Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
What is the sum of all the three digit whole numbers?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal 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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
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?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?
Use the information to work out how many gifts there are in each pile.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Investigate the different distances of these car journeys and find out how long they take.
Generate large numbers then give the values of each digit.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
Number problems at primary level that may require resilience.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Find the next number in this pattern: 3, 7, 19, 55 ...
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
What is happening at each box in these machines?
If the answer's 2010, what could the question be?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Number problems at primary level to work on with others.
How would you count the number of fingers in these pictures?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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 challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?
Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?
This task follows on from Build it Up and takes the ideas into three dimensions!
Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
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?
Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
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?