Mathematicians are often interested in exploring the structure of number sequences. In these problems, we invite you to explore and describe sequences, and explain the patterns you notice.
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Can you find a way to identify times tables after they have been shifted up or down?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.