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 use the information to find out which cards I have used?

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?

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?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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?

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?

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.

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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?

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?

You have 5 darts and your target score is 44. How many different ways could you score 44?

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?

Can you make square numbers by adding two prime numbers together?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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?

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.

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant 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?

A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?

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?

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!

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

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.

These two group activities use mathematical reasoning - one is numerical, one geometric.

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

This task follows on from Build it Up and takes the ideas into three dimensions!

Can you find all the ways to get 15 at the top of this triangle of numbers?

This dice train has been made using specific rules. How many different trains can you make?

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?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.