Find a great variety of ways of asking questions which make 8.
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?
How can we help students make sense of addition and subtraction of negative numbers?
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
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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?
Find the sum of all three-digit numbers each of whose digits is
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 clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
This number has 903 digits. What is the sum of all 903 digits?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the numbers
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Find out about Magic Squares in this article written for students. Why are they magic?!
The picture shows a lighthouse and many underwater creatures. If
you know the markings on the lighthouse are 1m apart, can you work
out the distances between some of the different creatures?
What is the sum of all the three digit whole numbers?
Can you substitute numbers for the letters in these sums?
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?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
Investigate the different distances of these car journeys and find out how long they take.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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
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?
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
In sheep talk the only letters used are B and A. A sequence of
words is formed by following certain rules. What do you notice when
you count the letters in each word?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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 the 'double-3 down' dominoes to make a square so that each side
has eight dots.
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
This is an adding game for two players.
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?
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Investigate what happens when you add house numbers along a street
in different ways.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Can you arrange fifteen dominoes so that all the touching domino
pieces add to 6 and the ends join up? Can you make all the joins
add to 7?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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?
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.
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
What is happening at each box in these machines?