In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Find the sum of all three-digit numbers each of whose digits is
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.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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 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 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?
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
How can we help students make sense of addition and subtraction of negative numbers?
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 each work out the number on your card? What do you notice?
How could you sort the cards?
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 missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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.
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
There are nasty versions of this dice game but we'll start with the nice ones...
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?
What is the sum of all the three digit whole numbers?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
Find a great variety of ways of asking questions which make 8.
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?
Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
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
Can you substitute numbers for the letters in these sums?
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
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
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?
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.
Investigate the different distances of these car journeys and find out how long they take.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
Investigate the different distances of these car journeys and find
out how long they take.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?