Thursday, 26 June 2014

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???

Monday, 16 June 2014

Maths and Inquiry

Maths as Inquiry and Maths in Inquiry

I was fortunate to spend 2 days at a workshop last week with a personal hero of mine - Kath Murdoch, inquiry guru and inspiration to a generation of teachers and students.

Check out Kath's website or follow her on Twitter @kjinquiry

Anyway, the question came up - okay, I brought it up - about inquiry and Mathematics. It's something I've been playing with for a while now and wanted to get some perspective on. All the work I've been doing in my classroom and the writing I've been doing on this blog about inquiry - how does it all fit together?

Is "Inquiry Maths" all about using inquiry in maths OR about using maths in inquiry?

That was my big question. I am so glad I had the chance to put it to Kath.

And like a great inquiry teacher, she put it back to me. What did I think?

And then a revelation hit me.

It's both.

Seems obvious now...

...but then so does gravity and that thing where you get in the bath and all the water overflows out the top. But to Newton and Archimedes, it was a life changing moment. And me too.

Inquiry in Maths

So - we can use the inquiry cycle to explore into the discipline of Mathematics. It helps us to find links and patterns in what we already know so that we can find out about what we do not yet understand.

Maths in Inquiry

And we can use mathematical skills and knowledge to further our inquiries into transdisciplinary themes. Mathematics is a tool that we can use across all learning - not just within the maths lesson but further afield in literacy, art, PE, science...

So what?

It may not be that big a deal to you, but it was a real "a-ha" moment for me. 

Inquiry in maths AND maths in inquiry.

Thanks Kath.

Another "A-ha" moment for all those who remember the 80s...

Wednesday, 4 June 2014

Year 2 Rock the Clock

I went down to visit Year 2, to catch up with all my friends down there and to see what they were doing.

Capitano Amazing, aka Mr Black, had them making their own clocks. They were pretty good at it - here is one clock face that has been divided into 60 equal parts. Great job!

The next challenge was to make some hands so we asked the kidlets, what two shapes could you use to make a clock hand?

You guessed it - a triangle and a rectangle. Wonder if there are any other combinations?

Then we all had to make a big one and a little one...

Nice going!

Oops! Too big!

Well, after we'd made the clocks and had a play with them, I wanted to explore a few number ideas that are related to time.

I put up the 100 chart on the Smartboard and started counting in 10s. What's the pattern? How do we know?

Then we counted in 5s. Same questions. What does it look like on the chart?

Then we did counting by 6. We've had a few parents getting anxious about kids needing to know their tables facts so I was interested to see how these Year 2 champs would come with counting by 6.

They smashed it.

Then we started to look at the patterns that were made.

"Well," said one legend, "If you look at the diagonal pattern on the right, the numbers are going up by 12. If you look at the diagonal pattern on the left, they are going up by 18."

Nice. And this is Year 2.

Next followed a conversation about multiples of 6, the number of minutes in an hour, the number of seconds in an hour, etc. Very enlightening.

Time for the final challenge

"Okay," I said, "You know that there are 60 minutes in an hour. What would an hour look like if one minute looked like this:

or this.....

or this....


"Show me what an hour would look like."

And this is why I love teaching...

Because the kids come up with some crazy ideas that I had never anticipated.

There we go - 60 minutes!

Not convinced? Let me show you...

Ta da! 10 rows of 6 = 60

Or try this...

Don't believe this is 60 minutes?

How about this then? 12 x 5 = 60

And how long is an hour?

Ooh, about this long...

...or maybe this long.

Then we had the "Hour Tower"...

...and the "Block Clock"

What are you talking about???

And finally one bright little champion came up to me and said, "Here is an hour Mr Ferrington":

"What are you talking about? You've only got two blocks!" I exclaimed.

"Well, each block is 30 minutes," he replied patiently.

Come on teacher - keep up!

The End

So we got to the end of the afternoon and I congratulated the kids on doing a great job and working on maths for an hour and half.

"No - it was only and hour and quarter," said one.

"I think it was about an hour an 17 minutes," said another...