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
Missing Multipliers
Age
7 to 14
Challenge level
What is the smallest number of answers you need to reveal in order to work out the missing headers?
game
Favourite
The Remainders Game
Play this game and see if you can figure out the computer's chosen number.
problem
Favourite
Consecutive Numbers
Age
7 to 14
Challenge level
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
problem
Favourite
5 by 5 Mathdokus
Age
7 to 16
Challenge level
Can you use the clues to complete these 5 by 5 Mathematical Sudokus?
problem
Favourite
Remainders
Age
7 to 14
Challenge level
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
problem
Favourite
Method in multiplying madness?
Age
7 to 14
Challenge level
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
problem
Favourite
Two and Two
Age
7 to 16
Challenge level
How many solutions can you find to this sum? Each of the different letters stands for a different number.
problem
Favourite
Number Daisy
Age
11 to 14
Challenge level
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
problem
Favourite
Largest product
Age
11 to 14
Challenge level
Which set of numbers that add to 100 have the largest product?
problem
Favourite
Cinema Problem
Age
11 to 14
Challenge level
A cinema has 100 seats. How can ticket sales make £100 for these different combinations of ticket prices?
problem
Favourite
Consecutive Seven
Age
11 to 14
Challenge level
Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?
problem
Favourite
Fractions jigsaw
Age
11 to 14
Challenge level
A jigsaw where pieces only go together if the fractions are equivalent.
problem
Favourite
Round and round and round
Age
11 to 14
Challenge level
Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?
problem
Favourite
Keep it simple
Age
11 to 14
Challenge level
Can all unit fractions be written as the sum of two unit fractions?
problem
Favourite
Countdown fractions
Age
11 to 16
Challenge level
Here is a chance to play a fractions version of the classic Countdown Game.
problem
Favourite
Going round in circles
Age
11 to 14
Challenge level
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
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
Strange Bank Account
Age
11 to 14
Challenge level
Imagine a very strange bank account where you are only allowed to do two things...
problem
Favourite
Making a difference
Age
11 to 14
Challenge level
How many different differences can you make?
game
Favourite
Up, down, flying around
Play this game to learn about adding and subtracting positive and negative numbers
problem
Favourite
Can you Make 100?
Age
11 to 14
Challenge level
How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?
problem
Favourite
Almost One
Age
11 to 14
Challenge level
Choose some fractions and add them together. Can you get close to 1?
problem
Favourite
Have you got it?
Age
11 to 14
Challenge level
Can you explain the strategy for winning this game with any target?
problem
Favourite
Egyptian Fractions
Age
11 to 14
Challenge level
The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.
problem
Favourite
Twisting and Turning
Age
11 to 14
Challenge level
Take a look at the video and try to find a sequence of moves that will untangle the ropes.
problem
Favourite
More Twisting and Turning
Age
11 to 16
Challenge level
It would be nice to have a strategy for disentangling any tangled ropes...
problem
Favourite
Connect Three
Age
11 to 16
Challenge level
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
problem
Favourite
Weights
Age
11 to 14
Challenge level
Different combinations of the weights available allow you to make different totals. Which totals can you make?
problem
Favourite
Impossibilities
Age
11 to 14
Challenge level
Just because a problem is impossible doesn't mean it's difficult...
problem
Favourite
Overlaps
Age
11 to 14
Challenge level
Can you find ways to put numbers in the overlaps so the rings have equal totals?
problem
Favourite
Same Answer
Age
11 to 14
Challenge level
Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?
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
Consecutive negative numbers
Age
11 to 14
Challenge level
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
problem
Favourite
the greedy algorithm
Age
11 to 14
Challenge level
The Egyptians expressed all fractions as the sum of different unit
fractions. The Greedy Algorithm might provide us with an efficient
way of doing this.
problem
Favourite
The Root of the Problem
Age
14 to 18
Challenge level
Find the sum of this series of surds.
Image
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.