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?
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 happening at each box in these machines?
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.
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?
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.
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come 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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
This number has 903 digits. What is the sum of all 903 digits?
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.
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
What is the sum of all the three digit whole numbers?
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?
Number problems at primary level to work on with others.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
Use the information to work out how many gifts there are in each pile.
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.
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?
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?
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?
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
This task combines spatial awareness with addition and multiplication.
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?
Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
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?
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?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
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?
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
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.
Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?
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.