NCTM (National Council of Teachers of Mathematics) has a very clever online game that helps students understand vectors. I introduced it to my precalculus students today, and they spent more than 30 minutes completely absorbed in it.
The game involves determining the correct velocity vector for a boat to accomplish several tasks. There is a vector for the water’s current, and you can also have the resultant vector displayed. Here’s a screenshot:
Players can adjust the boat’s velocity vector, as well as the water current’s vector. After some trial and error, my students eventually realized that simply pointing the boat’s vector towards the island won’t work, and they began to add the two vectors at the boat’s bow to get a better idea of where it would end up.
There are several levels of the game, and after playing with it, my students all agreed that they had better understanding of what is involved in vector addition.
Here’s a short video of what it looks like to play: