Visualising and representing

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?

How can visual patterns be used to prove sums of series?

If you know some points on a line, can you work out other points in between?

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

Mark a point P inside a closed curve. Is it always possible to find two points that lie on the curve, such that P is the mid point of the line joining these two points?

Which curve is which, and how would you plan a route to pass between them?

Which line graph, equations and physical processes go together?