Develop your skills in systematic mathematical enquiry

Explore a task from our Wild site on each day in the run up to Christmas

We have been exploring what mastering mathematics in the context of problem solving means to us at NRICH.

Resources to accompany NRICH team presentations at UKMT 2015 Teacher Meetings.

NQT Inspiration Day: Nurturing Creative Problem Solvers - Summer 2015 event in Cambridge

Develop your skills of mathematical argument and proof.

Develop your skills of visualisation of mathematical objects

Resources to accompany Tabitha's and Charlie's workshops at the Prince's Teaching Institute's New Teacher Days.

Resources to accompany Fran's and Charlie's workshops at the ATM & MA Easter Conferences.

These CMEP resources explore the proof and use of trigonometric identities.

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

Discover how different mathematical representations can help us to understand mathematical objects.

Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.

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?

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

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?

Can you locate these values on this interactive logarithmic scale?

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

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

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

Can you build a distribution with the maximum theoretical spread?

Draw graphs of the sine and modulus functions and explain the humps.

There are many different methods to solve this geometrical problem - how many can you find?

Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?

To break down an algebraic fraction into partial fractions in which all the denominators are linear and all the numerators are constants you sometimes need complex numbers.

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

Can you find the area of the central part of this shape? Can you do it in more than one way?

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.

A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?

How fast would you have to throw a ball upwards so that it would never land?

At what positions and speeds can the bomb be dropped to destroy the dam?

This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different?. . . .

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.

How high will a ball taking a million seconds to fall travel?

Can you work out the equations of the trig graphs I used to make my pattern?

Can you work out which of the equations models a bouncing bomb? Will you be able to hit the target?

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

Solve these differential equations to see how a minus sign can change the answer

We asked what was the most interesting fact that you can find out about the number 2009. See the solutions that were submitted.

It is believed that weaker snooker players have a better chance of winning matches over eleven frames (i.e. first to win 6 frames) than they do over fifteen frames. Is this true?

Given the equation for the path followed by the back wheel of a bike, can you solve to find the equation followed by the front wheel?

Look at the advanced way of viewing sin and cos through their power series.

This is our secondary collection of favourite mathematics and sport materials.

Infinity is not a number, and trying to treat it as one tends to be a pretty bad idea. At best you're likely to come away with a headache, at worse the firm belief that 1 = 0. This article discusses. . . .

This is our collection of favourite mathematics and sport materials.

Are these statistical statements sometimes, always or never true? Or it is impossible to say?