N people visit their friends staying N kilometres along the coast. Some walk along the cliff path at N km an hour, the rest go by car. How long is the road?

How many noughts are at the end of these giant numbers?

How can you work out the equation of a parabola just by looking at key features of its graph?

If you know some information about a parabola, can you work out its equation?

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

Can you find out in which order the children are standing in this line?

Can you find the solution to this equation? Each of the different letters stands for a different number.

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Have you seen this way of doing multiplication ?

A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed .

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

Resources to accompany Charlie's NRICH workshop at NEU's Celebrating Education Conference.

This problem explores the shapes and symmetries in some national flags.

The activities on this page are based on those written for the National Young Mathematicians' Award.

Helen Joyce interviews the neuropsychologist Brian Butterworth whose research has shown that we are all born with a "built-in" sense of cardinal number.

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Can you find the value of this expression, which contains infinitely nested square roots?

The diagram shows the net of a cube. Which edge meets the edge X when the net is folded to form the cube?

The net shown here is cut out and folded to form a cube. Which face is then opposite the face marked X?

Without taking your pencil off the paper or going over a line or passing through one of the points twice, can you follow each of the networks?

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.

This article discusses the revised Early Learning Goals for mathematics which were announced in June 2018.

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?

We hope the new ideas and situations in these activities will make you curious to know more.

Can you match up the entries from this table of units?

From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

Find the next number in this pattern: 3, 7, 19, 55 ...

The challenge for you is to make a string of six (or more!) graded cubes.

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

There are nasty versions of this dice game but we'll start with the nice ones...

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?