What is the difference between the sum of the first 2014 odd numbers and the sum of the first 2014 even numbers?

A collection of short Stage 3 and 4 problems on Posing Questions and Making Conjectures.

Page of resources for STEP Prep Summer School 2014

Are you at risk of being a victim of crime? How does your perception of that risk compare with the facts and figures?

Resources to accompany NRICH team presentations at UKMT 2014 Teacher Meetings.

Consider two arithmetic sequences: 1998, 2005, 2012,... and 1996, 2005, 2014,... Which numbers will appear in both?

This challenge combines addition, multiplication, perseverance and even proof.

This task combines spatial awareness with addition and multiplication.

A collection of short Stage 3 and 4 problems on Representing.

All the activities in this year's primary Advent Calendar have a food or drink theme. Yum yum!

A collection of short Stage 3 and 4 problems on Thinking Strategically.

This brief article, written for upper primary students and their teachers, explains what the Young Mathematicians' Award is and links to all the related resources on NRICH.

A collection of short Stage 3 and 4 problems on Mathematical Modelling.

A mathematical challenge for each day during the run-up to Christmas.

Problem Solving Unpacked: Engage, Inspire and Motivate all students. Resources from the one day conference held at CMS in December 2014.

Resources from Charlie's Science Festival sessions, March 2014

Read a range of reports from different schools about embedding rich mathematics in their setting

A collection of short problems on Pythagoras's Theorem and Trigonometry.

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

A collection of short Stage 3 and 4 problems on Working Systematically.

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

A collection of short problems on number operations and calculation methods.

Develop your skills of visualisation of mathematical objects

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?

A collection of short problems on patterns and sequences.

This feature focuses on generalising and proving.

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

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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.