Can you find a way of counting the spheres in these arrangements?
Watch this animation. What do you see? Can you explain why this happens?
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?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Delight your friends with this cunning trick! Can you explain how it works?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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?
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?
Can you explain how this card trick works?
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 ...?
Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
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?
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?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?
Can you describe this route to infinity? Where will the arrows take you next?
This challenge asks you to imagine a snake coiling on itself.
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!
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?
How many moves does it take to swap over some red and blue frogs? Do you have a method?
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Got It game for an adult and child. How can you play so that you know you will always win?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Find out what a "fault-free" rectangle is and try to make some of your own.
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 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.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.