How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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.

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?

Can you explain the strategy for winning this game with any target?

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Here is a chance to play a version of the classic Countdown Game.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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?

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. . . .

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.

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

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?

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?

Match pairs of cards so that they have equivalent ratios.

A collection of resources to support work on Factors and Multiples at Secondary level.

Can you complete this jigsaw of the multiplication square?

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!

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?

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?

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

If you have only four weights, where could you place them in order to balance this equaliser?

Find out what a "fault-free" rectangle is and try to make some of your own.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

Here is a chance to play a fractions version of the classic Countdown Game.

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.

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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?

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....?

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

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?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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?