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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
If you have only four weights, where could you place them in order to balance this equaliser?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Here is a chance to play a version of the classic Countdown Game.
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!
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?
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
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?
Choose a symbol to put into the number sentence.
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?
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?
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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....?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
An environment which simulates working with Cuisenaire rods.
A collection of resources to support work on Factors and Multiples at Secondary level.
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.
Work out the fractions to match the cards with the same amount of money.
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.
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
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?
Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
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 interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Can you find all the different triangles on these peg boards, and find their angles?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
A generic circular pegboard resource.
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?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
Can you complete this jigsaw of the multiplication square?
How many different triangles can you make on a circular pegboard that has nine pegs?
Try out the lottery that is played in a far-away land. What is the chance of winning?
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.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Can you coach your rowing eight to win?