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?
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?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
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?
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.
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Find the next number in this pattern: 3, 7, 19, 55 ...
Use the information to work out how many gifts there are in each
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
What is the sum of all the three digit whole numbers?
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
This number has 903 digits. What is the sum of all 903 digits?
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?
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?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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.
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?
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.
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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?
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 challenge focuses on finding the sum and difference of pairs of two-digit numbers.
What is happening at each box in these machines?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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 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!
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?