Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
If the answer's 2010, what could the question be?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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?
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.
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?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
What is the sum of all the three digit whole 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?
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?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
This number has 903 digits. What is the sum of all 903 digits?
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?
Number problems at primary level that require careful consideration.
Number problems at primary level that may require resilience.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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.
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
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?
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.
This task combines spatial awareness with addition and multiplication.
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?
Use the information to work out how many gifts there are in each pile.
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 happening at each box in these machines?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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.
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?
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?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .
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 the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
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?
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?
Can you complete this jigsaw of the multiplication square?
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!
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?