Pirate swords
This problem solving activity has a number (multiplication and division) focus.
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?
- Solve problems involving halves, quarters and thirds.
- Devise and use problem solving strategies to explore situations mathematically.
This problem helps students to think about how to solve a problem, how to plan their approach, and how to keep track of their work as they progress. In this problem, students have to use logic and 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 different operations must 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)
- Poem, story, song, or video about pirates (to engage students in the context)
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
- Introduce the problem with your chosen song, video, poem, or story.
- Pose the problem and ask students to retell it in their own words.
- Check that the students know what they need to find out. Look for them to recognise that they need find 1/2 and 1/4 of the total swords. They will need to subtract and add using their knowledge of the fractions-of-swords. They will also need to find 1/3 of the new total of swords.
- 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
Extension
Adjust fractions and numbers as appropriate for your students.
You may also find these pirate themed problems of interest: Cannon Balls or Treasure to Ship.
Solution
If each pirate has 2 of 24 swords, then there must be 12 pirates. If half the pirates (6) lost 1 sword in battle, this means they lost 6 swords. 6 swords are lost, leaving 18 swords (24 - 6 = 18).
The total number of pirates is 12. 12 divided by 4 is 3, meaning a quarter of the pirates is 3 pirates. If a quarter of the pirates gained a new sword, there would be 3 new swords, making 21 swords altogether.
One third of 21 (total number of swords) is 7. If 7 swords were lost, there would be 14 swords remaining (21 – 7 = 14).