In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
This is an adding game for two players.
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?
Who said that adding couldn't be fun?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
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.
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
There are nasty versions of this dice game but we'll start with the nice ones...
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?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Use the number weights to find different ways of balancing the equaliser.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
If the answer's 2010, what could the question be?
Choose a symbol to put into the number sentence.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Can you substitute numbers for the letters in these sums?
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?
Here is a chance to play a version of the classic Countdown Game.
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?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
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?
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.
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?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
A game for 2 players. Practises subtraction or other maths
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.
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 the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
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.
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 hang weights in the right place to make the equaliser
How would you count the number of fingers in these pictures?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?