Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
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?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
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.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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.
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?
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?
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 task follows on from Build it Up and takes the ideas into three dimensions!
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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
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?
An investigation that gives you the opportunity to make and justify
Here are two kinds of spirals for you to explore. What do you notice?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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.
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Find out what a "fault-free" rectangle is and try to make some of
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
This challenge asks you to imagine a snake coiling on itself.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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?
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.
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. . . .
Strike it Out game for an adult and child. Can you stop your partner from being able to go?