In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
Find the sum of all three-digit numbers each of whose digits is
How many solutions can you find to this sum? Each of the different letters stands for a different number.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
What is the sum of all the three digit whole numbers?
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
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?
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?
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.
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 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
There are nasty versions of this dice game but we'll start with the nice ones...
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?
Who said that adding couldn't be fun?
How can we help students make sense of addition and subtraction of negative numbers?
Find a great variety of ways of asking questions which make 8.
Can you substitute numbers for the letters in these sums?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
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?
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?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
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?
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?
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?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
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?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Are these domino games fair? Can you explain why or why not?
Have a go at this game which involves throwing two dice and adding
their totals. Where should you place your counters to be more
likely to win?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
You have 5 darts and your target score is 44. How many different
ways could you score 44?
What is happening at each box in these machines?
Investigate the different distances of these car journeys and find
out how long they take.
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
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?
This is an adding game for two players.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.