Dice patterns A

Hello there mathematicians! Let's investigate dice patterns.

So today you need a pencil and some paper or a book and we'll need those straight away to get started and later we'll need this sheet of paper and some scissors so you can cut them up to make some cards. It's OK if you don't have a printer at home, you can copy them like I did it onto a piece of paper; you'll need to do that really carefully. OK, let's start investigating dice patterns. You may already know some dice patterns and you might already know a lot of things about them. They are really important patterns that we see a lot as we work and learn like mathematicians. So it's really important to us that we can recognise them, trust them, draw them, but also make meaning from them and use them to help us solve problems.

OK, let's get started. So how many dots can you see here? One, that's right, say it with me. One. I can see one dot. We might see one of something when we look up into the sky. For example, I can see one warm yellow sun. When we see this dice pattern, we know it represents one. We can record how many dots we see using symbols. And using words. OK, so this is the dice pattern for one and it's still one, even if it's really small or orientated a little bit differently and in a different colour. It's still one if it's big, it's actually still one, even if I replace the one dot with a unicorn and it's still one, even if that one thing is slightly off centre. So this is something now that I can trust. So what we know as a mathematician, is that drawing representations helps our brain to remember them, so watch the screen.

OK, now let's use your mathematical imaginations, and draw the dice pattern for one in the air. Use your pointy finger.

Great, how many dots did you draw? That's right one. Now let's draw the dice pattern for one on a piece of paper with your pencil ready, draw one. Oh yes, I can see. So have a look at it and describe how many dots you have. Does it look a little bit like this from Willow and Meila? Does your picture look similar? Great! Now, as mathematicians, we know that we can represent ideas in different ways, so we can use drawings. But we can also use symbols, so watch the screen to look at how to draw the symbol for one. OK, now using our imaginations, put your pointy finger up into the air and write the number one. Great, now write it on your piece of paper next to the dice pattern for one that you drew. Have a look at what you wrote and read it to me. Does your picture look similar to these? Yes, that's the symbol for one next to your drawing for one. And here is what the word one looks like.

OK, should we have a look at the next dice pattern? Yes, let's do it. How many dots can you say here? Two, I can see two dots. We might see two of something when we look up into the sky to discover why has it grown so dark. And then we see two dark clouds are blocking the sun. So here is the dice pattern for two, we can represent two also using symbols, and using words. And the dice pattern for two can look like this one we see on the screen, but this also represents two, and even if it's a little bit turned around, it still represents two. Even when it's a different colour, I can see two, and even when it's big and the dot's a, a different colour, it's still two. It's two when the dots are close together, or when one dot is bigger than the other, and in fact it's still two even if I don't have dots at all, but I have snowmen, that's right.

So this pattern of two doesn't always have to look exactly the same, but it does always have to represent two of something. That's why it's a pattern, look, I still have two things; one, two or one, and two. This is something that we can trust. So as we know, drawing mathematical representations helps our brain to remember them. So watch the screen. OK, take a picture and put it in your mind. Great, now let's use our mathematical imaginations using your pointy finger. Draw a dice pattern for two in the air for me. Off you go.

Great, how many dots did you do? Two. OK, let's draw the dice pattern for two on a piece of paper with your pencil. OK, draw two. Oh, I can see some of you are being very careful in colouring in the two things. And that's right, some of you don't have dots and you're drawing. Oh, I see, two love hearts! Or two squares. That's right because it just has to be two things. OK. Does your picture look similar to these ones from Willow and Meila?

Great, now let's write the number 2. We know that mathematicians represent ideas in lots of different ways. So watch the screen. OK, now let's imagine. Pick up your pointy finger and draw the number 2 in the air. Great, now let's write 2 next to the dice pattern you drew. Off you go. OK, have a look and read to me what you wrote. Yes, that's a symbol for two. And here's what the word 'two' looks like.

OK, should we have alook at another dice pattern? Yes, let's do it. Three. How many dots can you see here? That's right, this is three. We might see three of something when we notice some of the houses around us. Some of them have strong, sturdy roofs that look like triangles. I can see a triangle in the roof of this house. The triangle has three corners, 1, 2, 3 and three sides. 1, 2, 3. When we see this dice pattern, it represents three. We can record how many dots we see using symbols. This is the symbol for 3 and using words, here's the word 'three'. So the dice pattern doesn't always have to look exactly like this, look, here's three with the middle dot a little bit wonky. Here's three, even though it's now on its corner, it's orientated differently. Yes, and I see that too. It looks a little bit like a traffic light now. And I can still see three here even when it's really small or here when it's really big and the dots are pointing in a different direction, and in fact some of the dots are different colours and look, I can still see three, even though there's no outline of my dice and I can see three, even though there's no dots at all and I have dinosaurs, right?

So the pattern of three doesn't always have to look exactly the same, but it does always represent a collection of three. Look, we still have three things - 1, 2, 3 or 2, 3. Yes, I just realised that too. Look, inside of three, we can see two and one more. That's three, so this dice pattern represents three and it's something that we can trust. So let's have a look at how we might draw three. Watch carefully now. OK, take a picture in your brains. And now let's imagine the dice pattern for three. Use a pointy finger and draw the three pattern in the air, off you go. Great, now let's draw the dice pattern for three on a piece of paper with your pencil, off you go. Oh! I can see! Yes, some of you have drawn two on a dice pattern first and are putting the one in the middle for three. OK, let's have a look at your pictures. Can you describe it to me?

Let's have a look at these ones from Willow and Meila. Does your picture look similar? Great. OK, let's write the number 3. Ready, watch the screen. Good job! Now, let's imagine drawing the number 3 in the air with our pointy finger. Off you go. Great! Now let's write the number 3 next to the dice pattern that you drew. OK, write 3. OK, have a look at what you wrote. Can you read it to me? Great. Does your symbol for three look like Willow and Meila's? Yeah, that's what 3 looks like and here's what the word 'three' looks like.

What do you think we might look at next? Four? Yes! Yes, I know we're using a pattern as we investigate patterns. Each time we look at the next dice pattern it increases by one. OK, let's explore four. OK, how many dots can we see here? Four, I can see four dots. We might see four of something when we're looking at the television, we can see a rectangle on the surface of our TV screen, and the rectangle has four corners. And four sides, look, 1, 2, 3, 4. And this is the dice pattern for four, represents four, and we can record it using symbols, and using words. But four doesn't always have to look exactly like this. Let's have a look. This is still four even if it's twisted on its side. And even if it's four and, it's really teeny tiny. If it has four squares instead of four dots, it's still representing four even if the four are different colours, it still shows us four. The four could be different sizes and three could be one colour and one could be another, and in fact I can still see it's four even when there's no outline of my dice, it's still a mathematical pattern that represents the quantity four. I still have four things. Look 1, 2, 3, 4 or two, four.

And yes, little mathematicians, I can see that too. Look, inside of four, we can see two, that I imagined turning around like this and then, two more and that is.. four. So this dice pattern represents four and it's something that we can always trust. Let's have a look at how we might draw it. Watch carefully now. OK, take a picture in your mind's eye and let's imagine. Use your pointy finger and draw the dice pattern for four in the air. How many dots did you draw?

Great! Now let's draw the dice pattern four on a piece of paper with your pencil ready, draw four. That's OK, keep going. I can wait for you. OK, let's have a look. Did your picture looks similar to these ones? Great. Alright mathematicians, now we know it's really important to be able to represent four using, using its symbol as well, the number 4. So let's have a look at how we would draw that. OK, now using your imagination, pick up your pointy finger and draw four in the air. Great, now write the number 4 next to the dice pattern you drew. ave a look at what you wrote and read it to me. Yes, that's the symbol for four.

This is what Willow thought about and Meila's. Let's look at what the word 'four' looks like. There it is.