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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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.
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?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
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.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
An investigation that gives you the opportunity to make and justify
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Find out what a "fault-free" rectangle is and try to make some of
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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 challenge asks you to imagine a snake coiling on itself.
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 activity involves rounding four-digit numbers to the nearest thousand.
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Find the sum of all three-digit numbers each of whose digits is
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
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.
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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?
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
Can you explain how this card trick works?
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .