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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
What is the sum of all the three digit whole numbers?
Find the sum of all three-digit numbers each of whose digits is
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
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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
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?
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.
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?
How can we help students make sense of addition and subtraction of negative numbers?
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?
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
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).
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
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?
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.
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
There are nasty versions of this dice game but we'll start with the nice ones...
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?
Can you substitute numbers for the letters in these sums?
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
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
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?
Find a great variety of ways of asking questions which make 8.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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?
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?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Choose four of the numbers from 1 to 9 to put in the squares so
that the differences between joined squares are odd.
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
As you come down the ladders of the Tall Tower you collect useful
spells. Which way should you go to collect the most spells?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
What is happening at each box in these machines?