Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
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 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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 happening at each box in these machines?
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?
This Sudoku, based on differences. Using the one clue number can you find the solution?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
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?
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
Whenever two chameleons of different colours meet they change
colour to the third colour. Describe the shortest sequence of
meetings in which all the chameleons change to green if you start
with 12. . . .
Use the information to work out how many gifts there are in each
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?
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).
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
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
Find the numbers in this sum
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
In the following sum the letters A, B, C, D, E and F stand for six
distinct digits. Find all the ways of replacing the letters with
digits so that the arithmetic is correct.
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.
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.
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.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received 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?
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?
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
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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 challenge focuses on finding the sum and difference of pairs of two-digit 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?
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.
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Here is a chance to play a version of the classic Countdown Game.
Find the next number in this pattern: 3, 7, 19, 55 ...