In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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?
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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.
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
How many centimetres of rope will I need to make another mat just
like the one I have here?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
An investigation that gives you the opportunity to make and justify
Find out what a "fault-free" rectangle is and try to make some of
This challenge is about finding the difference between numbers which have the same tens digit.
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?
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 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 challenge asks you to imagine a snake coiling on itself.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
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?
Find the sum of all three-digit numbers each of whose digits is
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?
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
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Can you work out how to win this game of Nim? Does it matter if you go first or second?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any 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.
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.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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 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 this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Got It game for an adult and child. How can you play so that you know you will always win?
It starts quite simple but great opportunities for number discoveries and patterns!
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
This activity involves rounding four-digit numbers to the nearest thousand.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?