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.
Can you make square numbers by adding two prime numbers together?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Number problems at primary level that may require resilience.
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Use the information to work out how many gifts there are in each pile.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
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?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
What is the sum of all the three digit whole numbers?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
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!
Find the sum of all three-digit numbers each of whose digits is odd.
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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?
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.
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Can you substitute numbers for the letters in these sums?
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?
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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!
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
This dice train has been made using specific rules. How many different trains can you make?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
Investigate the different distances of these car journeys and find out how long they take.