If you haven’t already read my rant Stop teaching simile! then I’d suggest starting with that first. However, having started something, now things keep cropping up that I think the same sort of thing about, so here’s an addition to what seems to be turning into a series of “Stop teaching….” posts.
Stop teaching thousands
This will seem silly at first. Of course we need to teach thousands. But I’m coming to the conclusion that we tackle it in the wrong way in some ways. We expect children to work with increasingly large numbers as they go through primary education, and so once they seem to have grasped hundreds, it seems to make sense to move them onto thousands. Except, there’s a difference in the way the numbers work here, and it’s not always obvious when we teach it in that way.
The problem is not so much the thousands, and the next ‘column’ in our place value system. We often call it the ‘ten-thousands’ column, but like with the ‘tens’ column, we don’t often use that language for numbers that include a digit in that place.
Consider the number 54,321.
We don’t treat the 5 as a digit in its own right here; rather it becomes the tens digit of the section of the number that we describe as 54 thousand. It works just like the tens digit.
The same is true as we move over one more column. Consider 654,321
Here the 6 is merely part of the 654 thousands that are needed. It’s why we use commas after every third digit starting from the right. It’s not just a handy number, it actually helps us to read them.
So when we teach thousands, we should teach them as a block. It makes dealing with larger numbers much simpler. Recognising that each section of up to 3 digits is read as a single ‘chunk’ of a number makes it easier to read large numbers, and to avoid the common errors with placeholder zeroes. When a child needs to write four hundred and six thousand, and seventy four, it’s much easier to think of the blocks of 406 in the thousands block, and then 74 in the units section. It even invites the ‘punctuation’ of the number:
(I grant you that the last section is lacking a name. I’m tending to prefer to call the very right-hand column “ones” and then refer to the last three digits as units, but there may be a better term. Suggestions welcome!)
The wondrous thing about so much of maths is that patterns are often scalable. The same system now allows us to consider millions, billions (so long as you’ve come to terms with the US billion) and to extend the system in groups of three, rather than one place at a time. Children are then very quickly able to read
as 123 million, 456 thousand, 789.
It also allows them to see the structure of the system so that they can identify any point in the place value structure. So, in the case above the digit 5 is clearly in the tens position within the thousands block: it shows us how many tens of thousands there are.
So, in truth, the argument is not for teachers to stop teaching thousands, but rather to consider thousands as a block of three digits in the numbering system following the HTO pattern.
Perhaps most importantly, before even thinking about numbers larger than 999, we should ensure that children have a secure understanding the relationships between the first three digits and their positions, fully grasping the nature of powers of 10. Once that is secure, rather than simply extending to thousands, it should be easier to teach the whole thousands block, right up to 999,999 with ease – and then to further extend.
Since posting this, Alex Weatherall has raised some perfectly reasonable points about the use of this structure. As with so many things, there is a risk that it becomes a prop which fails to secure clear understanding. So let me stress, I’m not proposing that we extend place value grids in this way. I present the image merely to make the point. My personal view is that if a child still needs a place value chart to organise numbers, then they shouldn’t be dealing with anything greater than a three-digit number.