reSolve double decker bus 1

Hello there mathematicians, welcome back.

Today I invited my great mathematical friend Kristin Tripit from reSolve at the Australian Academy of Science to send us a task today. And she sent the reSolve double-decker bus. So let's have a look at what the problem is.

Where would you like to sit on the reSolve double decker bus? Luke wants to sit up the top, right at the front. Lara wants to sit at the top but at the back. Leo would like to drive the bus. And James wants to stand at the door. Slowly the bus fills with all the other children.

There are 7 children on the top of the double decker bus and 8 children on the bottom. How many children altogether?

So over to you mathematicians. How many children all together? Get out your pencils, your paper and write down your ideas. Mm-hmm and remember because we're thinking like mathematicians, you might have more than one different way to solve this problem. So press pause here, and over to you to do some thinking.

Ok mathematicians. Welcome back. How did you go? Okay let's have a look at some of the strategies for solving the double-decker bus problem. Yeah and some of these might be like the ways that you thought and you might have had some different strategies too. So let's have a look.

Here's what Zoe was thinking. She thought I could count all of the children on the bus. Mm-hmm and what Zoe did, if we can use a rekenrek to model her thinking, was that she counted everything first. So she counted, 1, 2, 3, 4, 5, 6, 7 on the top of the bus. See that? Mm-hmm and then she counted on the bottom of the bus, that there were 8 children. And then she counted them again all together. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15. Mm-hmm, and so she used a count all strategy. And we can have a look at what that looks like on the rekenrek. Let's see it happening in action.

So here's Zoe. 1, 2, 3, 4, 5, 6, 7. 1, 2, 3, 4, 5, 6, 7, 8 and then she counted them again. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. 15. So what she counted all, to work out. And yes, that is quite a lot of counting isn't it? Mm-hmm.

Did you come up with a counting strategy? Okay, should we see another one? Excellent idea.

Let's have a look at what Ahmed was thinking about. Aha, did you think about this too? Ahmed was thinking about this idea of collecting a ten. So he thought, if I could think about, there's 7 at the top and if I, you know, collect 3 more from down the bottom that makes a group of ten. And then there's 5 left, which would make 15.

So if we model his strategy on a rekenrek, here's what it would look like in pictures. Where he had 7 on the top row of the rekenrek and 8 down the bottom. And he thought if I moved this chunk of 3 across, and bring the other chunk of 3, my 7 and my 8 becomes 10 and 5. Let's have a look at that.

So here's the 7 and the 8, and then what he was thinking of is, hold on a second, this chunk of 3 down the bottom, I could exchange for chunk of 3 at the top. And now I have 1 ten at the top and 5 more down the bottom. Yes, which makes 15.

So let's have a look at this in a different representation. Here we have a whole bunch of numbers that could look a little confusing, but also a balanced scale. Yes, so here's the 7. And here's the 8. To represent what was on the top and the bottom rows of the bus. Then what happened was, he kept the 7 but thought about 8 as 3 and 5 more, and then said, well I know 3 and 7 actually could be exchanged for a different, to put a number on a different peg.

So I could swap my 3 and my 7 and change that into a 10. And so now I can see that 7 and 8 is equivalent in value to 5 and 10. And we call 1 ten and 5 more, 15. And I can tell that because the sides of my balance scale now balance out. Did you use a strategy like this too? Where you thought about grouping 10 and some more?

Ahh, okay, you had a different way? Let's see if it's like Penny's thinking. So what Penny was thinking about, is that there's 7 children at the top and there's actually 7 children at the bottom. Yes, because 8 is composed of 7 and 1 more. So then she said well, I know double 7 is 14 and 1 more makes 15. That's right. So she used a near double strategy.

And let's have a look at what this would look like using the rekenrek. So here's her collecting her 7, because she knows it's made up of 5 and 2. And then she collected the 8 as 5 and 3, and then she partitioned off the 1, went double 7 is 14, put the one back to get 15.

Mmm, so there are 3 really interesting ways of solving the double deck, double-decker bus problem from Kristen at reSolve. Yes and you might have had another different strategy.

So let's talk quickly about what the mathematics was that we saw today. We know this is a really important question to ask as a mathematician. So there's a couple of really important points that we should talk about.

There are lots of different strategies that you can use to solve the same problem. We found three today that we talked about but you might have had others, which is really awesome. Some strategies are more efficient than others, so with Zoe's strategy, even if she'd just counted all the people on the bus that would have taken her 15 steps. Whereas Ahmed's strategy took 3 steps, and that's how we know something's efficient. It's not based on how fast you do it, it's based on the number of steps that you take.

Mm-hmm and here's the other really cool thing that we saw today, that as the mathematicians we get to be in charge of the numbers. Yeah, so even when I see something like 8 and 7, I can rethink that as 5 and 10 or 3 and 5 and 7. So I can use numbers in a way that makes sense to my brain and connect to knowledge that I already have so I can use it.

All right mathematicians, great work today! I look forward to chatting to you soon and until then happy mathing!