Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?
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?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
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?
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.
Is there an efficient way to work out how many factors a large number has?
Are these statements always true, sometimes true or never true?
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. . . .
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Try out this number trick. What happens with different starting numbers? What do you notice?
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?
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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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.
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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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. . . .
An investigation that gives you the opportunity to make and justify predictions.
Here are two kinds of spirals for you to explore. What do you notice?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
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.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
This task follows on from Build it Up and takes the ideas into three dimensions!
These tasks give learners chance to generalise, which involves identifying an underlying structure.
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 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.
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. . . .
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Surprise your friends with this magic square trick.
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?
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?
Can you explain the strategy for winning this game with any target?