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?
Investigate the different distances of these car journeys and find out how long they take.
This article for teachers suggests ideas for activities built around 10 and 2010.
If you have only four weights, where could you place them in order to balance this equaliser?
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!
A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?
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?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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?
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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?
Replace each letter with a digit to make this addition correct.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
These two group activities use mathematical reasoning - one is numerical, one geometric.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
Can you substitute numbers for the letters in these sums?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
An environment which simulates working with Cuisenaire rods.
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?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
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?
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.