Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

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?

How many different symmetrical shapes can you make by shading triangles or squares?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

How many solutions can you find to this sum? Each of the different letters stands for a different number.

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

Find out about Magic Squares in this article written for students. Why are they magic?!

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?

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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.

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Given the products of diagonally opposite cells - can you complete this Sudoku?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

A Sudoku that uses transformations as supporting clues.

The clues for this Sudoku are the product of the numbers in adjacent squares.

Two sudokus in one. Challenge yourself to make the necessary connections.

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Two sudokus in one. Challenge yourself to make the necessary connections.

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?