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?
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
How can we help students make sense of addition and subtraction of negative numbers?
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?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Find the sum of all three-digit numbers each of whose digits is
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?
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
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 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.
What is the sum of all the three digit whole numbers?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal 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
Can you substitute numbers for the letters in these sums?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?
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?
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.
This number has 903 digits. What is the sum of all 903 digits?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
These alphabet bricks are painted in a special way. A is on one
brick, B on two bricks, and so on. How many bricks will be painted
by the time they have got to other letters of the alphabet?
As you come down the ladders of the Tall Tower you collect useful
spells. Which way should you go to collect the most spells?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
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?
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?
There were 22 legs creeping across the web. How many flies? How many spiders?
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?
In this section from a calendar, put a square box around the 1st,
2nd, 8th and 9th. Add all the pairs of numbers. What do you notice
about the answers?
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?
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
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.
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.
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 big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?
Use these four dominoes to make a square that has the same number
of dots on each side.
What is happening at each box in these machines?
Investigate the different distances of these car journeys and find
out how long they take.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10