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.
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.
How did you begin?
Could you change your route so that you collect more gems?
Once children are familiar with Level 1, encourage them to explore levels 2 and 3 of the interactivity using the Settings menu.
Some learners might find it helpful to have a printed copy of their on-screen grid to make jottings on as they work.