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?
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?
Number problems at primary level that may require resilience.
Number problems at primary level to work on with others.
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?
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?
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Number problems at primary level that require careful consideration.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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?
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.
What is the sum of all the three digit whole numbers?
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.
What is happening at each box in these machines?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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?
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 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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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.
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.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Use the information to work out how many gifts there are in each pile.
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?
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?
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Can you make square numbers by adding two prime numbers together?
Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
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?
Got It game for an adult and child. How can you play so that you know you will always win?
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.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
This task combines spatial awareness with addition and multiplication.
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?
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?
Investigate the different distances of these car journeys and find out how long they take.
This number has 903 digits. What is the sum of all 903 digits?
If the answer's 2010, what could the question be?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Find the next number in this pattern: 3, 7, 19, 55 ...