Number problems at primary level that may require resilience.
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?
What is the sum of all the three digit whole numbers?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
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?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?
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?
What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
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.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Use the information to work out how many gifts there are in each pile.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
What is the sum of all the digits in all the integers from one to one million?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Got It game for an adult and child. How can you play so that you know you will always win?
Number problems at primary level to work on with others.
Investigate the different distances of these car journeys and find out how long they take.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?
This number has 903 digits. What is the sum of all 903 digits?
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This task follows on from Build it Up and takes the ideas into three dimensions!
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
Can you make square numbers by adding two prime numbers together?
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?
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?
Replace each letter with a digit to make this addition correct.
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?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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?
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?
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?
Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?