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?
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?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Got It game for an adult and child. How can you play so that you know you will always win?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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.
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?
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?
An investigation that gives you the opportunity to make and justify
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Find out what a "fault-free" rectangle is and try to make some of
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Here are two kinds of spirals for you to explore. What do you notice?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Are these statements always true, sometimes true or never true?
This task follows on from Build it Up and takes the ideas into three dimensions!
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
This activity focuses on rounding to the nearest 10.
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?
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
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?
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.
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.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Stop the Clock game for an adult and child. How can you make sure you always win this game?
This challenge asks you to imagine a snake coiling on itself.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
This challenge is about finding the difference between numbers which have the same tens digit.
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.
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.
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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.