Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
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?
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?
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?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Can you explain the strategy for winning this game with any target?
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 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.
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
Can you find all the ways to get 15 at the top of this triangle of numbers?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
This activity involves rounding four-digit numbers to the nearest thousand.
This task follows on from Build it Up and takes the ideas into three dimensions!
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 it works?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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.
Find out what a "fault-free" rectangle is and try to make some of your own.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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.
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?
This challenge asks you to imagine a snake coiling on itself.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
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?
Got It game for an adult and child. How can you play so that you know you will always win?
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.
An investigation that gives you the opportunity to make and justify predictions.
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Can you explain how this card trick works?
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 moves.
Find the sum of all three-digit numbers each of whose digits is odd.
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. . . .
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?