This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This is an adding game for two players.
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?
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?
Find the sum of all three-digit numbers each of whose digits is odd.
This task follows on from Build it Up and takes the ideas into three dimensions!
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?
Can you substitute numbers for the letters in these sums?
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
You have 5 darts and your target score is 44. How many different ways could you score 44?
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
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!
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
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?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
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.
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
These two group activities use mathematical reasoning - one is numerical, one geometric.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Find the next number in this pattern: 3, 7, 19, 55 ...
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Number problems at primary level that require careful consideration.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Investigate the different distances of these car journeys and find out how long they take.
In this game for two players, the aim is to make a row of four coins which total one dollar.
Can you follow the rule to decode the messages?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?