Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
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?
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?
56 406 is the product of two consecutive numbers. What are these two numbers?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
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?
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?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
Are these domino games fair? Can you explain why or why not?
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?
Can you make square numbers by adding two prime numbers together?
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?
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.
How many different sets of numbers with at least four members can you find in the numbers in this box?
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?
Can you work out what a ziffle is on the planet Zargon?
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.
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
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?
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?
The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.
An investigation that gives you the opportunity to make and justify predictions.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
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?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
Can you find what the last two digits of the number $4^{1999}$ are?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
Given the products of adjacent cells, can you complete this Sudoku?
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
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?
What is the smallest number with exactly 14 divisors?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
If you have only four weights, where could you place them in order to balance this equaliser?
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?
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?
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!
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?