Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Find out what a "fault-free" rectangle is and try to make some of
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
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?
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.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Delight your friends with this cunning trick! Can you explain how
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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 work out how to win this game of Nim? Does it matter if you go first or second?
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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.
Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
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 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.
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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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 a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
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?
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.
This task follows on from Build it Up and takes the ideas into three dimensions!
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Can you find all the ways to get 15 at the top of this triangle of numbers?
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?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
We can show that (x + 1)² = x² + 2x + 1 by considering
the area of an (x + 1) by (x + 1) square. Show in a similar way
that (x + 2)² = x² + 4x + 4
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 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.
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
A collection of games on the NIM theme