Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Can you each work out the number on your card? What do you notice? How could you sort the cards?
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Can you hang weights in the right place to make the equaliser balance?
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.
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.
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?
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?
Investigate what happens when you add house numbers along a street in different ways.
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
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?
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.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
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?
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?
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!
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
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?
Find all the numbers that can be made by adding the dots on two dice.
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?
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?
This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?
If the answer's 2010, what could the question be?
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?
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.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.
Can you use the information to find out which cards I have used?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Choose a symbol to put into the number sentence.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
If you have only four weights, where could you place them in order to balance this equaliser?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?