Exploring and noticing

Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

There are lots of ideas to explore in these sequences of ordered fractions.

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

If you move the tiles around, can you make squares with different coloured edges?

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

Can you work out what step size to take to ensure you visit all the dots on the circle?

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?