In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
This is an adding game for two players.
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
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...
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 game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
Can you follow the rule to decode the messages?
Who said that adding couldn't be fun?
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.
How would you count the number of fingers in these pictures?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
A game for 2 players. Practises subtraction or other maths
Can you hang weights in the right place to make the equaliser
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
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?
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.
If the answer's 2010, what could the question be?
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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 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.
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
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?
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?
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
If you have only four weights, where could you place them in order
to balance this equaliser?
What is happening at each box in these machines?
Number problems at primary level to work on with others.
An old game but lots of arithmetic!
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Number problems at primary level that require careful consideration.
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three