Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
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.
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?
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?
Are these statements always true, sometimes true or never true?
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.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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?
Try out this number trick. What happens with different starting numbers? What do you notice?
Find the sum of all three-digit numbers each of whose digits is odd.
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?
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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. . . .
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
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?
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?
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?
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Here are two kinds of spirals for you to explore. What do you notice?
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.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
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?
Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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.
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?
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.
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?
A collection of games on the NIM theme
This activity involves rounding four-digit numbers to the nearest thousand.
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?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
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.
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?
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 task follows on from Build it Up and takes the ideas into three dimensions!