On the pirate ship there are 24 pirate swords. Each pirate has 2 swords.

If half the pirates lost a sword in battle and a quarter of the pirates each gained a new sword, how many swords would there now be on the pirate ship?

If a third of the swords were then lost how many would there be left?

This problem helps students to think about how to solve the problem, how to plan their approach, and to keep track of their work as they go along. Students have to work using logic and to be careful with their recording.

The problem requires students to have, and to develop, knowledge of the use of fractions in a practical situation. Problems such as this lay the foundation for algebra as a number of different operations have to be used together and in the correct combination to solve this problem. Algebra helps to sort out such problems and simplify them.

Copymaster of the problem (Māori)

Copymaster of the problem (English)

Rods (black for swords and orange for pirates)

### The Problem

On the pirate ship there are 24 pirate swords. Each pirate has 2 swords.

If half the pirates lost a sword in battle and a quarter of the pirates each gained a new sword, how many swords would there now be on the pirate ship?

If a third of the swords were then lost how many would there be left?

### Teaching Sequence

- A pirate play or poem could introduce the problem.
- Pose the problem and ask students to retell it in their own words.
- Check that the students know what they need to find out.
- Brainstorm for ways to solve the problem and make materials available.
- Use questions to focus on the steps used to solve the problem.

*What do you have to find out?*

How can you work it out?

What do you need to help you work it out?

How are you keeping track of what you are doing?

How do you know that you have solved the problem correctly? - As solutions emerge have students share these and explain how and why they used their particular strategy

#### Other contexts

Adapt for a current class inquiry, use a sport team scoring scenario, story book characters

You may also find these pirate themed problems of interest Cannon Balls or Treasure to Ship .

#### Extension

Adjust fractions and numbers appropriate for your students.

### Solution

A range of strategies, including drawing, use of equipment, or writing equations show there are 12 pirates, and that 6 swords are lost, leaving 18 swords.

12 divided by 4 is 3, so this is the number of swords gained, making 21 swords altogether.

One third of 21 is 7 and so 7 swords have then been lost. 21 – 7 = 14 so 14 swords left at the end.