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?
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
The Zargoes use almost the same alphabet as English. What does this birthday message say?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.