Does this 'trick' for calculating multiples of 11 always work? Why or why not?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
56 406 is the product of two consecutive numbers. What are these two numbers?
Can you work out what a ziffle is on the planet Zargon?
Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?
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?
One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
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?
Can you make square numbers by adding two prime numbers together?
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.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
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!
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?
The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?
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?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
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?
Can you explain the strategy for winning this game with any target?
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?
Number problems at primary level that may require resilience.
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?
Number problems at primary level to work on with others.
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Got It game for an adult and child. How can you play so that you know you will always win?
Is there an efficient way to work out how many factors a large number has?
Can you work out some different ways to balance this equation?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
If you have only four weights, where could you place them in order to balance this equaliser?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
Can you find different ways of creating paths using these paving slabs?
An investigation that gives you the opportunity to make and justify predictions.