Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
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
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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 explain the strategy for winning this game with any target?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This challenge asks you to imagine a snake coiling on itself.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
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?
Delight your friends with this cunning trick! Can you explain how
Got It game for an adult and child. How can you play so that you know you will always win?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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.
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Find out what a "fault-free" rectangle is and try to make some of
Here are two kinds of spirals for you to explore. What do you notice?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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.
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.
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.
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.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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?
This activity involves rounding four-digit numbers to the nearest thousand.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
An investigation that gives you the opportunity to make and justify
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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?