This challenge encourages you to explore dividing a three-digit number by a single-digit number.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
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'.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Surprise your friends with this magic square trick.
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
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.
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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.
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?
This challenge asks you to imagine a snake coiling on itself.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
An investigation that gives you the opportunity to make and justify predictions.
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?
It starts quite simple but great opportunities for number discoveries and patterns!
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
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?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
Try out this number trick. What happens with different starting numbers? What do you notice?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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.
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
Find the sum of all three-digit numbers each of whose digits is odd.
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?