Exploring and noticing

Which of these roads will satisfy a Munchkin builder?

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

Take a look at the video and try to find a sequence of moves that will untangle the ropes.

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?