# Let's share to be fair

A thinking mathematically targeted teaching resource focused on sharing fruit equally into groups.

## Syllabus

Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus (2022) © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2024.

## Outcomes

- MAO-WM-01
- MAE-RWN-01
- MAE-RWN-02
- MAE-FG-01
- MAE-FG-02

## Collect resources

You will need:

20 pegs or other small items, for sharing

20 beads or other small items, for sharing

5 plastic or paper plates.

## Let's share to be fair – part 1

Watch Let's share to be fair – part 1 video (8:20).

[A title over a navy-blue background: Let’s share to be fair. Below the title is text in slightly smaller font: (Early Stage 1). Small font text in the lower left-hand corner reads: NSW Mathematics Strategy Professional Learning team (NSWMS PL team). In the lower left-hand corner is the white waratah of the NSW Government logo.]

### Speaker

Hello, mathematicians. Let's share to be fair.

[A title on a white background reads: You will need…

Bullet points below read:

- 20 pegs or other small items for sharing
- 20 beads, or other small items for sharing
- 5 plastic or paper plates.

Under the points is a row of 5 images of 5 white plates. Next to the points is an image of pegs, below this is an image of beads.]

You will need 20 pegs or other small items for sharing, 20 beads, or other small items for sharing and five plastic or paper plates.

[Text over a navy-blue background: Let’s share!]

Let's share.

[In the middle of a table is a white rectangular cutting board with a bowl of strawberries on top.]Speaker

Hello, mathematicians. I am a little bit hungry, so I think I'll have some fruit for a snack. I have some delicious strawberries.

[The speaker places her two hands on the edge of the bowl.]

Let's count how many I have all together.

[She moves the bowl slightly down. She begins to take out each fruit, lining them up at the top of the board as she counts.]

One, two, three, four, five…

[Under the row of fruits, she starts a new line while counting.]

…six, seven, eight, nine, ten…

[Under the row of fruits, she starts a new line while counting.]

…eleven, twelve. That's right. Altogether…

[She takes the bowl away.]

…I have 12…

[She circles the row of fruits.]

…delicious strawberries. Uh-oh, my brother has just come into the room and he wants to eat strawberries too. I am going to have to share them with him. What am I going to do to share them so that we both get the same amount? Which in maths is called an equal share. Hmm. I know. I can share them like this.

[She moves the board down the table.]

One share for me…

[She places the plate over the top left side of the board.]

…and one share for my brother.

[She places another plate over the top right side of the board.]

One for me…

[She places a strawberry in the plate on the left.]

…one for my brother.

[She places a strawberry in the plate on the right.]

One for me, one for my brother.

[She places a strawberry in each plate one at a time, as she says it’s for her or her brother until the board is empty.]

One for me, one for my brother. One for me, one for my brother. One for me, one for my brother. One for me, one for my brother.

Sharing them like this one at a time helps me to make sure that we both get an equal share. Because my brother won't be happy if I get more strawberries than him, and I won't be happy if he gets more than me. So, I have 12 strawberries…

[She circles the 2 plates of fruits.]

…all together, and now I've put them into two equal shares. Can you see? This is one share for me…

[She points to the left plate.]

…and one share for my brother.

[She points to the left plate.]

How many do I have? That's right. Count them with me.

[She points to each strawberry on the left plate.]

One, two, three, four, five, six. I have six strawberries in my share.

[She circles the left plate.]

How many does my brother have? Yes, that's right, he has six too. Let's check.

[She points to each strawberry on the right plate.]

One, two, three, four, five, six. So, my brother has six strawberries…

[She points to the right plate.]

…and I have six strawberries.

[She points to the left plate.]

We both have the same. We both have an equal share. Uh-oh. My two cousins have just come over to visit and they want some strawberries too.

[She places a bowl on the board.]

So, let's put all of the strawberries back together again…

[She empties the two plates into the bowl.]

…and I'm going to need another two plates for my two cousins.

[She moves the empty two plates to the top left of the board. She places two more plates on the top right side of the board.]

Can you tell me how I can make sure that all four of us…

[She circles the row of plates.]

…now have an equal share?

Yes, that's right. If I give them out one at a time, this will help to make sure that we all have an equal share, that we all have the same amount.

[She places a strawberry in each plate one at a time, as she says it’s for her, her brother, her cousin, and her other cousin.]

One for me. One for my brother. One for my cousin. One for my other cousin.

[She places a strawberry in each plate one at a time until the plate is empty.]

One for me. One for my brother.

[She takes the bowl away.]

So, I have 12 strawberries altogether and now I have put them into four equal shares. Can you see?

[She points to each plate.]

This is one share. This is another share. This is another share, and another share. How many strawberries do I have in my share now?

[She points to the first plate from the left.]

That's right. I have three strawberries in my share. How many do my brother and cousins have each? That's right.

[She points to the other plates from left to right.]

They also have three strawberries each. My brother has three strawberries and my cousins have three strawberries each. Well, I think I will still be hungry if I only eat three strawberries.

[She points to the first plate from the left.]

I have some grapes in the fridge too.

[She places a bowl of grapes on the board.]

Count them with me to find out how many grapes I have all together.

[She moves the bowl slightly down. She begins to take out each fruit, lining them up at the top of the board as she counts.]

One, two, three, four, five, six…

[Under the row of fruits, she starts a new line while counting.]

…seven, eight, nine, ten…

[Under the row of fruits, she starts a new line while counting.]

…eleven, twelve, 13, 14, 15, 16…

[Under the row of fruits, she starts a new line while counting.]

…17, 18, 19, 20.

[She takes the bowl away.]

So, all together, I have 20 juicy green grapes to share among my four plates. I wonder. Can you work out how many grapes we will each get so that we have an equal share? Maybe you can use 20 of your pegs or other small items that you have to help you to share them to work this out.

[Text over a navy-blue background: Over to you!

Back to the table.]

How did you go? Did you remember to share them one at a time? Let's do it together to find out.

[She places a grape in each plate one at a time.]

We have one grape each. But I'm going to keep going because there is still more to share out.

[She places a grape in each plate one at a time.]

We have two each. But I'm going to keep on going.

[She places a grape in each plate one at a time, until there were none on the board.]

How many grapes does each share have? That's right. There are five grapes in each share.

[She points to the first plate from the left.]

I have five on my plate…

[She points to the other plates from left to right.]

…my brother has five grapes on his plate, my cousin has five grapes, and my other cousin also has five grapes. And because we have five grapes each and three strawberries each, we have been able to make equal shares and we have made four equal shares.

[She each of the plates from left to right.]

This is one share, this is another share, another share, and our fourth share.

[Over a grey background, the red waratah of the NSW Government logo appears amongst red, white and blue circles. Text: Copyright State of New South Wales (Department of Education), 2021.]

[End of transcript]

### Instructions

- Can you help me share my 20 green grapes?
- Use your 20 beads to help me work out how many grapes we will each get.

## Let's share to be fair – part 2

Watch Let's share to be fair – part 2 video (1:45).

[Text over a navy-blue background: Over to you mathematicians. Small font text in the upper left-hand corner reads: NSW Department of Education. In the lower right-hand corner is the white waratah of the NSW Government logo.]

### Speaker

Over to you, mathematicians.

[The table from Part 1. Except the second plate from the left only has 1 strawberry.]

Oh no, my brother has dropped…

[She points to the second plate.]

…two of his delicious strawberries on the floor and squashed them. And now my sister has come home. We all have to share the fruit that he's left with her too so that all shares are equal. So let's put all of the fruit back into the bowl.

[She empties each plate into the bowl.]

And now that my sister has come home, we need to give her a plate as well…

[She places an empty plate on the right side of the board, under the other plate.]

…because we now need to make five equal shares. So remembering that we have 20 grapes…

[She places a grape on the top right corner of the board.]

…and now we are left with ten strawberries.

[She places a strawberry on the left side of the grape.]

So it's over to you, mathematicians. Can you work out how many we each would have on our plate now if there are ten strawberries and 20 grapes to share?

[A title on a white background reads: Over to you, mathematicians…

Text below reads: Use your pegs, beads or blocks to help you work out how many strawberries and how many grapes each person would get if there are 10 strawberries and 20 grapes to share. Under the text is an image of the table with 4 empty plates under a board, and 1 on the left. On the board is a bowl of fruit.

[Text over a navy-blue background: What’s (some of) the mathematics?]

What some of the mathematics?

[A title on a white background reads: What’s (some of) the mathematics?

Bullet points below read:

- A collection of objects can be shared by giving them out one at a time.
- An equal share is when all groups have the same amount.

Next to the points are 2 images on top of each other. The image below is of 2 plates of 5 strawberries each. Above is an image of the plates of strawberries with some strawberries being counted on the board below the plate.]

A collection of objects can be shared by giving them out one at a time. An equal share is when all groups have the same amount.

[Over a grey background, the red waratah of the NSW Government logo appears amongst red, white and blue circles. Text: Copyright State of New South Wales (Department of Education), 2021.]

[End of transcript]

### Instructions

Put the strawberries (pegs) and grapes (beads) all together again in one bowl. Spread out your 5 plates and share them out again. Remember that now we only have 10 strawberries and 20 grapes to share.

How many will we each get now?

Is it an equal or fair share? How do you know?

Tell someone, if you can, how you know that this is an equal share.