# Fair Feast

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

Here is a picnic that Petros and Michael are going to share equally.

Image

Can you tell us what each of them will have?

How many tomatoes are there? So how many will they get each?

What fraction of the whole pizza is one slice? How many slices will each boy get?

How can you share the apple out fairly?

What fraction of the whole pizza is one slice? How many slices will each boy get?

How can you share the apple out fairly?

We have been inundated with solutions to this problem - thank you so much! It is very difficult to pick some names to mention. Deiniol explained:

I found the answer by dividing the total number of each item of food by 2 (because there were two boys!). Each boy will have - 2 slices of pizza, 4 tomatoes, a carton of orange juice, half an apple and 2 muffins.Year 2 Oak Class at Twyford St Mary's have been learning about fractions and the teacher wrote,

We have had a go at the Fair Feast problem and here is our solution for you.

We used what we know about fractions, halving numbers and division to find out what would happen if 4 people shared this picnic.

If we share between four people each person would get 1 slice of pizza or 1/4 of the pizza. They would get 1 muffin each because there are 4 and that shares easily by 4 people. They could also have two halves of a muffin, because that is the same as one whole. For the tomatoes, we used division and said that 8 divided by 4 equals 2, so they each get 2. The apple would be equally cut into 4 slices or quarters. Each person would have 1 quarter as that is 1 out of 4. If the carton was 200ml, each person would get 100ml because half of 200 is 100. Two people would share one carton.

Now we challenge other children to try and find out if the picnic can be shared by 8, 10, 12 or 20 people!

Anna and Eden from West Hill Primary wrote:

They would split the apple in half. They would have half a pizza each, two muffins each, four tomatoes each and one drink each.Of course this is exactly the same as Deiniol's solution, but the amount of pizza is given in a slightly different way.

Alisha and Madalena at Victoria Road Primary sent a very clear solution:We found out that we had to split all the food and drink in to half because there are two people.

We know they get half a pizza each and this is 2 slices because the pizza is cut in quarters and we know that two quarters is the same as a half.

They would get 4 tomatoes each because half of 8 is 4.

Half of an apple each because they only have 1 apple and 1 whole cut in to 2 is half.

2 muffins each because half of 4 is 2.

1 juice each because half of 2 is 1.

Children from Oakfield Prep School drew pictures to help them work out how much picnic each boy would get. You can see their pictures in the following files:

Henry.pdf

Harris_Zain.pdf

Ryan.pdf

Sadie.pdf

Sinead.pdf

Thank you to everyone and I'm sorry that we cannot mention you all.

**Why do this problem?**

In this problem, the familiar context of sharing provides an opportunity in which to explore fractions in a variety of ways. The task involves finding fractional quantities of whole numbers as well as dividing a unit into equal pieces.

*You may be interested in this report, originally published on the NCETM website. It outlines a collaborative project between six primary schools, intended to develop fluency and understanding of fractions through rich mathematical tasks. All participating schools used this Fair Feast task with their learners. (The two appendices can be found here and here.)*

### Possible approach

You may want to create your own 'picnic' consisting of empty boxes and cartons, or the real thing. Alternatively, the problem could be introduced by displaying the photo on the board. No matter how you present the food to be shared, you could contextualise the picnic by telling a 'story' to your class.

Allowing learners to talk, perhaps in pairs, about the solution will give them a chance to articulate what they know about halving. Walking around the room listening to their discussions may be a good assessment opportunity for you.

When you come to talking about the solution as a whole class, it would be helpful to be able to physically share the picnic, if using real food or models. If you're using the photograph, it would be good to be able to annotate it, for example on the interactive whiteboard, so children could come up and group/split the images of the items. Encourage pupils to explain how they know each part
of the picnic has been shared equally, listening out for responses which refer to the two parts being exactly the same. You can discuss different ways of describing the share of pizza - two slices, two quarters, one half ...

### Key questions

How many/much of these/this is there altogether?

How would we share that fairly between two?

### Possible extension

What would happen if the picnic was split between four children instead of two? Are there other numbers of children that it would be easy to split the picnic for?

### Possible support

Some pairs might find it easier to have a print out of the photo to work from. Having items to share physically will make this problem more accessible.