Visualising and representing

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

What can you see? What do you notice? What questions can you ask?

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

What's the largest volume of box you can make from a square of paper?