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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### Advanced mathematics

### For younger learners

# Exploring Diagonals

*This resource is part of "Dotty Grids - Exploring Coordinates and Vectors"*

Move the top right-hand corner of the rectangle.

Can you work out what the purple number represents?

What would be the dimensions of a rectangle with a purple number of 24? Is there more than one?

If I tell you the coordinates, can you find a quick way to work out the purple number?

What other interesting questions might you explore?

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Age 11 to 16

Move the top right-hand corner of the rectangle.

Can you work out what the purple number represents?

What would be the dimensions of a rectangle with a purple number of 24? Is there more than one?

If I tell you the coordinates, can you find a quick way to work out the purple number?

What other interesting questions might you explore?

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?