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# Reasoning Geometrically

### Coordinate Patterns

### Route to Infinity

### Marbles in a Box

### Kite in a Square

### Geometry: A History from Practice to Abstraction

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Geometrical reasoning can involve coordinate geometry and properties of 2d and 3d shapes, and may even lead to algebraic representations. These problems invite you to explore geometry in a variety of contexts.

Age 11 to 14

Challenge Level

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

Age 11 to 14

Challenge Level

Can you describe this route to infinity? Where will the arrows take you next?

Age 11 to 16

Challenge Level

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Age 14 to 18

Challenge Level

Can you make sense of the three methods to work out what fraction of the total area is shaded?

Age 11 to 18

This article gives a brief history of the development of Geometry.