Being resilient

How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Use your skill and judgement to match the sets of random data.

How many different triangles can you draw on the dotty grid which each have one dot in the middle?