Daisy and Akram were making number patterns. Daisy was using beads that looked like flowers and Akram was using cube bricks. First they were counting in twos.

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Think of a number... follow the machine's instructions. I know what your number is! Can you explain how I know?

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

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?

Explore the two quadratic functions and find out how their graphs are related.

Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?

Here are some more quadratic functions to explore. How are their graphs related?

The NRICH Stage 5 weekly challenges are shorter problems aimed at Post-16 students or enthusiastic younger students. There are 52 of them.

Find the relationship between the locations of points of inflection, maxima and minima of functions.

Consider these analogies for helping to understand key concepts in calculus.

Observe symmetries and engage the power of substitution to solve complicated equations.

Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!

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

Many of you worked out where you would stand to be chosen, no matter how many people are in the group. Fantastic!

Several of you worked out methods of calculating the number of L triominoes needed to tile different sizes of L triominoes.

Herschel sent us a lovely clear explanation using algebra to explain why the areas were the same.

Most primary teachers are not maths specialists. Do letters seem threatening when they are not in words? How can we minimise what seems to be the difference between primary and secondary approaches to the beginning of algebra?

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.

Step back and reflect! This article reviews techniques such as substitution and change of coordinates which enable us to exploit underlying structures to crack problems.