Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
If you have only four weights, where could you place them in order to balance this equaliser?
Can you complete this jigsaw of the multiplication square?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
A game in which players take it in turns to choose a number. Can you block your opponent?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
A game that tests your understanding of remainders.
Use the interactivities to complete these Venn diagrams.
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?
Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?
In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?
Given the products of adjacent cells, can you complete this Sudoku?
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
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...
Can you make square numbers by adding two prime numbers together?
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
Can you work out what a ziffle is on the planet Zargon?
56 406 is the product of two consecutive numbers. What are these two numbers?
An environment which simulates working with Cuisenaire rods.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?
Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.