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.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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 substitute numbers for the letters in these sums?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Number problems at primary level that require careful consideration.
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 task follows on from Build it Up and takes the ideas into three dimensions!
Using the statements, can you work out how many of each type of rabbit there are in these pens?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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!
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?
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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?
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?
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 multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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.
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
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!
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?
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.
Ben has five coins in his pocket. How much money might he have?
Can you find all the ways to get 15 at the top of this triangle of numbers?
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.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
Can you use the information to find out which cards I have used?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
This dice train has been made using specific rules. How many different trains can you make?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!