'Ducks Away' follow up

Hello mathematicians! This lesson today follows up from the reading of 'Ducks Away' by Emma Watkins on ABC iView. It's OK if you haven't seen it. You can still join us, but if you'd like to go watch that first, press pause now and go do that and then come back and join us. See you soon!

Welcome back young mathematicians. I hope you really enjoyed watching the story of 'Ducks Away'. It's OK if you haven't seen it yet, we can still play around with some really interesting ideas in the story. What happens is a mother duck goes for a walk with her young ducks and her ducklings and they walk across a bridge and look, here's my representation of the mother duck, Quack, Quack, Quack, Quack, Quack, Quack. And she starts walking along the bridge and along come her little baby ducks, her ducklings.

Quack, Quack, Quack one baby duckling, Quack, Quack, Quack, Quack, a second baby duckling Quack Quack Quack Quack. Her third baby duck, the duckling, Quack, Quack, Quack, Quack a fourth duckling and Quack Quack, Quack, Quack, Quack, a fifth duckling. And then what happens is these poor ducklings, one of them gets caught up by the wind and splashes into the water, down below, and then all of the other ducklings start to get really curious.

And they look over the edge of the bridge and splash into the water and then the next duck looks over the bridge and you guessed it, splash! Into the water and it happens with the next duck splashes in and finally, the last little duckling left on the bridge loses its footing and stumbles into the water down below.

And what this made me think about is what we know about the number 5 or what this story reveals to us about this number, because the mother duck has five ducklings.

Let's count them to check 1, 2, 3, 4, 5. So she has five ducklings, but sometimes she has five of them on the bridge and none down below. Sometimes she has four of them on the bridge and one down below.

Sometimes she has three of them on the bridge and two down below. Sometimes she has two of them on the bridge and three down below. Sometimes the has one of them on the bridge and four down below and by the end of the story, all of her five ducks, her ducklings, are in the water down below, and what this made me think about is it's a bit like when we count, that even once we know that we have five, it didn't matter if some of them were on top of the bridge or below in the water, we still know and can trust that there's five, so let's have a look at what this tells us about the number five, 'cause I can now start to think like a mathematician and record what's happening. So at the moment there's five ducks at the top, and there's none down the bottom, so we know that five and zero is equivalent to five, so I can say five is five and zero, and then one tips over the edge.

And now I still know that there's five ducks altogether, but this time I can see my five as four and one more, so five is four and one. And then another one tumbles over the edge and now I still know that there's five 'cause it doesn't matter that they have moved, but this time I can see five as... yes, three and two. And then what happens next in the story?

Yes! Another duck falls over into the water and how many ducklings are there altogether? Yeah, five because it doesn't matter that they have moved, the quantity of the total number of ducklings is still five. And there's how many on top of the bridge?

Two and how many down below? Three. So five is two and three, and then another one falls off and what happens now? How can we see the five ducklings? That's right, they're partitioned, aren't they? There's one on top of the bridge, one, and there's four down below.

And then the very last duckling tumbles into the water. And what does that tell us now about five? That's right, there's no ducks on top and then five ducks down below. And so what we could see in our story 'Ducks Away', is it told us some things about five that five is five and zero, here's five. There are none. But five is also... four and one more, but I still have five ducks altogether. That five is... three and two.

But I still have five altogether, that five is two and three. Yes, and I still have five altogether. That I can also move one more across. And now I have one and four.

And if I move the last one across. That's right, I could say that five is zero and five. This book really helps us see the small numbers that nest inside the bigger ones. What a great mathematical thing to discover!

So as we like to ask, what was the maths?

So the story of ducks away helped us uncover some really important mathematical ideas. It showed us that five can be made up or composed in lots of different ways. For example, you can have five ducklings, when one is on the bridge and there's four ducklings in the water below, so one and four still makes five ducklings. We also started to realise that smaller numbers like four, three, two, and one can be found inside of five. This is a really tricky idea, and it's something that we will come back and explore as time goes on. Looking forward to the next time we get together mathematicians!