article
Train Spotters' Paradise
Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.
Conjecturing and generalising
problem
Summing geometric progressions
Age
14 to 18
Challenge level
Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
problem
Interpolating polynomials
Age
16 to 18
Challenge level
Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
problem
Take three numbers
Age
7 to 11
Challenge level
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
problem
Odd times Even
Age
5 to 7
Challenge level
This problem looks at how one example of your choice can show something about the general structure of multiplication.
problem
Two numbers under the microscope
Age
5 to 7
Challenge level
This investigates one particular property of number by looking closely at an example of adding two odd numbers together.
problem
Magic Letters
Age
11 to 14
Challenge level
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
problem
Steps to the Podium
Age
7 to 14
Challenge level
It starts quite simple but great opportunities for number discoveries and patterns!
problem
Method in multiplying madness?
Age
7 to 14
Challenge level
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
problem
polygonals
Age
7 to 11
Challenge level
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.