reSolve fruit shop 2

Hi there mathematicians, when we left you, we left you with this challenge of can you make any other connections?

I'll share with you something that I saw.

Hi there mathematicians. Welcome back. I thought I'd share with you some of the connections that I made. Yes, and I don't have a printer, so I've recreated my, the reSolve fruit shop for you. So over here I have counters that are representing my apricots and I have blocks for watermelons, 'cause I figure they take a bit more space than a counter and the watermelons are so big, and I think the girl in this story I'm going to call her Kaitlyn 'cause I know a Kaitlyn who loves watermelons and so Kaityn's represented by C3PO.

I'm not sure how she'll feel about that, but we thought we'd go with it anyway. So here's some things, and I recreated these ones 'cause these were the first connections I made, just to share with you some things I thought, so that that might inspire you to think of a few other things.

So one of the first things I noticed is firstly I really like apricots, so when I was looking at the apricots I noticed it's a square number. Yes, because there's four rows and four in each row, and so therefore it's a square, and I really like square numbers, so I know that's sixteen. But when I look to the strawberries I can see half a square number. Yes, because if I had another two rows of four. I think you can still just see that let me check.

Not quite. I will move it up for you. So here's my row of strawberries. My array of strawberries with two fours. And I can tell that they're fours and if I made another two rows, of four, Yeah my. I've had the same square array. Look. This might just be the right size, let's see.

Oh yes, my old blueberry punnet sort of shows this. And the same, yeah, and it's got the same little bits hanging over. Can you see that? Yes, and so if I fold this in half, that covers my red portion, which shows to me that there's half as many strawberries, as there are apricots. And also if I doubled my number of strawberries, I could make a square number which I really like doing.

And then because I really like square numbers just because I think they're quite fun. I notice something about my watermelons and that is that there was one hanging in the basket, and if I joined that to here, and if Kate hadn't of bought or be buying a watermelon, there would be another one here. And so I have almost a square number in my watermelons, and so if I had one more, I would have a square number, so my, in my collection of watermelons, what I have are 3 threes minus one, which is 8, and technically there's one in the basket, but I think that's still belongs to the shop and I think Kate's about to buy one and so, so now what there are is 3 threes, minus two, which will leave seven in the shop.

But it also made me think about this, mathematicians. Look inside of sixteen, sorry Kate to take your watermelon that if I put them up here. Yes, that inside of my square array of sixteen, is an array of nine. If I had one more watermelon. I know and that made me start thinking about arrays inside arrays, which is sort of what the fruit shop did.

Ok, so I hope this has inspired you to think about a few other things, and then we'll look at our next challenge.

OK, and now we are onto our challenge for today. Back into the fruit shop we go.

And did you notice something in the fruit shop? Everything is arranged really beautifully. The mangoes, the apples, the peaches, the strawberries, except for the lemons. Look. They're really messy and are not in a nice array like all the other fruit. So here comes our challenge for you.

There are four bags of lemons. The owner of the fruit shop wants to take the lemons out of the bags and arrange them in a box like the oranges, apples, peaches, apricots and mangoes. She wants more than one lemon in each row and column. How could the owner arrange all of the lemons in just one array? Can you find more than one way?

Alright mathematicians, it's back over to you. Your job is to think about what are the different arrays that you could make, arrangements that you could make. Using equal rows and equal columns for the lemons. And draw pictures up so the owner of the fruit shop can make some decisions about which one she likes. Yes, and it could be based on how much space she has to put them. Ok, enjoy.