Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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 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 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!
Got It game for an adult and child. How can you play so that you know you will always win?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Can you find all the ways to get 15 at the top of this triangle of numbers?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Find out what a "fault-free" rectangle is and try to make some of
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
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 the sum of all three-digit numbers each of whose digits is
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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.
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
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.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle 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?
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?
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.
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.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
An investigation that gives you the opportunity to make and justify
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?
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Delight your friends with this cunning trick! Can you explain how
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 activity involves rounding four-digit numbers to the nearest thousand.
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.