Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

How much of the square is coloured blue? How will the pattern continue?

Collect as many diamonds as you can by drawing three straight lines.

How many moves does it take to swap over some red and blue frogs? Do you have a method?

Can you picture how to order the cards to reproduce Charlie's card trick for yourself?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

Can you find the squares hidden on these coordinate grids?

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

What's special about the area of quadrilaterals drawn in a square?

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

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

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

A collection of short Stage 3 and 4 problems on Visualising.

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

Can you make a tetrahedron whose faces all have the same perimeter?

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!

Explore the lattice and vector structure of this crystal.