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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This activity involves rounding four-digit numbers to the nearest thousand.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Find out what a "fault-free" rectangle is and try to make some of
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Delight your friends with this cunning trick! Can you explain how
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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?
Can you explain the strategy for winning this game with any target?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Find the sum of all three-digit numbers each of whose digits is
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?
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
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
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 continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
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.
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