What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
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?
Number problems at primary level that may require resilience.
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
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?
56 406 is the product of two consecutive numbers. What are these two 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?
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?
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?
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
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?
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?
An investigation that gives you the opportunity to make and justify predictions.
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
Can you find a way to identify times tables after they have been shifted up or down?
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.
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?
Can you find different ways of creating paths using these paving slabs?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Is there an efficient way to work out how many factors a large number has?
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?
Given the products of adjacent cells, can you complete this Sudoku?
Can you find any perfect numbers? Read this article to find out more...
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
How many different sets of numbers with at least four members can you find in the numbers in this box?
Number problems at primary level to work on with others.
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?
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .
Can you make square numbers by adding two prime numbers together?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?"
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
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 find any two-digit numbers that satisfy all of these statements?
Follow the clues to find the mystery number.
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
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?
"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 ...?