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This game provides an engaging introduction to using vectors to describe a path. The condition that the gems must be brought home means that the path has to be a closed loop, so gives students the opportunity to deduce for themselves that a closed loop has a resultant vector of zero.
We hope that by playing this game students will develop a resilient attitude to problem solving by challenging themselves to collect as many gems as possible, and persevering to look for a better strategy.
This game works best if students have access to computers or laptops. However, if this is not possible, there is a "print" function in the activity that allows you to print a worksheet of a particular arrangement of gems. This can also be used so that everyone in the class can work on the same example.
A particular arrangement can be loaded on any computer by using the code in the Settings menu, which can be accessed using the purple cog in the top right corner.
To start with, students could work on finding strategies for Level 1, with the preview mode turned on. This draws a dotted line on the screen as each vector is drawn so that students can easily keep track of where they are.
As they become more adept, encourage them to try a harder level, where the gems are not so enticingly placed, or to play with the previews turned off so they have to keep track of where they are after each vector is added.
Can you find more than two gems in a line?
How can you work out the vector needed to get you home?
This version of the game uses a map and compass directions instead of vectors, and could be useful for introducing the more tricky Vectors version.
Students could apply their understanding of vectors in Vector Journeys
If p is a positive integer and q is a negative integer, which of these expressions is the greatest?
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?