reSolve bakery 2

Hi there mathematicians. Welcome back to our task sent to us by Kristen Tripit at reSolve. So this was the problem she posed for us. Remember. And it was really about how many cupcakes does Charlie bake each day.

So we know from the image that there is eight 12's. Look here is one 12, a second 12, a third 12, 12, a four 12, five, six, seven and eight twelves and we had to work out how many individual cupcakes is that? How many altogether? What's the product?

So let's have a look at some strategies. So one thing you could have done because you had the image was actually to count, count all of them by ones. Or you could have done something like skip counting by fives, and this was pretty easy to do because we had the picture, but it's also pretty inefficient in this context of the problem.

If we have other knowledge and understanding that we could use. You could have also have counted in a different way by 10s maybe instead of by fives and look if you had partitioned up the array you might have done something like this, ten, twenty, thirty forty and you could have kept going.

But we still really wondered, are there some other more efficient strategies we could have used? You know if we had the skills and understanding of the mathematics of to do it. So let's have a look at how else we could have thought about this problem. So here's Theo and this is how he solved the problem. Can you make sense of his thinking from this diagram?

Yeah, OK, so like you too. I can see that I think he's partitioned some of the cupcakes from the tray anyway or he has partitioned what looks for us to be like an array? So let's have a look 'cause then there's all the symbols around the outside, which might make your mind boggle a little bit. So let's have a look at what he did originally.

This was the array and it was 8 times 24 or eight 24's and he was like, well, I'm not entirely sure I know that. So what he decided to do is use what he knows and he partitioned out and said. Well, I know eight 24's is equivalent in value to eight 20s and eight fours. So what that means is that eight 20's over there on the left that's 160 eight 4's is 32 and if I join that together I get 192. Uh-huh alright.

How else could we have thought about this problem? Let me show you another way. This is Toby and what do you think he did to solve the problem? OK, should we have a look together. OK, let's see. So Toby sees the 24 each collection of 24 inside the larger array. Then he doubles. He joins those together. So he doubles 24 to find 48, then he joins those together. He doubles 48 to get 96 and then he doubles one more time. So he has doubled three times to work out it's 192. OK.

Let's have a look at a third different strategy. We could have used to solve the problem. This is May and let's see about, see if you can make sense of what she did. Yeah, you might be noticing that too. It's very similar to Toby's way of thinking. Yet she started with the 24. And then doubled that to find 48. Doubled 48 to get 96. And doubled the 96 to find 192. Yeah, so let's have a look at those two strategies for a moment. What do you notice here that similar about these two strategies?

OK, and what are some things you notice that are different? OK, I'm going to get you to write your ideas in your notebook, and I'm going to give you today's challenge. So here you go thanks to Kristen Tribute at reSolve, here's the next part of the challenge for us.

Charlie's cupcakes shop might be might only be small, but he takes a lot of orders. His cakes are used for school fundraisers and are also a favourite at birthday celebrations. Today is a big day as there are a lot of cakes to bake.

Amy has put us in a special order. She would like Charlie to bake 2 special flavours for a very special birthday celebration. Orange Jaffa and cookies and cream. She would like 2 trays of each. Barry has ordered two trays of original flavour for his school's fate. Demi has ordered cupcakes to serve after a show in the Town Hall. She has ordered one tray of each original flavour. She likes the sound of Orange Jaffa and Cookies and Cream and so she's ordered two trays of these as well. Charlie also needs to make an extra tray of the 8 original flavours to be sold in his shop. That is 4 trays of each flavour. Four trays of 10 flavours.

That is 40 trays of cakes. 40 trays of 24 cakes. How many cakes does Charlie need to bake? Oh, is your brain sweating? Great because that's the goal.

So Kristen gives this tip. She says 40 trays of cakes can be represented as a grid. Each large rectangle represents one tray of cupcakes, each small grid square is that rectangle in that rectangle represents an individual cake. How many cakes does Charlie bake?

Create a poster to show how you solve the problem. You might like to use a copy of the grid array to help explain how your strategy works. You might also like to think about the strategies we explored today and how we could use those to help you solve this.

Over to you mathematicians.