Dice patterns B

And what do you think we might look at next? Five? Yes, you're right. We are using a growing pattern, so each dice pattern that we look at increases by one each time. That means we're adding one each time.

OK, let's explore five. How many dots can you see here? Five. So we can see five of something when we see one hand or one glove, I can see five fingers on the gloves look - 1, 2, 3, 4, 5, fingers in total. And this is the dice pattern for five. It represents five, and this is how we can represent five using symbols and using words so the dice pattern for five doesn't always have to look exactly like this look. I still have five, even when there's no outline of my dice or when it's orientated differently or even if some of the dots are a bit wonky, it doesn't matter either if the dots are different colours or even if I made the dice pattern for five out of apples. Every time I see things arranged like this, I know it's a collection of five things. It's a mathematical pattern that represents five. I have five things look - 1, 2, 3, 4, 5 or 1, 2, 3, 4, 5 or you might have also spotted this... Smaller dice inside bigger numbers of dice. Look here is four and one more makes... five. You might have seen it like this too, look, if we look really carefully, here's two that I can imagine turning around,and three more,it's five! It still represents five.

Now, as mathematicians, it's really important that we can draw mathematical ideas. So watch the screen. Watch carefully now. Yes, it's five. Take a picture in your brain. Now let's visualise. So can you draw the dice pattern for five in the air for me please? Off you go. Excellent! How many dots did you draw? Five! OK, now let's draw the dice pattern for five on a piece of paper with your pencil, off you go. I can see some of you are starting to think about the little dice or the little quantities, the little numbers inside the bigger numbers, so as you're drawing five, you started with four and then you're adding one more and some of you started with two and now you're doing the dice pattern for three because you know inside of five there's two and three. And some of you, yes, are not drawing dots, you're drawing squares or triangles, I see. And rainbows! They're nice things to include. OK, have a look at your picture and describe it to me. Does it look similar to these ones from Willow and Meila? Excellent, OK, now mathematicians, let's look at how we write the number five. Remember that as a mathematician you can represent ideas in lots of different ways, so we need to be able to know about all of them. Watch the screen. OK, now use your imagination and your pointy finger and draw the number for five in the air. Great, write it next to the dice pattern you just drew. Write the number 5. Have a look at it and read it to me. Does it look like the symbol for five? Yes, and here's what the word looks like, five.

OK. Should we have a look at another dice pattern? What do you think it might be that we look at next? Yes, six, because one more than five is six. That's the same as saying the number after five is six, 'cause we're using this pattern where we add one each time. OK, let's explore six. Here it is. How many dots can you see here? Six. So we might see six of something when we're out investigating nature, we might be in our gardens, at a park or even at school. Here I saw a beautiful butterfly with six white spots for each wing there were three white spots. Look 1, 2, 3 on the left and 1, 2, 3 on the right, that's six spots in total. And this is what the dice pattern for six looks like. Here's how we can represent that in symbols. And here's how we can represent it in words.

And you might have noticed that too, little mathematicians, that inside of six you can see the dice pattern for four in the four corners and the dark blue dots, see that? And then two more. That still shows us... six! There it is. So the dice pattern doesn't always have to look exactly like this, so look, even when their collection of dots are a bit wonky, or they're small, and they don't need the boundary outside the die, or even when they're turned sideways, the dots can be different coloured. Yes! Like we saw in the traffic lights with three and this time we see 2 threes which is six, and you don't actually need dots at all, you could get out some sport equipment and make the dice pattern for six using things like soccer balls and basketballs. Because every time I see things arranged like this, I know it's a collection of six things. It's a mathematical pattern that represents six. Look! Three and three more, is still six, or four and two, I have six things.

OK, as we know drawing mathematical ideas and representations helps our brain to remember them. So watch the screen. OK, watch carefully now. And. Ah ha. OK, take a picture of that in your mind. And now let's imagine. Use your pointy finger and draw a dice pattern for six in the air for me, off you go. How many things did you draw? Six, great! Now let's draw the dice pattern for six on a piece of paper with your pencil, off you go. Yes, this one might take a while 'cause there's so many things in our collection. I can wait for you though, it's OK. Oh, I can see some of you are starting to think about using different colours too. Yes. That's right, because it's not about what it looks like so much as what it represents, the quantity that it represents. And so there's some things that we can play around with. But you still have to be able to see the structure of the six. That's right. OK, let's have a look at your drawing. Can you describe it to me? OK. Did your picture looks similar to these ones? Great. Let's look at the symbol for six. Ready? OK, now imagine the symbol for six and using your pointy finger, draw the number six in the air, off you go. Great, now let's write the number 6 next to the dice pattern you drew. OK, have a look at what you wrote and read it to me please. Let's see, yes, that's the symbol for six, and here is what the word 'six' looks like.

OK, it's almost time to play a game, but before we do, let's talk really clearly about some of the important mathematics that we just discovered. So we realised when we look at all of those collections of two, that it doesn't matter what colour, orientation, or even what shape or size the dots are, the most important information was how many things there are, the quantity. And so, for example, we can look look at all the different ways we can still see two. We also realise that inside some of the bigger dice numbers, the bigger dice patterns, we can see some of the smaller dice patterns. So look, we noticed that three is two... and one more. And that four is two and two. We also saw that with five, we can imagine three on the dice and two on the dice, and that would show us five and that with five, we could also imagine four on the dice and one more in the middle,and we can also see four inside of six. They're some really important mathematical discoveries.

And now, let's play. OK, it's time to get ready to play, so the first we need to do is cut up our cards. And when we've done that, we shuffle them around. And turn them over. And set up an array. So we're going to have four rows. With six cards in each row. So 1, 2, 3, 4, rows. That's right, now I have four rows, one row, the second row, third row, and a fourth row, and there's six in each row. Look 2, 4, 6. OK. So then you just take turns. If you're playing with someone else, or you can play by yourself to look for a pair that epresent the same quantity, so I might turn over this one and that says, 'one' and this one, said....that's not a pair. They don't match. That six, and that's one. OK, your turn. Did you get one? Not yet, I'm going to try again. I'm gonna try four and... that was one again, wasn't it? So I need to make sure I remember which cards I've turned over. Your turn. OK, my go. That's the number one, and I think one was here, yes, and now I have a pair, so I can take those two and put them here. And then we keep playing until we've found as many pairs as possible. Over to you mathematicians! Have fun!