reSolve bakery 3

Ok, mathematicians, welcome back. Let's explore some thinking around this problem sent to us by our friends Kristin Tripit and Rikiya at reSolve. So this was the problem that we were asked to solve.

And really, what this was getting at was this idea of you know what is 40 twenty fours or 24 forties, which is the same as saying 24 X 40. So let's have a look at some strategies.

So here's how Suin solved the problem. Can you make sense of her thinking? Let's have a look together. So there's forty, twenty four. Yes, and she partitioned the four tens into one, ten each to get ten, twenty fours. Yes, and she did that, three, four times. And what she knew is that she could writethat as instead of 10 X 24 plus, 10 X 24 plus, 10 X 24 plus, 10 X 24, it would be more efficient as a mathematician to record that as 10 X 24 and do that four times. So she did.

She renamed, 10 twenty fours as two hundred and forty. Then she used her knowledge of doubling, to join those together first. Uhm 'cause two, two hundred and forty's is four hundred and eighty and then joined and doubled the remaining portion to get nine hundred and sixty. Yeah, and so that's an insight into Suin's brain, and how she thought about the problem and what her poster looked like.

Shall we have a look at another strategy? Ok. So here's our starting problem and here's another way you could have thought about it using the same idea as of partitioning. You could change twenty four, forties into two lots of twelve, forties. And then. Uhm, use that to double one number and halve the other. So twenty four, forties can become twelve, eighties and I can rename it. And then what I'm going to use is my knowledge of tens and renaming, so we're going to partition now the twelve, eighties into ten, eighties and two, eighties more. And ten, eighties is just renamed eight hundred. And two, eighties is a number fact I know. Double eighty is one hundred and sixty.

Then I join those two quantities together, to get nine hundred and sixty. So that's another strategy you could have used. Yes, and sometimes it's really tricky from a poster to work out what's happening inside someone else's brain. Alright, let's have a look at the next challenge that we've been sent by Kirstin and Rikiya.

Here it is, cupcake boxes. Charlie has a box that has twelve cakes and he has a box that holds ten cakes. Inside each box is a flat cardboard tray. The tray fits snugly in the boxes and has circles cut out of it so the cakes have places to safely sit. Charlie was folding up boxes for ten and twelve cakes. He put the tray into the box for ten cupcakes. He noticed that the packaging said one side of the tray was twenty five centimetres and the other side was also twenty five centimetres. It was a square. He looked at the tray for twelve cupcakes. It measured twenty two centimetres on one side and twenty eight centimetres on the other.

Both sets of side lengths added to fifty. Charlie was surprised. Does this mean that both trays would be the same size? Surely, he thought the tray that holds twelve cupcakes would have a bigger area than the tray that held ten cupcakes. Do you think the trays have the same area? If not, which tray do you predict has the biggest area? Select an efficient strategy to determine which area is larger.

Over to you mathematicians.