What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
56 406 is the product of two consecutive numbers. What are these
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?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
This task combines spatial awareness with addition and multiplication.
Can you work out what a ziffle is on the planet Zargon?
A 3 digit number is multiplied by a 2 digit number and the
calculation is written out as shown with a digit in place of each
of the *'s. Complete the whole multiplication sum.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Find the next number in this pattern: 3, 7, 19, 55 ...
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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?
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 number has 903 digits. What is the sum of all 903 digits?
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.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can 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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
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
What is the least square number which commences with six two's?
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.
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
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?
What is happening at each box in these machines?
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?
This challenge combines addition, multiplication, perseverance and even proof.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
This problem is designed to help children to learn, and to use, the two and three times tables.
All the girls would like a puzzle each for Christmas and all the
boys would like a book each. Solve the riddle to find out how many
puzzles and books Santa left.
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?
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?
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?
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
Use the information to work out how many gifts there are in each
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the
operations x and ÷ once and only once, what is the smallest
whole number you can make?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .