This is part of our collection of favourite rich tasks arranged by topic.
If you are a teacher, you can find the whole collection on our Secondary Curriculum teacher page.
Alternatively, if you are a student, you'll find the same problems on our Secondary Curriculum student page.
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Which of these pocket money systems would you rather have?
In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
Can you match these calculations in Standard Index Form with their answers?
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?
