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?
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 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?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
"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 ...?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
An investigation that gives you the opportunity to make and justify predictions.
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.
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
How many different sets of numbers with at least four members can you find in the numbers in this box?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Got It game for an adult and child. How can you play so that you know you will always win?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
Can you work out some different ways to balance this equation?
Can you explain the strategy for winning this game with any target?
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.
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
Number problems at primary level that may require resilience.
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
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. . . .
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?
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 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?
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?
If you have only four weights, where could you place them in order to balance this equaliser?
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 complete this jigsaw of the multiplication square?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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?
Are these statements always true, sometimes true or never true?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...
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?
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?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
Number problems at primary level to work on with others.
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?