One third of the animals in the barn are chickens. The rest are pigs.

There are 20 legs in all.

How many pigs are there?

The focus of this problem is on fractional parts of a set. The problem encourages students to approach fraction operations through number sense and logical thinking rather than through the memorisation of rules.

### The Problem

One third of the animals in the barn are chickens. The rest are pigs. There are 20 legs in all. How many pigs are there?

### Lesson Sequence

- Read the problem to the class.
- Brainstorm for possible approaches (draw, guess). Encourage the students to plan ways of recording their work so that others will be able to understand what they have done.
- As the students solve the problem ask questions that focus them on their thinking about fractions.
*How do you work out a third?* - Share solutions and records.

#### Extension to the problem

Write your own barn fraction problem which has 6 as the answer.

#### Other contexts for the problem

Bicycles, tricycles and a number of wheels

Spiders and bugs, and a number of legs

### Solution

4 pigs

One way to do this problem is to use a table. Before we start though, notice: (1)that if one third of the animals are chickens then two thirds are pigs and (2)since there are a whole number of chickens there must be three times a whole number of animals.

animals | chickens | pigs | legs |

3 | 1 | 2 | 10 |

6 | 2 | 4 | 20 |

Noticing part (2) has made it possible to get the answer very quickly.