Mathematicians seek and find patterns in a variety of situations.
The Number Patterns and Infinity pathway on wild.maths.org invites students to explain patterns, explore their underlying structure, and make sense of infinity...
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 Number Patterns and Infinity pathway on wild.maths.org invites students to explain patterns, explore their underlying structure, and make sense of infinity...
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
Crossed Ends
Age
11 to 14
Challenge level
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
problem
Favourite
Odds, Evens and More Evens
Age
11 to 14
Challenge level
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
problem
Favourite
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
Favourite
Summing Consecutive Numbers
Age
11 to 14
Challenge level
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
problem
Favourite
Frogs
Age
11 to 14
Challenge level
How many moves does it take to swap over some red and blue frogs? Do you have a method?
problem
Favourite
Number Pyramids
Age
11 to 14
Challenge level
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
problem
Favourite
Route to infinity
Age
11 to 14
Challenge level
Can you describe this route to infinity? Where will the arrows take you next?
problem
Favourite
Triangle Numbers
Age
11 to 14
Challenge level
Take a look at the multiplication square. The first eleven triangle
numbers have been identified. Can you see a pattern? Does the
pattern continue?
problem
Favourite
Tower of Hanoi
Age
11 to 14
Challenge level
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
problem
Favourite
Always a multiple?
Age
11 to 14
Challenge level
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
problem
Favourite
Where can we visit?
Age
11 to 14
Challenge level
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
problem
Favourite
Marbles in a box
Age
11 to 16
Challenge level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
problem
Favourite
Differences
Age
11 to 14
Challenge level
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
problem
Favourite
Steel Cables
Age
14 to 16
Challenge level
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
problem
Favourite
Pair Products
Age
14 to 16
Challenge level
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
problem
Favourite
Mystic Rose
Age
14 to 16
Challenge level
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
problem
Favourite
Attractive Tablecloths
Age
14 to 16
Challenge level
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
problem
Favourite
Painted Cube
Age
14 to 16
Challenge level
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?