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### Number and algebra

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### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Dynamic Explorations

### Polygon Rings

### Shifting Times Tables

### Semi-regular Tessellations

### Using Geogebra

### Quad in Quad

### Surprising Equalities

### Pentagon Construction

### Fantastic Fractals

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Mathematicians often use tools to help them to make discoveries. The problems in this feature encourage you to use dynamic geometry and other interactive tools to explore, pose questions, make conjectures and prove ideas.

Age 11 to 14

Challenge Level

Join pentagons together edge to edge. Will they form a ring?

Age 11 to 14

Challenge Level

Can you find a way to identify times tables after they have been shifted up or down?

Age 11 to 16

Challenge Level

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Age 11 to 18

Never used GeoGebra before? This article for complete beginners will help you to get started with this free dynamic geometry software.

Age 14 to 18

Challenge Level

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

Age 14 to 18

Challenge Level

Take any triangle, and construct squares on each of its sides. What do you notice about the areas of the new triangles formed?

Age 16 to 18

Challenge Level

Follow the instructions to create a regular pentagon. Can you prove it is indeed regular?

Age 11 to 18