How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
How many different sets of numbers with at least four members can you find in the numbers in this box?
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?
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?
An investigation that gives you the opportunity to make and justify predictions.
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.
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
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 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.
56 406 is the product of two consecutive numbers. What are these two numbers?
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
If you have only four weights, where could you place them in order to balance this equaliser?
Number problems at primary level to work on with others.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
Can you find any perfect numbers? Read this article to find out more...
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?
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?
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.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Number problems at primary level that may require determination.
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?
Can you make square numbers by adding two prime numbers together?
Got It game for an adult and child. How can you play so that you know you will always win?
"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 ...?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
Follow the clues to find the mystery number.
Can you work out some different ways to balance this equation?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
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?
Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
An environment which simulates working with Cuisenaire rods.
Have a go at balancing this equation. Can you find different ways of doing it?
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
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?
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?