Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?
If the answer's 2010, what could the question be?
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.
Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?
Investigate what happens when you add house numbers along a street in different ways.
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
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.
Find all the numbers that can be made by adding the dots on two dice.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?
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.
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
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.
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!
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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!
At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?
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?
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.
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
Find the next number in this pattern: 3, 7, 19, 55 ...
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
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!
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
You have 5 darts and your target score is 44. How many different ways could you score 44?
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
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?
This number has 903 digits. What is the sum of all 903 digits?
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?