Saturday, 28 January 2012

Counting to 100 and understanding place value

Most children get the hang of counting to ten without too much trouble. It's usually learned through a mixture of nursery rhymes, games, playing with objects and lots of practice!  Many parents do a great job in getting their children to this point before they start attending nursery school.

However, getting to grips with what happens beyond ten is another matter, and full of pitfalls.  Those with good memories can do well when taught by rote, but what about the children who don't learn well using this method? Some children aren't prepared to learn this way, and are looking for a purpose or an understanding before committing valuable memory space.  How often do children who don't join in counting by rote sessions get labelled as 'a bit dim', or 'slow at maths'?

The vast majority of them are perfectly capable of memorising other things, such as how to get through the levels on their favourite iPod touch game, or the words to a catchy pop song.  Even those who learn the number order successfully by rote can be left with misconceptions, or without any real understanding of how our number system works.

During the year I spent as an Every Child Counts maths specialist I gained a good understanding of how to help children learn, or even better discover, the number system.  These ideas worked very well with Year 2 children who had fallen behind, and are working very well with my current Nursery class...

I like to bring place value into consideration as early as possible.  The first step here is to know that the units form a repeating, or circular, pattern...

Arranging Numicon in this circular pattern and pointing to each piece in turn when practicing counting, sets-up the starting point for place value nicely.

Children might tell you that it's a counting circle, or even ask why it goes from 10 back to 1?  These are signs that they are ready to progress.

There's no harm in progressing to the next stage now anyway, even if they are not secure in remembering all of the number labels 1-10.







You simply pick up another 10 and use it to point to the Numicon as you go round the circle again, saying the numbers as you go...eleven, twelve, thirteen...

Eleven...or should it be tenty one?
The children will get the hang of the pattern way before they can remember the number names, and that can lead to good things a little later on!
















However, saying the numbers beyond ten brings us to a major 'road block' in understanding how the number system works...

The number labels between 10 and 20 are simply stupid (in my humble opinion).  Whoever came up with them is responsible for holding back the maths learning progression of pretty much everyone who speaks English, and for confusing some for life...either that or I've missed something!?

If only it was tenty one, tenty two, tenty three, tenty four etc....

It's even worse than that though...when listening and speaking, the teen numbers are easily confused with the tens...

Thirteen can sound very similar to thirty, and seventeen very similar to seventy etc.

Try listening very carefully to children counting in this range...are they really saying all the teen numbers correctly?  Teen/ten confusion is very common, and often remains undiagnosed.

Eighteen...or should it be tenty eight?
Hang on though, did he say eighty?
I'm quite happy to gloss over the number names for 11-19 at this stage in favour of establishing the number pattern beyond...

Pick up another 10 and we're off round the circle again...

Twenty one, twenty two, twenty three...

Most children will be joining in with you by now.  You've just taught them twenty, and they can see what's happening with the units.

There's no need to explain what you're doing.  You've created an excellent model of the number system for them, and it's easy to follow and join in.

Pick up another ten, and before you know it you've led them all the way to 99!




It's a bold statement to make, but the children will have gained a solid grounding in place value before they can count securely to 20, or even 10 in some cases!

At this point it's really useful to start counting in tens.  Ever noticed a child struggling at a tens boundary?

37, 38, 39, err....

They understand the repeating units pattern, but need to learn that 40 comes after 39, and 50 after 49 etc.  It can seem really odd focusing on counting in tens when you've only just introduced the idea of 11, but once a child has that grounding in place value it really does help.  The children can see the point in learning the tens when you use the circular model, and of course you're leading them towards 100 and beyond!

It's still going to take lots of practice before all the children are secure, but this method pays dividends beyond.  Remember to practice with and without Numicon, as some children can become reliant on seeing the circular model when counting (a Numdrum is another excellent resource to use).

Oh yes, and now you can go back and help them learn 11-19 by rote...they'll probably tell you that the number names are stupid though!  To help iron out any teen/ty confusion you can put pictures of tea cups (as in tea/ty) next to the tens on a number line, and pictures of teenagers next to the teen numbers.

Finally, next time you hear someone from Key Stage 2 in the staffroom complaining that their children 'just don't get place value'...

I'd like you to remember tenty one, tenty two, tenty three...

Click here for a video demonstration of the counting wheel.

The Edgazette
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