This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.
Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.
What numbers can we make?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Odds, evens and more evens
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
Beach huts
Growing surprises
Days and dates
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
Picturing triangular numbers
Picturing square numbers
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Elevenses
Shifting times tables
Can you find a way to identify times tables after they have been shifted up or down?
Charlie's delightful machine
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Seven squares
What numbers can we make now?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
1 step 2 step
Seven squares - group-worthy task
Coordinate patterns
Squares in rectangles
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.
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.