Are these statements relating to odd and even numbers always true, sometimes true or never true?
Here are two kinds of spirals for you to explore. What do you notice?
Are these statements always true, sometimes true or never true?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. 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 ...?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
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?
This challenge asks you to imagine a snake coiling on itself.
An investigation that gives you the opportunity to make and justify
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 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.
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?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Got It game for an adult and child. How can you play so that you know you will always win?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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.
A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.
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?
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?
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.
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.
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
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.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Find out what a "fault-free" rectangle is and try to make some of
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
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.
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
A game for 2 players with similaritlies to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.
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
Delight your friends with this cunning trick! Can you explain how
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
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?