Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
This article for teachers suggests ideas for activities built around 10 and 2010.
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?
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?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you complete this jigsaw of the multiplication square?
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
What is the sum of all the three digit whole numbers?
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?
Can you replace the letters with numbers? Is there only one solution in each case?
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.
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
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.
All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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 work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
What is happening at each box in these machines?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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!
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. . . .
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
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.
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 group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
If the answer's 2010, what could the question be?
Here is a chance to play a version of the classic Countdown Game.
Choose a symbol to put into the number sentence.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
This problem is designed to help children to learn, and to use, the two and three times tables.