If you have only four weights, where could you place them in order to balance this equaliser?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
Can you complete this jigsaw of the multiplication square?
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 activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
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?
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
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?
You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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 will you work out which numbers have been used to create this multiplication square?
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?
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 trains can you make which are the same length as Matt's and Katie's, using rods that are identical?
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 work out how to balance this equaliser? You can put more than one weight on a hook.
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.
One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?
How many different rectangles can you make using this set of rods?
This activity focuses on doubling multiples of five.
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
56 406 is the product of two consecutive numbers. What are these two numbers?
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
Number problems at primary level to work on with others.
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?
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.
Help share out the biscuits the children have made.
I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?
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?
Play this game and see if you can figure out the computer's chosen number.
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?
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?
Number problems at primary level that may require resilience.
This article for teachers describes how number arrays can be a useful representation for many number concepts.
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Can you find different ways of creating paths using these paving slabs?