Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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.
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?
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. . . .
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?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Can you explain the strategy for winning this game with any target?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Try out this number trick. What happens with different starting numbers? What do you notice?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
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.
Got It game for an adult and child. How can you play so that you know you will always win?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
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?
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.
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?
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
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?
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?
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. . . .
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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
An investigation that gives you the opportunity to make and justify predictions.
What happens when you round these three-digit numbers to the nearest 100?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
This challenge asks you to imagine a snake coiling on itself.
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.
This activity involves rounding four-digit numbers to the nearest thousand.
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
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. . . .
This task encourages you to investigate the number of edging pieces and panes in different sized windows.