Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?
Find the sum of all three-digit numbers each of whose digits is odd.
Number problems at primary level that may require determination.
Number problems at primary level that require careful consideration.
Who said that adding couldn't be fun?
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?
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.
What is the sum of all the three digit whole numbers?
Use the information to work out how many gifts there are in each pile.
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
What is happening at each box in these machines?
Can you score 100 by throwing rings on this board? Is there more than way to do 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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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.
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
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?
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.
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?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Number problems at primary level to work on with others.
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
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?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
This task combines spatial awareness with addition and multiplication.
Find the next number in this pattern: 3, 7, 19, 55 ...
This number has 903 digits. What is the sum of all 903 digits?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
If the answer's 2010, what could the question be?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Can you find all the ways to get 15 at the top of this triangle of numbers?
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.
This challenge combines addition, multiplication, perseverance and even proof.
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!