Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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 horizontal axis?
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?
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?
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Got It game for an adult and child. How can you play so that you know you will always win?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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 your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This task follows on from Build it Up and takes the ideas into three dimensions!
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 find all the ways to get 15 at the top of this triangle of numbers?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
This activity involves rounding four-digit numbers to the nearest thousand.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Delight your friends with this cunning trick! Can you explain how it works?
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?
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?
Can you explain the strategy for winning this game with any target?
Find the sum of all three-digit numbers each of whose digits is odd.
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 happens?
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?
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle 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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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?
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.
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
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 stations?
Here are two kinds of spirals for you to explore. What do you notice?
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?