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?

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

Links to the curriculum
Number (Level 3)
- solve practical problems which require finding fractions of whole number and decimal amounts

Mathematical processes
- devise and use problem-solving strategies (draw a picture, guess and check)

Resources
paper
Blackline master of the problem (English)
Blackline master of the problem (Maaori)

Specific Learning Outcomes
The children will be able to:
- find fractions of whole numbers

Lesson Sequence

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

Extension for early finishers
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.