# 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?

## Problem

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

Can you tell us what each of them will have?

## Getting Started

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?

## Student Solutions

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.

## Teachers' Resources

**Why do this problem?**

*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

### Key questions

### Possible extension