Place gives value

Have you ever unpacked what ‘place value’ actually means? What does the ‘place’ mean, what does ‘value’ refer to, and when we put them together what are we actually talking about?

I think about place value a lot (and by association so do my family)!

This became very apparent to me as we watched 'Phar Lap' as a family last week.

For those unfamiliar with Phar Lap, it is the true story of one of Australia's greatest ever thoroughbred racehorses. Phar Lap won 37 races from 51 starts, including the 1930 Melbourne Cup. It is the perfect rags to riches/underdog story. Very sadly, Phar Lap died in the US in 1932 in suspicious circumstances. An exhibit showing Phar Lap now proudly stands in the Melbourne museum and I remember on several occasions sharing the story with my students during our excursions to the museum.

My husband and I are currently trying to introduce our children to the movies we loved growing up. This has been a very 'hit and miss' process! Some movies have stood the test of time... others have not!

'Phar Lap' was actually a big winner. Everyone, from my 5-year-old up to my 15-year-old thoroughly enjoyed the story. My 5 and 8 year olds were a little confused as to why the story started with Phar Lap dying, when chronologically that should be the end of the story- but once we got over the 'I thought he died, how is he alive again?' questions, it was smooth sailing!

While we were watching 'Phar Lap', there was a scene where his trainer, Mr Telford, was having money troubles. Unfortunately, Mr Telford miscalculated his debts, reading the value of a digit as 6 hundreds instead of 6 thousands. As my 12 year old pointed out 'Mum, even Mr Telford needs help with place value'!

Of course, this got me thinking a little more about place value.

Place value is a term we use over and over with parents, students and fellow teachers, yet what are the words ‘place’ and ‘value’ referring to?

If I asked you ‘what is place value?' What would you say? Possibly you would say ‘it's our number system- for example hundreds, tens and ones’ and while this is true, place value is not easy to define in a way that does justice to the immense complexity of the construct.

It is worth considering ‘place’ as both a noun and verb. If we think about the noun- it refers the location of an object. The object we are referring to in the context of our number system is a digit.

This brings us to the verb ‘place’. This means to ‘put’ and object in a particular position. In our number system we ‘put’ the digits in particular columns.

Both the noun and verb make reference to an object (the digit) being put in specific locations.

The next critical part is the word ‘value’. Value means estimating the worth of an object. The important thing about our number system is that the value of the digits change according to their place.

So, when we combine place with value, we are referring to the idea that the value of a digit (what it is worth), changes according to where it is located. 

This can be explained by the positional property, whereby the value of each digit is indicated by its relative position in the numeral. In the numeral 356, the position of the digit ‘3’ indicates a count of hundreds, ‘5’ a count of tens and ‘6’ a count of ones.

This is an idea that is unique to place value... if we see a chair, and its position changes, it remains a chair, but if a digit changes position in a numeral its value changes! Complex ideas for novice learners!!

It is then the multiplicative property that allows us to calculate the value of each digit. For example, in 356 the face value of ‘3’ is multiplied by its positional value, which is hundreds, meaning its value is ‘three hundreds’ or ‘300’.

Abstract, complex and multiplicative- place value is not for the faint-hearted!

This week I encourage you to think about the vocabulary we use in our maths classroom. Consider the importance of taking time to unpack seemingly 'familiar' words and ideas with our students (I would also encourage you to watch Phar Lap if you haven't already!)

Have a great week!

Ange🎲🎓

P.S. You can download the PDF version of this blog to print or share with colleagues here.