Exploring patterns 2

Welcome back little mathematicians and you can see, and I can see here, or in fact, is it a pattern? Because we know we've discovered a few things about patterns. One is that it has a repeating core and this is the part that repeats over and over and over again and last time we were together we were playing around with how we could work out what our repeating core is and we discovered that you can see the part that repeats over and over and over again, the repeating core, by moving objects around to check your thinking, so I already can see or hear that you're thinking about what is the

repeating core of this pattern? I can hear lots of you think that you have found it.

Yeah, that's really good thinking, little mathematicians. It's a circle and a triangle. That's the core, and it repeats over and over and over and last time we investigated that you can move things down like this and we can use this movement or imagining this movement in our brains to check that our core, that we found the core of our pattern and that we can then move things back and that this strategy of moving the objects around, either by physically moving them or imagining that they're moving in our brains also helps us work out things like... what part or element of my pattern is now missing? Because if we move these things down... That's right, we can see that the circle or a circle belongs here in order for us to have a pattern that has a core that repeats over and over and over.

And so what we were thinking about today is talking about how we can describe these patterns and then make them in different ways. Because this pattern has a circle and a triangle, that's the repeating core and I can move this down like this to prove that that's the part of my pattern that is repeating. But what if I didn't have a circle? What if I had wanted to replace them with squares? So if I move my circles away, I could now put squares here. And even though my pattern now looks a bit different, actually the core is pretty similar because it still has two things in it, and so we could call this a 'two' pattern and some people do, but sometimes it gets really confusing in our brains around do we mean the number 2? Or are we describing a pattern, and so mathematicians would call a pattern that has two parts inside its repeating core an AB pattern. This is A and this is B and so it doesn't matter in my AB pattern whether my A represents a square like it does here, or like I had before, if my A represents a circle, and so when I call this an AB pattern, what it allows me to do is think about what are some other AB patterns that I could think about making and patterns that have a similar repeating core?

So sometimes we do this thing at school where we can do things with our bodies like we can say the circle represents a click and the triangle represents a clap. So we can say Click, Clap. Click, Clap (click, clap, click, clap). That's right, and it's still a repeating pattern because, yeah, it's got two parts, the click and the clap, two different ways of making sound and it repeats over and over and over. Can you come up with another way using body sounds? Ah, I heard someone doing a 'click' with their tongue and a 'stomp' on the floor - so a (Click), Stomp. (Click), Stomp. (Click), Stomp. (Click), Stomp. Yeah, and that's an AB pattern too 'cause there's two parts, that repeat over and over and over. Well, I wonder if you could go around your house or pick up your book now and what's another way that you could make an AB pattern? So we made one here using circles and triangles and we also then said, 'Well, we don't have to have circles, we could have squares and triangles' and it's still an AB pattern. We also said that you could do a click and a clap (click, clap, click, clap, click, clap). And one of you suggested that you could do a click with your tongue and a stomp (click, stomp, click, stomp, click, stomp).

Over to you to go see what you can do and make some other AB patterns and draw them down on your notebook and I'm going to go do the same and we'll come back together. Over to you, little mathematicians!