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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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 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.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
Can you work out some different ways to balance this equation?
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?
Number problems at primary level that may require resilience.
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 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.
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?
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?
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?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
Follow the clues to find the mystery number.
"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?
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?
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.
Can you complete this jigsaw of the multiplication square?
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
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?
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?
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Number problems at primary level to work on with others.
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Given the products of adjacent cells, can you complete this Sudoku?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
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.
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.
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.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?
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?"