Max and Mandy put their number lines together to make a graph. How
far had each of them moved along and up from 0 to get the counter
to the place marked?
Use the information to work out how many gifts there are in each
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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?
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.
If the answer's 2010, what could the question be?
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 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.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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?
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
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.
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
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?
This is an adding game for two players.
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
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.
Investigate the different distances of these car journeys and find
out how long they take.
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?
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
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
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.
Investigate what happens when you add house numbers along a street
in different ways.
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?
Number problems at primary level that may require determination.
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
Find the sum of all three-digit numbers each of whose digits is
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.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this 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?
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?
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?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
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.
What is happening at each box in these machines?
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?
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
This task combines spatial awareness with addition and multiplication.
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?