Gathering gems
Using compass points, can you describe up to ten paths on this map so that you bring as many gems back home as possible?
Age
5 to 11
Challenge level
Problem
You have been given a mission - to collect as many gems as possible and bring them home.
In the interactivity below you can draw straight lines through the gems using the four points of the compass (North, South, East and West). You can use up to ten lines to make a route from home and back again.
Have a go!
Can you improve your route so that you collect even more gems? Is it possible to collect all the gems each time?
You can work off-screen by printing the grid, if you prefer.
If you click on the Settings menu (the purple cog in the top right-hand corner), you could copy the code for a particular grid so that a friend could work on that same grid on their computer.
In the interactivity below you can draw straight lines through the gems using the four points of the compass (North, South, East and West). You can use up to ten lines to make a route from home and back again.
Have a go!
Can you improve your route so that you collect even more gems? Is it possible to collect all the gems each time?
You can work off-screen by printing the grid, if you prefer.
If you click on the Settings menu (the purple cog in the top right-hand corner), you could copy the code for a particular grid so that a friend could work on that same grid on their computer.
Getting Started
How could you start?
Is there a line you can draw straight away that collects more than one gem?
Don't forget that you need to get back home with your gems!
Is there a line you can draw straight away that collects more than one gem?
Don't forget that you need to get back home with your gems!
Student Solutions
The following solutions arrived from Peak School in Hong Kong:
Jamie:
First, I will find a way to get all the gems. Then I counted how many times I went and then if it is more than 10, I need to make it to 10 or lower. Then I will have the answer.
Cassie and HazeӬ:
How we did it was first we went West 7 times then we went East once. After that, we went North 5 times and South 1 time. Then we went East 5, North 8, West 6, South 6 and East 3 times.
Our strategy was whenever we went too far we would go back 1 space and after our hard work, we finally made it to the end.
Guillermo:
It doesn't matter what solution you enter because it is random every time so you can never get a straight answer. So the directions I used where N5 E6 S8 W8 N1 E5 N6 W2 S4 W1 and that was the solution that got me all 20 gems and got home.
William & Evelyn:Ӭ
We tried to calculate how many moves we needed to use in order to get from the closest gem to the farthest while using as few moves as possible, while collecting as many gems on the way and still saving enough moves to get back "Home". By using this method we collected all 20 gems.
Jamie:
First, I will find a way to get all the gems. Then I counted how many times I went and then if it is more than 10, I need to make it to 10 or lower. Then I will have the answer.
Cassie and HazeӬ:
How we did it was first we went West 7 times then we went East once. After that, we went North 5 times and South 1 time. Then we went East 5, North 8, West 6, South 6 and East 3 times.
Our strategy was whenever we went too far we would go back 1 space and after our hard work, we finally made it to the end.
Guillermo:
It doesn't matter what solution you enter because it is random every time so you can never get a straight answer. So the directions I used where N5 E6 S8 W8 N1 E5 N6 W2 S4 W1 and that was the solution that got me all 20 gems and got home.
William & Evelyn:Ӭ
We tried to calculate how many moves we needed to use in order to get from the closest gem to the farthest while using as few moves as possible, while collecting as many gems on the way and still saving enough moves to get back "Home". By using this method we collected all 20 gems.
Teachers' Resources
Why do this problem?
This task gives learners the opportunity to practise using points of the compass, but in particular it is a chance to reflect on, and improve, their own solutions. In this context, 'improve' might mean collecting more gems than a previous solution, or it might mean collecting the same number of gems but using fewer lines.In a classroom situation, learners can share strategies for collecting as many gems as possible, giving everyone the opportunity to refine their method. By focusing on different ways of approaching the task and learning from each other, children can become more resilient problem solvers.
Possible approach
Ideally, children would have access to computers or tablets so they can explore the interactivity with a partner. Give the class a short amount of time (five minutes or so) just to get used to the interactivity and 'play'. (See the article Using Digital Manipulatives and Interactivities to Develop Curiosity.) Bring them together and invite general comments or noticings, and address any misconceptions about the task or questions about the interactivity itself.Explain that you would now like them to try to collect as many gems as they can, but to begin to think about good strategies for doing this. Give the group more time to work and while they are doing so, circulate and listen out for good reasoning about where they are placing their lines. Each grid generated by the interactivity has a unique code, so if there is a particular grid that you would like to share with the whole class, you can access the code in the Settings menu by clicking on the purple cog in the top right corner. When you enter a code, you need to click on the box before re-starting the interactivity (the border of the box will become pink).
Bring everyone together again and invite some pairs to explain their approach. They might say, for example:
"We looked for groups of gems that were on a straight line first."
"We began by drawing a line from 'home' so that it went through as many gems as possible."
Invite questions and/or comments so that everyone begins to build up a range of possible ways of going about this task. You could then give the whole class copies of the same grid (using the code and/or printing facility) so that they have chance to try out one of the strategies they have heard about, should they wish."We began by drawing a line from 'home' so that it went through as many gems as possible."
Key questions
How did you begin?Could you change your route so that you collect more gems?