Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

Let N be the smallest positive integer whose digits add up to 2015. What is the sum of the digits of N+1?

Amy misread a question and got an incorrect answer. What should the answer have be?

Schools around the world are invited to take part in a Maths and Science lesson hoping to set a Guinness World Record.

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.

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

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

Which parts of these framework bridges are in tension and which parts are in compression?

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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?

In how many ways can you fit all three pieces together to make shapes with line symmetry?

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

Prove that 3 times the sum of 3 squares is the sum of 4 squares. Rather easier, can you prove that twice the sum of two squares always gives the sum of two squares?

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

In this short problem we investigate the tensions and compressions in a framework made from springs and ropes.

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

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?

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

Can you locate these values on this interactive logarithmic scale?

Explore the effect of reflecting in two parallel mirror lines.

Which of these games would you play to give yourself the best possible chance of winning a prize?

Do you have enough information to work out the area of the shaded quadrilateral?

When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.

The Tower of Hanoi is an ancient mathematical challenge.

You are organising a school trip and you need to write a letter to parents to let them know about the day. Use the cards to gather all the information you need.

Explore the effect of combining enlargements.

This short question asks if you can work out the most precarious way to balance four tiles.

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

Can you build a distribution with the maximum theoretical spread?

Can you make square numbers by adding two prime numbers together?