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?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
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
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?
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 each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Find the sum of all three-digit numbers each of whose digits is
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
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 many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Find out what a "fault-free" rectangle is and try to make some of
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
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?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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?
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?
Delight your friends with this cunning trick! Can you explain how
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
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.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Can you find the values at the vertices when you know the values on
How many moves does it take to swap over some red and blue frogs? Do you have a method?
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?
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?
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.
Triangle numbers can be represented by a triangular array of
squares. What do you notice about the sum of identical triangle
An investigation that gives you the opportunity to make and justify
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
This activity involves rounding four-digit numbers to the nearest thousand.
What happens when you round these three-digit numbers to the nearest 100?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
How many different journeys could you make if you were going to
visit four stations in this network? How about if there were five
stations? Can you predict the number of journeys for seven
This challenge asks you to imagine a snake coiling on itself.
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?
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.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.