Can you find different ways of creating paths using these paving slabs?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
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?
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?
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?
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?
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?
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?
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?
An investigation that gives you the opportunity to make and justify predictions.
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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.
Can you make square numbers by adding two prime numbers together?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Number problems at primary level that may require resilience.
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?
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?
Number problems at primary level to work on with others.
Are these statements always true, sometimes true or never true?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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.
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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.
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Given the products of adjacent cells, can you complete this Sudoku?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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.
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Follow the clues to find the mystery number.
How many different sets of numbers with at least four members can you find in the numbers in this box?
How many different rectangles can you make using this set of rods?
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?"
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 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?
"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 ...?
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?