The Special Numbers pathway on wild.maths.org invites students to take a closer look at some familiar categories of number and operations, and perhaps discover that there's a lot more to averages, fractions and square numbers than they might have initially thought.
The collection of related NRICH tasks below are ideal for teachers who want to promote creativity in the classroom. They are designed for classroom use, with accompanying Teachers' Notes and Resources.
Keep it simple
Can all unit fractions be written as the sum of two unit fractions?
M, M and M
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Power mad!
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Wipeout
Can you do a little mathematical detective work to figure out which number has been wiped out?
Unequal averages
Egyptian fractions
The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.
Peaches today, peaches tomorrow...
Twisting and turning
Searching for mean(ing)
The greedy algorithm
Big powers
Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.
Generating triples
Hollow squares
Plus minus
Fair shares?
What's possible?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?