Pirate Swords
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 the problem, how to organise their plan of attack, and to keep track of their work as they go along. So students have to work using logic and to be careful with their recording.
The advantage of this type of problem is that it can be tackled from a number of points of view and so is accessible to a range of abilities.
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 later on in the school 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.
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
This problem could form part of unit where Pirates are the theme. There are several other problem solving activities (Cannon Balls or Treasure to Ship)on the website involving pirates.
- The students performing a pirate play could introduce the pirate unit, for example, Winklepoo the Wicked School Journal, Part 2, Number 3, 1983 or Pirate Trouble School Journal, Part 1, Number 5 1990, or the poem Pirates by Pauline Cartwright, Part 3, Number 1, 2006.
- Pose the problem.
- Ask students to retell the problem in their own words.
- Check that the students know what they need to find out.
- Brainstorm for ways to solve the problem.
- 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?
Other Contexts for the Problem
The problem could be posed in the context of a classroom. The swords could be replaced by any popular item, such as clothes or CDs.
With some change of numbers it could apply to Snow White and the Seven Dwarfs.
Solution
The students need to be able to pair swords and count the pairs to work out the number of pirates. This can be done using a diagram or using equipment. This way they will know that there are 12 pirates.
Now again using equipment or some other means they can divide the pirates into two equal groups of 6 and see that 6 swords are lost. This leaves 24 – 6 = 18 swords.
Dividing the pirates up into four equal groups gives 3 in each and so 3 swords are gained. At this stage there are 18 + 3 = 21 swords.
Now using thirds in some form we see that a third of 21 is 7 and so 7 swords have been lost this time. 21 – 7 = 14. There are 14 swords left at the end.
| Attachment | Size |
|---|---|
| Pirate.pdf | 34.34 KB |
| PirateMaori.pdf | 49.22 KB |
Similar Resources
Fractional Magic Squares
Use addition with fractions;
Know the idea of, and be able to construct, magic squares.
Devise and use problem solving strategies to explore situations mathematically (be systematic).
Even More Pizzas And Things
Solve problems involving fractions
Devise and use problem solving strategies (draw a picture, use equipment, guess and check, be systematic, think)
Interpret information and results in context.
Names and Numbers
Perform addition with 10s and 5s.
Devise and use problem solving strategies to explore situations mathematically . This problem uses be systematic, and draw a picture.
Sharing More Lollies
Solve problems that involve halves and thirds
Used the terms greater than and less than in the solution of the problem
Snap!
These are level 3 number problems from the Figure It Out series.
