Wednesday, 12 September 2018

Adding 5

I was interested in exploring how we might represent the addition operation as a pattern. We had been playing with the addition algorithm and looking at adding numbers up to 4 digits.

So I took it way back and asked how we might make a pattern to represent adding 5.

And here is what happened:

I was underwhelmed. Surely we could come up with more than simple lines getting bigger by 5 each time. And was it a coincidence that just about every student had represented adding 5 in exactly the same way?

So, I drew a long breath and asked our favourite question:

"Can you do it a different way?"

And thankfully the answer was a resounding, "Yes!"

Here is what our next attempts looked like:

Several representations looked at groups of 5 being stacked up on top of each other. An interesting idea - take it into another dimension - but similar to the idea of parallel lines.

Two different students looked at representing the idea of adding 5 as an array. 

Then we had 2 who make a circular pattern. 

And also a radial pattern.

Then we had a few interesting ideas. Here, the student has decided to start at 3 (the central group of light blue lids) and then adding groups of 5 at each end. Her pattern went 3, 8, 13, 18...

This was a rather unusual idea. I can see the 5 blue lids. I can see several rows that have 5 yellow lids. But I could also see lots with 6 as well. What was going on?

"Well, you can start at any lid, and then count 5 in any direction. And then keep going."

Well, that certainly took it to places I wasn't expecting.

And then we had this one:

So, this student decided to reinvent numbers, place value, the counting system - everything.

Each group of lids represents a number in the counting by 5s pattern (5, 10, 15, 20, 25 etc) but the number of lids is not relevant. Each group has a unique arrangement, demonstrating an understanding that all numbers are unique and represent unique values. 

So much more interesting than a series of parallel lines.

Like it. Well done, Year 2.

Saturday, 8 September 2018

AMSI 2018 Excellence in Teaching Award

I was honoured yesterday by the Australian Mathematical Sciences Institute (AMSI) along with 9 other outstanding Australian teachers and received an "Excellence in Teaching" award. 

Image may contain: one or more people

This is me with BHP Principal, Inclusion and Diversity Fiona Vines.

The Canberra Times, our local newspaper, did a very sympathetic write up about me, though I'm not sure about the "rockstar" bit:

I would like to thank everyone who has supported me in my mathematical journey, starting with my inspirational and extremely patient wife, my family, my colleagues, you - the readers of this blog - and ultimately my students who challenge me to think clearly and to be creative every day.



Tuesday, 21 August 2018

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.

Thursday, 16 August 2018

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.

Friday, 27 July 2018

Knoks, Moks and Snocks

We have been looking at measurement of length this week.

Today when they came into the room, the kids were faced with this challenge:

"Overnight, there was an international disaster - all millimetres, centimetres and metres had disappeared. No-one could remember how long the units were. We had to make some new units of measurement. What would we do?"

After a few suggestions, like, "Let's use feet and inches." I encouraged the students to use their creativity to make a new system.

We were using our interlocking cubes to make patterns so it was natural that these blocks became out units.

I wasn't happy to have this unit be called a "block" so the kids decided to call it a "knok". 

Next step was to decide on the other units. Here is what they came up with:

It looked like this:

2 peas = 1 knok

8 knoks = 1 mok

6 moks = 1 snock

And once we had a measurement system, we needed to measure something.

"What shall we measure?" I asked.

"YOU!" was the emphatic reply.

So I became the first of many to be measured with our new measurement system.

Turns out I am 2 snocks, a mok, 3 knoks and 2 peas tall. (Astute students of place value will notice that the 2 peas should be converted to another knok to make 4 knoks.)

I don't think it will ever become an internationally recognised system of measurement, but it gave us an opportunity to explore the idea of standard units and how to convert between units of different sizes.

Monday, 12 February 2018

Is a picture a pattern?

So we are back into the swing of things here in Canberra, Australia. 

And I wanted to push on with the spatial reasoning and pattern making. Once again, it was going to be pattern making first up each morning.

Day 1 of making patterns and my new class surprised me. I put out a variety of materials - pattern blocks, Cuisenaire rods and tangram shapes - to see what they would produce.

And I could not believe how many of them produced pictures - symmetrical undoubtedly - but pictures just the same. So were they making patterns? Is a symmetrical picture a pattern? 

Rocket ships:

Monsters and funny faces:

Puppy dog:

So - nice pictures. Were they patterns? 

I'll leave that one with you.