Conjecturing and generalising

Can you tangle yourself up and reach any fraction?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

It would be nice to have a strategy for disentangling any tangled ropes...

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?