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?
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
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?
This article for teachers suggests ideas for activities built around 10 and 2010.
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
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 triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
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 game that tests your understanding of remainders.
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
Can you replace the letters with numbers? Is there only one solution in each case?
Here is a chance to play a version of the classic Countdown Game.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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?
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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?
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?
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
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!
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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.
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,. . . .
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Choose a symbol to put into the number sentence.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Given the products of adjacent cells, can you complete this Sudoku?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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!
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
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?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
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?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using 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?
Unmultiply is a game of quick estimation. You need to find two numbers that multiply together to something close to the given target - fast! 10 levels with a high scores table.