Nets of Cubes

We are exploring polyhedra in Year 2 this week. Yesterday we had a great time playing with shadows and looking at what could be made from a selection of different objects.

Today we wondered what a cube would look like if you "unfolded" it - laying out each face flat on the ground.

The kids, perceptive as ever, thought they knew how to do this. With little prompting, they headed off with paper and rulers to make some nets.

Once everyone had made a net, I asked them to bring them back to the group and share them. Every student had produced a net that looked like this:

Every student - except one. His net looked like this:

Time for some provocative teacher action. Was it possible that there would be more than one way to make the net of a cube? Is it really true? Are there more ways out there that we haven't found yet? Could we possibly explore and see what we might find?

The kids leapt into it. All except one student, who refused to believe there might be other ways. He was dogmatic - there could only be two ways - the two ways we had already found.

And then the other students started to produce new ways to unfold the cube. Here are a few examples:

It only took ten minutes and we already had about 8 different nets for the cube.

And in the process, we also discovered something else really interesting - there are some "nets" made up of 6 squares that wouldn't fold up into a cube. Here are a few of those:

Interesting learning for Year 2 students. Because by exploring the arrangements that wouldn't work, they were able to come up with some "rules" for their nets:

1. It has to have 6 squares

2. If it is based around a line of 4, you need one square off the the right of the line and another one of to the left.

Here is what the classroom floor looked like after 25 minutes of exploring:

We were not convinced that we had found all of them - in fact I knew that we hadn't.

So it was music to my ears when one girl asked, "Can we keep doing this at home tonight?"

Taking action. 

I wonder what we will see in the morning.

400 000

Data from the blog - cracked 400 000 views yesterday, thanks to some enthusiastic students at ACU Canberra looking at some of the work my kids had done - thanks people.

Looking forward to the next 400 000.

PS - Something happened about 18th March 2016. That's the big spike. Lots of traffic came from France - not sure why. 
A PYP event? Maths conference? Cyber hacker?

Kids - They Never Cease to Amaze

We were making patterns yesterday. I wanted the kids to make a staircase pattern using Cuisenaire rods. I do this each year with my kids - I just like to see how they will interpret "staircase" and how they will use the materials provided.

For some unknown reason, I seem to expect my present class to be "less" than my previous classes - less creative, less perceptive, less able. Maybe I glamourise my previous students and forget their falibilities, remembering only their moments of glory.

Recycling old tasks gives me the opportunity to be surprised - even though I have expectations of what the new students will do, they never cease to amaze me with their own, individual responses.

So when we sat down to make a staircase pattern, I thought it was not going to be as good as last year. 

Here is what we did in 2017:

Click here

And here is what my current class came up with. Just as creative. Just as intuitive. Just as good.

Kids - they never cease to amaze.