Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
Try out this number trick. What happens with different starting numbers? What do you notice?
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?
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?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Ben’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?
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?
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?
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
This task follows on from Build it Up and takes the ideas into three dimensions!
Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
An investigation that gives you the opportunity to make and justify predictions.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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.
What happens when you round these three-digit numbers to the nearest 100?
This challenge is about finding the difference between numbers which have the same tens digit.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Are these statements always true, sometimes true or never true?
Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?
This activity involves rounding four-digit numbers to the nearest thousand.
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 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?
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
What happens when you round these numbers to the nearest whole number?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
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.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?