Let's have a look at place value with Year 4.
The Australian Curriculum says:
Recognise, represent and order numbers to at least tens of thousands (ACMNA072)
So we did.
I got some 1mm grid paper and we started off with one tiny square.
Then we cut out a row of 10.
Then we cut out a square of 100.
Then a row of 1000.
It started getting a bit technical here. It seemed like I had hit a developmental barrier - a place that required some additional cognitive effort. I was a bit surprised but we worked our way through.
Obviously (to me at least) 10 000 was going to be 10 rows of 1000. It didn't appear to be that obvious to the students. Why was there this hesitation? Perhaps this is why the Australian Curriculum identifies this as the target size to go for in Year 4. However, once we started counting by groups of 1000, we soon got the idea of what 10 000 looked like.
One of my ambitions with this task was to get a visual experience of what happens when we start multiplying by powers of 10. Also to get the connection with the decimal place value system we use - more of this later.
Once we had 10 000 sorted, it was a smaller step for mankind to decide what needed to be done to represent
100 000. It's 10 of the 10 000 squares.
At this point, a few students began to see a pattern forming in the way we were representing the numbers:
1 = square
10 = line
100 = square
1000 = line
10 000 = square
100 000 = line
1 000 000 = square...
Well, we haven't quite finished the 1 000 000 square but we are nearly there.
And the classroom is a bit of a mess - just the time when a member of the executive chooses to walk in...
This is the room after we did a bit of a tidy up.
So now we have models of 1, 10, 100, 1000 etc.
A valuable experience.
But the other connection I wanted to make was with the decimal place value system. Because with my models, I can now choose any of the samples to be the unit - it doesn't have to be the tiny little square = 1. It could be any of the other models we have made. The very biggest square, that we thought was 1 million when we made it, may in fact become 1 unit, or 1 thousand or 1 anything.
And if that is the case, then what is the value of the other numbers? And where does that decimal point need to go?
Time to start playing...