What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
A introduction to how patterns can be deceiving, and what is and is not a proof.
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
This article for teachers discusses examples of problems in which
there is no obvious method but in which children can be encouraged
to think deeply about the context and extend their ability to. . . .
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.
Charlie has created a mapping. Can you figure out what it does?
What questions does it prompt you to ask?
Four rods of equal length are hinged at their endpoints to form a
rhombus. The diagonals meet at X. One edge is fixed, the opposite
edge is allowed to move in the plane. Describe the locus of. . . .
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Are these statements always true, sometimes true or never true?
Here are two kinds of spirals for you to explore. What do you notice?
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?
In sheep talk the only letters used are B and A. A sequence of
words is formed by following certain rules. What do you notice when
you count the letters in each word?
Find out about Magic Squares in this article written for students. Why are they magic?!
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Use the information about the ducks on a particular farm to find
out which of the statements about them must be true.
Take any whole number between 1 and 999, add the squares of the
digits to get a new number. Make some conjectures about what
happens in general.
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This challenge combines addition, multiplication, perseverance and even proof.
This task combines spatial awareness with addition and multiplication.
An investigation that gives you the opportunity to make and justify
Investigate and explain the patterns that you see from recording
just the units digits of numbers in the times tables.
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
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.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Is it possible to draw a 5-pointed star without taking your pencil
off the paper? Is it possible to draw a 6-pointed star in the same
way without taking your pen off?
Explore the relationship between simple linear functions and their
Becky created a number plumber which multiplies by 5 and subtracts
4. What do you notice about the numbers that it produces? Can you
explain your findings?
Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?