How We Organise Ourselves

We have started a new inquiry in the transdisciplinary theme of "How We Organise Ourselves". I find this theme really interesting in terms of mathematical thinking so I got a bit of a provocation going for the class.

I got a bucket load of what we call "paddle pop sticks" - probably have a different name in your town - do Queenslanders really call them by-jingo sticks?

The task was to find out how many sticks there were. The task itself was pretty meaningless - my prime interest was in how the kids would approach the challenge. What evidence would they show of mathematical thinking? How would they organise themselves?

Well, first off they fragmented into friendship groups and started grabbing for as many sticks as they could get - they are 7 years old after all. 

Anyway, they split up and started to count the sticks. They showed several different methods of getting organised. Here is what it looked like:

One group started counting the sticks and making a pile of the ones they had counted.

They were a bit stunned when I asked how they were going to check for accuracy.

It's a bit easier to see if they are spread out a bit.

But you have to do a lot of counting.

And turn a corner when you hit the wall.

Another group thought of lining up the sticks - in groups of 6...

…or groups of 14 - beautifully colour-coordinated.

Other groups had the idea of making bundles of 10.

 Some appeared more organised than others.

I had to drag them back to the original question…so, how many sticks are there?

Each group wrote up their individual totals

 - but it took insight to decide that they needed to add them all together.

An answer! We got 2637 sticks!

And then I threw them a wobbly - can you check that?

What? they exclaimed.

But, I continued, did you get any ideas from the other groups about good ways to organise yourselves?

Groups of 10 was the consensus - but I was still a bit worried about the way they were laid out on the floor. When we hit the wall we had a problem... 

...some chose to go around the corner and others decided to start new rows.

Finally we got the idea that maybe we can organise these sticks into:
a) bundles of 10
b) rows of 100
c) blocks of 1000

And that made it pretty easy to see 2 groups of 1000, 3 rows of 100, 2 bundles of 10 and 2 left over = 2322 sticks.

And you can see it just by looking.

What a good idea.

Place Value with Big Numbers

A Peter Sullivan Puzzle

We had a visit a few years ago from Peter Sullivan, former president of AAMT and a really inspirational mathematician. He showed us a puzzle that was like a 100 square cut into pieces like a jigsaw but the numbers were from 100 to 8000, counting up by 100s.

We were using them today as a bit of a fun challenge.

Here's what the finished puzzle looks like:

...and here's what it looks like when the kids start with it:

Bits everywhere and lots of disorganisation.

I had cut the pieces out differently for each puzzle - so looking at what your friend was doing was of little help.

I was really interested to see how the kids went about getting the puzzle back together again.

Here's a few examples:

 This one started at the right because that was where he found his 

first pieces that joined together.

 This one started at the top - same reason. It was where the first

pieces fitted together.

And this one is almost finished but it's not particularly straight and...

hey! I think a piece is missing!

 Oops! There it is on the floor!

Interestingly, none of the students went looking for the first square or the lowest number. They were able to complete the puzzle by just finding a few bits that went together and could work out the rest by going forwards, backwards, up and down from there.

So do I really need to get kids to solve puzzles and patterns by starting at the start? Why can't they start in the middle? Or at the end? Or...?

Time for me to reflect on some of my assumptions.

 

Me reflecting:

  

I wanted to use this pic - I saw it in a presentation this week. It's one of

those ones that pop up on Google searches.

Check out the cogs  - is it really going to work if they spin 

in the direction of the arrows???