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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
How many different rectangles can you make using this set of rods?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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.
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.
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
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 investigation that gives you the opportunity to make and justify predictions.
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?
"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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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 work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
How many different sets of numbers with at least four members can you find in the numbers in this box?
Can you make square numbers by adding two prime numbers together?
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.
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?
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?
Given the products of diagonally opposite cells - can you complete this Sudoku?
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
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?
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?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Can you complete this jigsaw of the multiplication square?
If you have only four weights, where could you place them in order to balance this equaliser?
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?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Follow the clues to find the mystery number.
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
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.
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
This article for teachers describes how number arrays can be a useful representation for many number concepts.
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
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?
Number problems at primary level that may require resilience.
Number problems at primary level to work on with others.
Can you find different ways of creating paths using these paving slabs?
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?