A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
This problem looks at how one example of your choice can show something about the general structure of multiplication.
This investigates one particular property of number by looking closely at an example of adding two odd numbers together.
What does logic mean to us and is that different to mathematical logic? We will explore these questions in this article.
Four of these clues are needed to find the chosen number on this
grid and four are true but do nothing to help in finding the
number. Can you sort out the clues and find the number?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
This article invites you to get familiar with a strategic game called "sprouts". The game is simple enough for younger children to understand, and has also provided experienced mathematicians with. . . .
Proof does have a place in Primary mathematics classrooms, we just
need to be clear about what we mean by proof at this level.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?
This article stems from research on the teaching of proof and
offers guidance on how to move learners from focussing on
experimental arguments to mathematical arguments and deductive