reSolve fruit shop 1

Hi there mathematicians, I've a task for you direct from

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Canberra and the team at the Australian Academy of Science

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with Kristen and Rakia. And they have sent us their reSolve fruit

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shop task, working with arrays.

Let's have a look.

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Ah, so here you can see the reSolve fruit shop.

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What are some of the fruit you

can see in the background?

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I see apricots too, 'cause they're one of my favourites actually.

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They're the little teeny tiny ones. Well, not as teeny, tiny

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as the blueberries.

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Yes, they're the next smallest, I think.

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Yeah, and the big watermelons.

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It looks like it's very heavy to hold, doesn't it?

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Ok, do you notice something about all of the boxes in

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the way that the fruit has

been arranged?

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Yeah, it's pretty neat, isn't

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it? Yeah look, let's zoom in.

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Here are the mangoes and here are the apples. What can you see

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there, that's similar between those two collections?

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And what can you see

that's different?

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Can you record a few of your

ideas? It might be a good place

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to press pause here so you can

record your ideas and then we'll

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share some together, Ok?

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Ok, welcome back mathematicians. Let's have a

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look at some ideas together. We

thought we talked together to

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look at some different things

that you might have seen that's

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similar or different with the mangoes and the apples at the

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reSolve fruit shop. So I have my boxes and I just wanted to put

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my fruit in there and I'm going

to represent the mangoes using

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the yellow counters. You could

use anything that you liked.

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And I'll use the apples for,

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red for the apples.

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And there's an array.

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I feel like I just gave you a

thing to think about that

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they're all arranged as arrays, aren't they? Where there's an equal

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number of rows and columns, look.

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This one has two's and two's or 3 and 3, and this one is

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4 or 3. And I might have also just told you something else that's

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similar. Let's have a

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look. Almost made them.

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Are you noticing things as I'm putting them down? Excellent.

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Ok, so what are some of things that you notice that's similar

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between the mangoes and the apples? I might write things

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that are similar in green.

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So, similar and actually if I was being a mathematician, I would

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do this as a table so I wouldn't

do it like that.

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Similar and

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different. Yes, and that helps us organise our

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ideas isn't it? Ok, So some things that are similar?

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Yes, is they're all organised like arrays. They all have an equal

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number of rows

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in each box and an equal number of columns.

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Ok, yes I know. And if you look down actually

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each column, in each box, has 3. Yeah, there's

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3 here, 3 here, 3 here, 3 here.

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So in all boxes

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each column

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has 3.

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Ah, yes, and that has made you

think about something different.

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isn't it? Because,

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yes, in the row, the rows are different, so the rows of apples

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are the same, but the rows of the mangoes versus the apples is different.

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In the mangoes there's 2 in each row and in the apples

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there's 4 in each row.

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Um.

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The mangoes have 2 in each row.

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The apples have 4 in each row.

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Yeah, and I wrote it

here because I thought these ideas, sort of, could be grouped together.

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What else is different?

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Yeah, the quantity, isn't it? So in each box of mangoes

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there's only 6 and in each box of the apples

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there's 12, so, there are 12 apples in each box.

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Nice spotting for those mathematicians who realised that,

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if you double the mangoes, double 6 is 12 and there's 6

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mangoes. I like your thinking; in each box.

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What else is something that's similar or different?

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I'm going to leave it to you now to note

down some other ideas in your

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notebook and then we'll come back together. Ok, back to you.

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[No sound]

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Here's the next question from Kristen and Rikia. And they

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said to us, Ok, how are the two boxes of oranges similar and how

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are they different? What are

you thinking mathematicians?

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What can you see?

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Yes, they are all orange. We're going to look for mathematical

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things that are similar or

different.

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So quantity or weight or size.

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Ah, I see this too. I think it's the same quantity, look.

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If I take the boxes from being

stacked on top of each other.

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And turn this one sideways and

then lay them over the top.

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Yeah, I think it's the same

number in each box.

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It's like the commutative property, look.

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Here I have an array, it has 5 sevens, which is 35 and over

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here, my array, I would call that 7 fives, which also has

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a product of 35, and if I turn it around,

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and lay it on the top,

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I can prove they both have 35.

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Yes, so I think we can use that

same imagining to say that both

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of our orange, both of our boxes of oranges have 15 in them.

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Oh, I saw this too. They both

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have arranged the oranges in equal rows and in equal columns.

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Ah, Ok, yes we'll come to that difference in a moment.

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I can also see this, that some of you also saw, that inside of the

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15 you can see 6

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and 9, look 1 six and 1 nine.

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And it's also in the bottom box. So that's something else that

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they have in common.

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Yes, and to your earlier point,

that in the top box we can

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see 5 rows, 1, 2, 3, 4, 5 but in the bottom box there's only 3 rows,

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look, 1, 2, 3. So that's one of the things that's different.

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Yes, and the same with

the columns, isn't it? In

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the top box there's 3 columns and in the bottom

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box there's 5 columns.

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Ok, let's have a look at the next challenge.

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So can you use the number of

mangoes in one box to help

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you work out the number of blueberry punnets?

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Oh, what are you thinking mathematicians? So yes, the

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punnet is the box that the blueberries sit in. And how

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can you use what you see with

the mangoes to help you think

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about the punnets?

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Shall we have a look at this

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together? Great idea.

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I thought we'd talk about this question

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together. I'll just move this over a little bit.

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Ok, and I'm going to use these pieces of paper to represent my

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punnets of blueberries.

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Now just make sure that you can

see them. Yes, I didn't actually

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have any, I think you can see that they're there. Ok, so Kristen

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has asked us this question, of how can we use the information that

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we can see here about the number

of mangoes to help us think

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about the punnets of

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blueberries. So what I do in my

brain is do some imagining and

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what I can see here is that

there's a structure of 6 on a

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dice pattern, and if I look

really carefully I can see that

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here also look.

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Because it's 2 rows of 3,

so I know that chunk is 6.

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And then there would be 3 more. And

I know 6, opps 6 and 3

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more is 9, so that's one way I

could have thought about it. The

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other thing I could have thought

about doing too, I'm going to

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use these, I'm going to make some

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miniature punnets. I could

have thought about my mangoes

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and said well if there was one

more column of threes it would

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look like this.

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And so that would make 9 'cause

3 threes are 9, and so that's

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how I could use the

representation of our mangoes

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is to help me work out the

punnets, the number of punnets of

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blueberries that I have. So 2

strategies that in, that happened

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in my brain. Would like to see

them again? OK, so one was I

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imagined the 6

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that I see here in the mangoes, here

in the punnets of blueberries.

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And then I know 6 and 3

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more is 9. And the other thing I

imagined and your brain is

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likely to have been entirely

different, which is one of the

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beautiful things about math, isyou get to see inside people's

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brains, is I imagined what the

quantity would be if there was

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another column of 3.

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And so that would give me 3

threes, which is 9. OK over

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to you mathematicians, to

think about how else you

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could use what you know

about the mangoes, to think

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about the blueberry punnets.

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OK, and now back to you

mathematicians. I have 2

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questions for you to go off and

explore now. One is this one.

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Can you use the number of apples

to help you workout the number

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of peaches? And can you draw

some diagrams for us so that we

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can get inside your brain and

see your amazing thinking?

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And our second question to leave

you with today is this one. Can

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you make any other connections,

as you're doing this task, using

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any of the fruit that you like?

I think I'm going to play with

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the apricots 'cause they're my

favourites and I think I can see

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relationship to the

strawberries. OK,

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mathematicians, over to you.