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.
problem
Favourite
Dozens
Age
7 to 14
Challenge level
Can you select the missing digit(s) to find the largest multiple?
problem
Favourite
Statement Snap
Age
7 to 14
Challenge level
You'll need to know your number properties to win a game of Statement Snap...
game
Favourite
Factors and Multiples Game
A game in which players take it in turns to choose a number. Can you block your opponent?
problem
Favourite
American Billions
Age
11 to 14
Challenge level
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...
problem
Favourite
Factors and Multiples Puzzle
Age
11 to 14
Challenge level
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
problem
Favourite
Multiples Sudoku
Age
11 to 14
Challenge level
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
problem
Favourite
How much can we spend?
Age
11 to 14
Challenge level
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?
problem
Favourite
Diminishing Returns
Age
11 to 14
Challenge level
How much of the square is coloured blue? How will the pattern continue?
problem
Favourite
Sieve of Eratosthenes
Age
11 to 14
Challenge level
Follow this recipe for sieving numbers and see what interesting patterns emerge.
problem
Favourite
Multiple Surprises
Age
11 to 16
Challenge level
Sequences of multiples keep cropping up...
problem
Favourite
Gabriel's Problem
Age
11 to 14
Challenge level
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
problem
Favourite
Number Families
Age
11 to 14
Challenge level
How many different number families can you find?
problem
Favourite
Funny Factorisation
Age
11 to 16
Challenge level
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
problem
Favourite
Take Three From Five
Age
11 to 16
Challenge level
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?
problem
Favourite
Stars
Age
11 to 14
Challenge level
Can you work out what step size to take to ensure you visit all the dots on the circle?
problem
Favourite
Product Sudoku
Age
11 to 16
Challenge level
The clues for this Sudoku are the product of the numbers in adjacent squares.
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
Power mad!
Age
11 to 14
Challenge level
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
problem
Favourite
Alison's quilt
Age
11 to 14
Challenge level
Nine squares are fitted together to form a rectangle. Can you find its dimensions?
problem
Favourite
Counting Factors
Age
11 to 14
Challenge level
Is there an efficient way to work out how many factors a large number has?
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
Shopping Basket
Age
11 to 16
Challenge level
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
problem
Favourite
Beelines
Age
14 to 16
Challenge level
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
problem
Favourite
Expenses
Age
14 to 16
Challenge level
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
problem
Favourite
LCM Sudoku
Age
14 to 16
Challenge level
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
problem
Favourite
Filling the gaps
Age
14 to 16
Challenge level
Which numbers can we write as a sum of square numbers?
problem
Favourite
Latin Numbers
Age
14 to 16
Challenge level
Can you create a Latin Square from multiples of a six digit number?
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You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.