Can you go through this maze so that the numbers you pass add to exactly 100?
Try out this number trick. What happens with different starting numbers? What do you notice?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Max and Mandy put their number lines together to make a graph. How far had each of them moved along and up from 0 to get the counter to the place marked?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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?
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?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
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.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?
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.
Find the sum of all three-digit numbers each of whose digits is odd.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
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?
These two group activities use mathematical reasoning - one is numerical, one geometric.
Number problems at primary level that require careful consideration.
Can you make square numbers by adding two prime numbers together?
Can you substitute numbers for the letters in these sums?
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.
A game for 2 players. Practises subtraction or other maths operations knowledge.
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?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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.
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?
Ben has five coins in his pocket. How much money might he have?
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?
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!
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
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!
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
This dice train has been made using specific rules. How many different trains can you make?
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
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?
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?
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
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?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?