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Exploring Diagonals

Move the corner of the rectangle. Can you work out what the purple number represents?

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Drawing Polygons

I wonder which polygons we can draw on dotty paper...

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Drawing Squares

Take a look at the video showing squares drawn on dotty grids...

Vectors Round a Square

Stage: 3 and 4

Here is a diagram showing how vectors can describe a journey round a square:
vectors forming a square

The journey starts along the black vector $\pmatrix{3\cr 1}$
What vectors describe the rest of the journey?
There are many interesting mathematical questions about vectors that describe journeys.

Explore journeys round various squares of your own and see what you can find out.

If you would like some ideas of interesting questions to explore, take a look below.

What happens if I add vectors together?

What is special about opposite sides of the squares?

What is special about adjacent sides of the squares?

If I know the vector for the diagonal can I work out the other vectors?
   vector square with diagonal  

What about other shapes?

Want to share what you've done? Got any interesting questions or ideas? 
Send us your thoughts.