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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Gathering Gems

## Gathering Gems

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.

### 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:

### Key questions

How did you begin?

Could you change your route so that you collect more gems?

### Possible extension

Once children are familiar with Level 1, encourage them to explore levels 2 and 3 of the interactivity using the Settings menu.

### Possible support

Some learners might find it helpful to have a printed copy of their on-screen grid to make jottings on as they work.## You may also like

### Six Places to Visit

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

Age 5 to 11

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

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 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.

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."

Could you change your route so that you collect more gems?

Can you describe the journey to each of the six places on these maps? How would you turn at each junction?