In some senses, all numbers are special, though some are perhaps given more attention than others...
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.
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.
problem
Favourite
M, M and M
Age
11 to 14
Challenge level
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
problem
Favourite
Keep it simple
Age
11 to 14
Challenge level
Can all unit fractions be written as the sum of two unit fractions?
problem
Favourite
Egyptian fractions
Age
11 to 14
Challenge level
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.
problem
Favourite
Peaches today, peaches tomorrow...
Age
11 to 14
Challenge level
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
problem
Favourite
Twisting and turning
Age
11 to 14
Challenge level
Take a look at the video and try to find a sequence of moves that will untangle the ropes.
problem
Favourite
Searching for mean(ing)
Age
11 to 16
Challenge level
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
problem
Favourite
Power mad!
Age
11 to 14
Challenge level
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
problem
Favourite
Wipeout
Age
11 to 16
Challenge level
Can you do a little mathematical detective work to figure out which number has been wiped out?
problem
Favourite
Unequal averages
Age
11 to 14
Challenge level
Play around with sets of five numbers and see what you can discover about different types of average...
problem
Favourite
Big powers
Age
11 to 16
Challenge level
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.
problem
Favourite
The greedy algorithm
Age
11 to 14
Challenge level
The Egyptians expressed all fractions as the sum of different unit
fractions. The Greedy Algorithm might provide us with an efficient
way of doing this.
problem
Favourite
Generating triples
Age
14 to 16
Challenge level
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?
problem
Favourite
Hollow squares
Age
14 to 16
Challenge level
Which armies can be arranged in hollow square fighting formations?
problem
Favourite
Plus minus
Age
14 to 16
Challenge level
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
problem
Favourite
Fair shares?
Age
14 to 16
Challenge level
A mother wants to share a sum of money by giving each of her
children in turn a lump sum plus a fraction of the remainder. How
can she do this in order to share the money out equally?
problem
Favourite
What's possible?
Age
14 to 16
Challenge level
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?