The fifth years are currently studying Vectors. These quantities are quite difficult to get to grips with as they don't conform to our usual view of describing space with coordinates, however, being freed from Cartesian coordinates can make a lot of geometric proof much easier.

Vector addition is especially difficult to understand since our eyes view 'lengths' not 'journeys', but this little applet from Waldomaths shows the result of adding two vectors beautifully:

The column vectors are also shown so that you can see the effect of addition on the components.

I used the applet on the board, drawing in parallel vectors so that we could see the 'equivalent journey'. Have a go and watch what happens to the resultant as you change the two vectors.

Once you've got the hang of vector addition, try this game from cut-the-knot.org

You have to choose the correct resultant from the four cards to enable the joker to climb the steps and reach the ball. Usefully, the vectors on the cards are draggable so you can work out the resultant before making your choice.

Have fun!

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