Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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.
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 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?
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Number problems at primary level that require careful consideration.
Number problems at primary level that may require determination.
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?
This number has 903 digits. What is the sum of all 903 digits?
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
What is happening at each box in these machines?
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Use the information to work out how many gifts there are in each pile.
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
If the answer's 2010, what could the question be?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
Have a go at balancing this equation. Can you find different ways of doing it?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
What is the sum of all the three digit whole numbers?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
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.
This task combines spatial awareness with addition and multiplication.
Can you work out some different ways to balance this equation?
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?
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!
There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?