In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
There are nasty versions of this dice game but we'll start with the nice ones...
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
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?
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.
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?
Who said that adding couldn't be fun?
This is an adding game for two players.
Can you follow the rule to decode the messages?
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?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
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 draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
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?
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.
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
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?
Can you hang weights in the right place to make the equaliser
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.
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 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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
A game for 2 players. Practises subtraction or other maths
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Can you substitute numbers for the letters in these sums?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
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?
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .
Use the number weights to find different ways of balancing the equaliser.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
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.
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?
Investigate the different distances of these car journeys and find
out how long they take.
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?
What is happening at each box in these machines?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.