If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
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?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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?
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
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.
This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Find out what a "fault-free" rectangle is and try to make some of
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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?
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?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
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 asks you to imagine a snake coiling on itself.
Here are two kinds of spirals for you to explore. What do you notice?
This challenge is about finding the difference between numbers which have the same tens digit.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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.
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?
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?
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.
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.
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?