Can you find all the different ways of lining up these Cuisenaire rods?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
If you have only four weights, where could you place them in order to balance this equaliser?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
Choose a symbol to put into the number sentence.
An environment which simulates working with Cuisenaire rods.
Can you complete this jigsaw of the multiplication square?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Can you find all the different triangles on these peg boards, and find their angles?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Find out what a "fault-free" rectangle is and try to make some of your own.
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Can you explain the strategy for winning this game with any target?
Use the interactivities to complete these Venn diagrams.
Here is a chance to play a version of the classic Countdown Game.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
Train game for an adult and child. Who will be the first to make the train?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
An interactive activity for one to experiment with a tricky tessellation
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .
Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?
Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?