Strike it Out game for an adult and child. Can you stop your partner from being able to go?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

This task follows on from Build it Up and takes the ideas into three dimensions!

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

This challenge is about finding the difference between numbers which have the same tens digit.

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Find the sum of all three-digit numbers each of whose digits is odd.

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?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Got It game for an adult and child. How can you play so that you know you will always win?

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

Here are two kinds of spirals for you to explore. What do you notice?

Find out what a "fault-free" rectangle is and try to make some of your own.

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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

This challenge asks you to imagine a snake coiling on itself.

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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

An investigation that gives you the opportunity to make and justify predictions.

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Can you work out how to win this game of Nim? Does it matter if you go first or second?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

What happens when you round these three-digit numbers to the nearest 100?

Nim-7 game for an adult and child. Who will be the one to take the last counter?