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.
Statement snap
You'll need to know your number properties to win a game of Statement Snap...
Factors and multiples game
A game in which players take it in turns to choose a number. Can you block your opponent?
Dozens
Can you select the missing digit(s) to find the largest multiple?
Factors and multiples puzzle
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Multiples Sudoku
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
How much can we spend?
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
Diminishing returns
How much of the square is coloured blue? How will the pattern continue?
Sieve of Eratosthenes
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Gabriel's problem
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Number families
How many different number families can you find?
American billions
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Stars
Can you work out what step size to take to ensure you visit all the dots on the circle?
Product Sudoku
The clues for this Sudoku are the product of the numbers in adjacent squares.
Route to infinity
Can you describe this route to infinity? Where will the arrows take you next?
Power mad!
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Alison's quilt
Nine squares are fitted together to form a rectangle. Can you find its dimensions?
Counting factors
Is there an efficient way to work out how many factors a large number has?
Funny factorisation
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Take three from five
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
Differences
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Shopping basket
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Beelines
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
LCM Sudoku
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Filling the gaps
Which numbers can we write as a sum of square numbers?
Expenses
What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?
Latin numbers
Can you create a Latin Square from multiples of a six digit number?
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.