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?
What is the sum of all the three digit whole numbers?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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.
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?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
How can we help students make sense of addition and subtraction of negative numbers?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Find a great variety of ways of asking questions which make 8.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .
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?
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.
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
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.
Can you score 100 by throwing rings on this board? Is there more
than way to 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?
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
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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?
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?
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?
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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
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.
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?
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.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Find the next number in this pattern: 3, 7, 19, 55 ...
If the answer's 2010, what could the question be?
How would you count the number of fingers in these pictures?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Here is a chance to play a version of the classic Countdown Game.
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.
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
What is happening at each box in these machines?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
There were 22 legs creeping across the web. How many flies? How many spiders?