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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Choose a symbol to put into the number sentence.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
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?
Can you hang weights in the right place to make the equaliser balance?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
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?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
If you have only four weights, where could you place them in order to balance this equaliser?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Here is a chance to play a version of the classic Countdown Game.
There are nasty versions of this dice game but we'll start with the nice ones...
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?
Find all the numbers that can be made by adding the dots on two dice.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
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!
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?
Use the number weights to find different ways of balancing the equaliser.
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?
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?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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!
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
Investigate the different distances of these car journeys and find out how long they take.
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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?