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.

Summing consecutive numbers
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?

Frogs

Number pyramids
Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Crossed ends

Odds, evens and more evens
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

Magic letters

Where can we visit?

Marbles in a box
How many winning lines can you make in a three-dimensional version of noughts and crosses?

Route to infinity

Triangle numbers

Tower of Hanoi
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Always a multiple?
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

Differences

Pair products
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Steel cables

Attractive tablecloths

Painted cube
