Staircase pattern

Hello there mathematicians. How are you today? That's really good to hear. So, I have some blocks here and I'm beginning to make a pattern.

Yeah, and I'm wondering if you can figure out what the next term or the next thing would be in my pattern if I continued it? Ah ha, so remember, a pattern is something that has a repeating core. So we're looking for what is the thing that's repeating over and over and over again. Yeah, and it's a bit different 'cause we've been working a lot on patterns like A,B, A,B. You know, like clap, click, clap, click, clap, click. But this is a different kind of pattern.

Ah, you think you can see something? Uh, huh. I think, I think I can see what you're seeing too. That there's one brown cube, two black cubes, three red cubes. So the colour is changing each time, so there's nothing there that's repeating. But it goes from one to two three and it's, yeah, there's one more block each time. Let's use our chunking strategy to see if that works. If I line them up. Does it increase by one more block each time? Ah, so what would be the next one? It would be three and one more. Four. Ok, I can get four together. And what would be the next term in my pattern?

Four and one more. Five. The number after four is five. Ah ha, look at that. So that's what it would look like if we put it all back together and we could keep building it out as a big tower of pattern. Oh, it reminds you of something else. It also. Yes, I agree with you. It reminds me too. If I turn it like this, you might have recently seen an episode of number blocks called Step Squad. Yes, and it does look exactly like our number blocks characters, doesn't it?

Let's work with them 'cause they're cute. So when you see our number blocks characters in a step squad formation, what are some things that you notice about the shape that they have? Ah yeah, it's like a triangle.

Let me write this down. So. How many bricks? How many steps do I need to draw? One for red, another one for orange, another one for three, another one for four and one for five, and so it's like, oh, a triangle with squares in it. So it's like a triangle shape. What else do you notice about it?

Oh yeah, it's like this. It goes up by one each time. Um, each column increases by one. Look, it's one, then two, then three. Yes, so each column increases by one. So each time we go up a step, it gets one bigger. What else can you see? Oh look, you're right. one, two, three, four, five blocks wide and one, two, three, four, five blocks high. That's cool. So five blocks wide and five blocks high. Oh, yes, and I can come in and mark those for you, so I'm going to come in and go, there and half and quarter. So, one, two, three, four, five.

One, two, three, four, five, yeah, and you're right, because it's a mathematical drawing, I don't have to draw all of the individual blocks. I can just draw the most important information. Yeah, and, and so, what our pattern is, our pattern core. How would we describe that? Yeah, the pattern core goes up by one each time. So our core is that each step up the staircase adds one more block. That's really cool mathematicians.

So now I was wondering something actually, and I was wondering what would happen if we make it so we go up by one each time, but when we get to five, what would it look like if we went down the other side? Ah. Yes, so if we had one less than five, how many would we have? How many blocks? Four because one less than five is four. There we go, look. Yes, 'cause If we had five and we take one away, that's one less than five.

And what would come next in our pattern? Ah, yes, three, because one less than four is three. Uh-huh. Ok mathematicians, over to you to finish what the rest of our staircase would look like if it goes up and down the other side. And can you draw a picture of this to to record your thinking? Over to you.

So over to you mathematicians. Draw the staircase pattern we've made, continuing it down the other side. And then we'll come back together. OK over to you.

Welcome back mathematicians, how did you go? Mm-hmm, did your pattern look a little bit like mine? Yeah, so what are some things that you notice about it when we when we make it go up by ones and then down by ones? Oh, you're right! It still does have a triangular shape but this time it's a different triangle isn't it?

Last time that the triangle looks like this, and this time the triangles peak is in the middle at five. Mm-hmm. Yeah, and this time it goes up by ones, one, two, three, four, five times and then down by ones, one, two, three, four, five times. Mm-hmm.

Yeah, and you know this made me start thinking about something mathematicians, of what if we thought about this in a different way? Yeah, cuz what we're seeing here is, it grows and then it shrinks and we could continue our pattern actually by saying, now I have to make it grow again, like this. And then when I get to five, I need to make it shrink again. And so we have this really nice structure to our pattern. But when we're looking at this portion, I was wondering about this. When it, when we look at it this way it goes up and it goes down, it grows and it shrinks, but what if we thought about it in this way.

How many blocks do we have in this column now? We can check. Remember, we knew that if we looked here that it was five blocks wide, so if I turn it back around we know that this is five. Mm-hmm. So we can use that information, so five, six, seven, eight, nine. Do you want to count them all to check? Okay, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Now there's 9 here. And what about in our next column now? Ah yes, it will be, it would be 9 if there were blocks here but there's not blocks there. Look if we put these guys here that would still be 9 wouldn't it? But I need to take one away, so the number before 9 is 8, and then the number before 8 is 7. Mmm ,so that should have seven blocks. Would you like to count to check? Ok, 1, 2, 3, 4, 5, 6, 7. Mm-hmm, and what about, what do we know about this column here now? Aha, if these was here, it would also have 7, but we need to take one away, the number before 7 is 6, mm-hmm, and the number before 6 is 5. So that column has five.

Oh, and are you starting to see a pattern? Look, 9, 7, 5. 7 is 2 less than 9. 5 is 2 less than 7 and 3, whoops, is 2 less then 5. 3. Whoa! This is got so many cool patterns in it! And the last one has one. Wow! So mathematicians, my challenge for you is, can you work out how many blocks we have altogether now? Over to you to think about that!

Okay over to you mathematicians, how many blocks are they all together? Draw a picture to record the thinking needed to work out the solution. See you soon!