Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Find the sum of all three-digit numbers each of whose digits is odd.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
An investigation that gives you the opportunity to make and justify predictions.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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?
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?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
Can you explain how this card trick works?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Delight your friends with this cunning trick! Can you explain how it works?
In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
This challenge asks you to imagine a snake coiling on itself.
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?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
How many moves does it take to swap over some red and blue frogs? Do you have a method?
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
It starts quite simple but great opportunities for number discoveries and patterns!
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?