Wednesday, 17 June 2015

Nets of 3D Objects

I don't think my kids have done much with nets before. It's important to be able to represent 3D objects in this way.

I was keen to see what they could do so we got out some equipment to have a play.

Here are a few of the 3D objects we looked at and some of the drawings the kids did:

Cube

Suggestion #1 - like a rectangle with a square off the side.

Suggestion #2 - Like a cross

Suggestion #3 - lots of square bits

Suggestion #4 - A cross made up of 6 smaller squares

So we had the general idea that the net of a cube is made up of lots of squares - just not too sure about the details.

Tetrahedron

Suggestion #1 - it's a triangle with some stripes

Suggestion #2 - it's got more than 1 triangle

Suggestion #3 - think I've seen one before with a square and triangles coming off it

So we don't really have a very good idea about this one. Lots of opportunity to learn here.

Cylinder

Suggestion #1 - it's got 2 circle shapes on top of each other

Suggestion #2 - It's definitely got 2 circles somewhere

Suggestion #3 - It's got circles AND rectangles

Suggestion #4 - yep, I've seen this one before

As teachers, we learn so much from the "fails" of our students. The "correct" responses are fine but they don't in themselves give us much insight into the mathematical thinking of the students.

BUT the errors, the mistakes, the ones that aren't quite right - they are the ones that tell us so much about what our kids are thinking and how they "see" mathematics.

Monday, 15 June 2015

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.