Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
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 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?
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?
Here is a chance to play a version of the classic Countdown Game.
If you have only four weights, where could you place them in order to balance this equaliser?
Can you explain the strategy for winning this game with any target?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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?
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?
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
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?
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....?
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
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?
Can you complete this jigsaw of the multiplication square?
A generic circular pegboard resource.
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
A collection of resources to support work on Factors and Multiples at Secondary level.
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
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.
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?
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 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.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Choose a symbol to put into the number sentence.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Use the interactivities to complete these Venn diagrams.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
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?
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?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Train game for an adult and child. Who will be the first to make the train?
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?