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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
Can you make square numbers by adding two prime numbers together?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
You have 5 darts and your target score is 44. How many different ways could you score 44?
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?
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Can you follow the rule to decode the messages?
Investigate the different distances of these car journeys and find out how long they take.
Dotty Six is a simple dice game that you can adapt in many ways.
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This task follows on from Build it Up and takes the ideas into three dimensions!
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Try out some calculations. Are you surprised by the results?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Got It game for an adult and child. How can you play so that you know you will always win?
Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?
How would you count the number of fingers in these pictures?
If the answer's 2010, what could the question be?
Number problems at primary level that may require resilience.
Number problems at primary level to work on with others.