundreds, tens and ones. 

Related articles

Place value - representation and misconceptions
What elements do children need to know?

Make your own interactive maths kit
There are some resources that could also be used for place value in this kit


Links for current Broadbent Maths users

Progression steps - number
The small steps of progression for number are useful for teaching Place Value

Models and Images - Place Value
Download, print and use the PV arrow cards and a number generator
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