Tens and ones

My son has got the hang of counting to 100 and beyond, but I've realised that he still gets confused about the difference between, say, 7+5 and 75 on occasion.  I've never really tried to explain about the way tens and units work and I found a use for a cardboard box which was heading for the recycling to try and show him the basics of place value.

Learning to use the 'counting machine'

I called it a 'counting machine' so he'd be interested, but it's not really a machine, in fact he had to do all the work to operate it!  The idea is that it has slots for units and then groups of ten slots for tens, and if you insert lolly sticks (popsicle sticks if you're in the US) into the slots one at a time.  I cut the slots with a Stanley knife - if you adjust the blade length right then you can just press it into the card repeatedly to make the slots, it only took me about 5 minutes to make the whole thing.  To count, you fill the slots in ascending order, i.e. from 1-9, on the units until it's full you count up to 9.  When you have too many, you take the tenth one, put it in the first set of tens slots and add all the other 9 from the units side so you have one ten.

I set it up with tens on the left, and units on the right.  I also added zero, without a slot, to the units side.  The idea is then that you can read the number you've counted by looking at where the slots are full.  For example, for 11, you'd have the slots next to the number 1 on the tens side full, and a single slot next to 1 on the units side full, so this is 10+1=11.  For 25, you'd have the slots next to the numbers 1 and 2 full on the tens side, and the slots next to 1, 2, 3, 4 and 5 full on the units.  Taking the highest number on both sides (the last one you filled the slots for), gives 2 and 5, or 2 tens plus 5 units.

Filling up the ones

I explained to my son how it worked, and after some initial scepticism, he quite liked it.  He's a fan of doing things in labour-intensive ways, so he enjoyed sticking the lolly sticks in the slots and moving them across!  We talked about the tens and ones, and how we wrote the numbers with them in and it seemed to be making sense to him.

Once he'd got the hang of it, I gave him a heap of lolly sticks and asked him to use his new machine to count them.  I was a bit worried that I'd given him too many, but he kept going with little encouragement and found that there were 57!

There were 57 lolly sticks!

It was a very simple concept and quick to make, but hopefully it helped him to understand a bit more about how tens and ones work and why place value is important when he's reading and using numbers.  There's also a quicker way to use it in future if he gets frustrated with pulling the sticks in and out as he could just fill the tens slots until he had fewer than ten sticks left and then put the remaining ones in the units - I won't suggest this until he seems bored of the current method though!