# Heads and Feet

## Problem

*Heads and Feet printable sheet*

On a farm there were some hens and sheep.

Altogether there were $8$ heads and $22$ feet.

How many hens were there?

## Getting Started

How many legs would eight sheep have?

What could you try next?

## Student Solutions

Answer = 5 hens.

5 hens would have 10 feet.

3 sheep would have 12 feet.

10+12= 22

Penny and Laura from Wellesworth Junior School in Canada wrote;

Each head represents an animal. We varied the number of legs under each animal until we got the number 22. Our final number is 5 hens in all.

Rowan from Ludgvan School, Cornwall sent in the following;

My dad helped with the pictures and photos.

Georgina Rothney from Brockton Primary School wrote;

Heads and feet.

If there are 8 heads and 22 feet then there are 5 hens = 10 feet.

There are 3 sheep = 12 feet.

5+3 heads = 8 heads

10+12 feet =22 feet

Leyi from Belvedere Infant school wrote;

I think it is 5 hens and 3 sheep because I used my 2 and 4 times tables

(5x2)+(3x4)= 10 +12=22 feet

then I made sure that they belong to 8 animals 5+3=8 heads or animals

Thanks for all your solutions!

## Teachers' Resources

**Why do this problem?**

This is an easily presented problem that requires a bit of thinking as it's not necessarily obvious to pupils what needs to be done to obtain an answer. It demonstrates the power of trial and improvement, combined with a systematic approach and you could also use children's work to focus on different ways of representing a solution.

### Possible approach

You might choose to start this activity by counting the children's legs - bring a group up to the front of the classroom and ask how many children there are, and then count the legs. What can they say about the numbers? If you told them how many legs there were, could they tell you how many children? Emphasise the connection and the inverse. (It's a good idea to resist the temptation to record
this centrally so that in the later task children don't have a preconceived idea of how to record, and so may be inventive.)

Having helped the children to make the connection between children (heads) and legs, you could then introduce the idea of animals with different numbers. Which animals have two legs? Which have four? Do they know of any animals which have another number?

Then introduce the idea of two different animals. How many legs would a hen and sheep have altogether? If we know how many hens and how many sheep, can we work out how many legs? What about the other way round? Take some suggestions and then offer the task to the class.

Children could work in pairs or small groups. Once they have spent some time on the task, share different children's approaches and ways of recording. Look for children who have a system to their work, or identify a pattern in the solutions.

### Key questions

### Possible extension

### Possible support