Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
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?
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.
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 and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Try out this number trick. What happens with different starting numbers? What do you notice?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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.
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?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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. . . .
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
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.
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Surprise your friends with this magic square trick.
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?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
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.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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?
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.
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
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.
Are these statements always true, sometimes true or never true?
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
Nim-7 game for an adult and child. Who will be the one to take the last counter?