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?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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?
How many moves does it take to swap over some red and blue frogs? Do you have a method?
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?
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
Find out what a "fault-free" rectangle is and try to make some of
What would be the smallest number of moves needed to move a Knight
from a chess set from one corner to the opposite corner of a 99 by
99 square board?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle 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?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
Imagine a large cube made from small red cubes being dropped into a
pot of yellow paint. How many of the small cubes will have yellow
paint on their faces?
Delight your friends with this cunning trick! Can you explain how
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 work out how to win this game of Nim? Does it matter if you go first or second?
Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
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
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.
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.
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Find the sum of all three-digit numbers each of whose digits is
With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.
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?
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?
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.
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
A collection of games on the NIM theme
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Can you find the values at the vertices when you know the values on
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?
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.