Number problems at primary level that require careful consideration.
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?
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.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
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?
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?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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!
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
This dice train has been made using specific rules. How many different trains can you make?
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.
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!
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
Can you make square numbers by adding two prime numbers together?
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Ben has five coins in his pocket. How much money might he have?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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 substitute numbers for the letters in these sums?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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?
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
These two group activities use mathematical reasoning - one is numerical, one geometric.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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?
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.
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?
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.
Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?
This task follows on from Build it Up and takes the ideas into three dimensions!
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
You have 5 darts and your target score is 44. How many different ways could you score 44?