Jennie the old sheep dog is lazing around in the paddock near the house.

She counts the number of animals in the paddock. There are 11 of them, pigs and ducks.

Then she counts the legs. She sees 28 legs.

How many ducks are there?

This problem uses the multiplication facts of 2 and 4. It also gives students the opportunity to combine the operations of addition and subtraction. As there are many ways to solve this problem it is accessible to a range of students.

Copymaster of the problem (Māori)

Copymaster of the problem (English)

Paper for drawing

Equipment for acting out

### The Problem

Jennie the old sheep dog is lazing around in the paddock near the house. She counts the number of animals in the paddock. There are 11 of them, pigs and ducks. Then she counts the legs. She sees 28 legs.

How many ducks are there?

### Lesson Sequence

- Read the problem to the class.
- Ask the students to highlight the important information.
- For beginning problem solvers you might like to use them to act out the problem.
- Start with 4 students at the front of the room. Ask 2 of them to be pigs (on all 4's) while the other 2 stand (ducks). Ask the class to count the legs.
- Ask the students to think about what would happen if you "turned" one of the pigs into a duck. How many animals? How many legs?
- Brainstorm other ways to solve the problem – list possibilities on board (draw, equipment, guess)
- Students solve the problem.
- Sharing of solutions and the strategies used.

#### Extension

Get the students to write and solve their own problems by changing the numbers of animals and legs.

#### Other contexts for the problem

Horses and riders

Tricycles and bicycles

### Solution

3 pigs, 8 ducks

There are many ways to do this problem. For instance, it is a good problem to introduce the use of a table and to use it for guess and improve. If the first guess was 5 pigs and 6 ducks there are 32 legs. At this point the students should realise that to reduce the number of legs we have to reduce the number of pigs. Some students may be able to reason that when you reduce the pigs by one and add a duck you have reduced the number of legs by 2.