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.
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?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
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 oponent.
An old game but lots of arithmetic!
If you have only four weights, where could you place them in order
to balance this equaliser?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
A game for 2 players. Practises subtraction or other maths
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?
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
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?
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.
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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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.
How would you count the number of fingers in these pictures?
Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Here is a chance to play a version of the classic Countdown Game.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Can you hang weights in the right place to make the equaliser
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
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.
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
This is an adding game for two players.
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 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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Use the number weights to find different ways of balancing the equaliser.
Can you substitute numbers for the letters in these sums?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?