In the game below, twenty gems have been placed on a grid.
You start at your home at the origin, and can specify up to eight vectors that describe a path. Any gem that lies on one of your vectors counts towards your total!
But be careful - your final vector must bring you back home again or all the gems will be lost.
Once you have explored the first level, you can challenge yourself to some harder arrangements of gems in Levels 2 and 3 using the Settings menu - just click on the purple cog in the top right corner.
Then click on the vector to edit it.
You can click on the + and - signs to increase or decrease the two components of the vector - see the screenshot below:
Once you have chosen all your vectors, click on "Close" and then click "Get a score" to find out how many gems you have collected!
Don't forget that your final vector needs to take you back home.
Why play this game?
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.
Possible approach
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.
Key questions
Can you find more than two gems in a line?
How can you work out the vector needed to get you home?
Possible support
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.
Possible extension
Students could apply their understanding of vectors in Vector Journeys