Commas and spaces

Discuss with pupils the way large numbers are written. Ask them to find examples in books, newspapers and magazines.
 
When grouping the sets of three digits in large numbers, spaces are more frequently used than commas when the numbers are typed, for instance 32 579 843.
 
Explain that the space or comma is a good way of showing where the words thousands and million are used when saying the number aloud.

Powers of 10

Discuss ways in which mathematicians use shorthand: = + ÷ √ π
 
Explain that large numbers can also be written using shorthand:
100 = 10 x 10 = 10²
1000 = 10 x 10 x 10 = 10³
18 x 10⁵ = 1 800 000
 
·      In pairs, pupils give each other a number such as 24 x 10⁴. This is written down and read back in full as above.
·      A target number is given to a partner, such as 245 000 000. They try to write this in shorthand using powers of ten.
 

Rounding numbers

Write a large number on the board, such as 38 465. Ask pupils to round this to the nearest 10, 100, 1000 and 10,000. Discuss the four approximations and the way they become less and less accurate.
 
Repeat with other five- and six-digit numbers.
 

Large number words

·      These are the prefixes used for SI units (the international system of units):
exa: 10¹⁸             giga: 10⁹
peta: 10¹⁵       mega: 10⁶
tera: 10¹²            kilo: 10³
 
·      Discuss ways in which we can work out the value and relationships between large numbers by looking at the beginnings of words. For instance: kilo, mega and giga. Giga is often used in computing for very large numbers, such as a gigabyte. It stands for 1 000 000 000 (a thousand million).
 
·      Talk about large numbers such as millions, billions and trillions. Explain how a new word, googol, has been invented to describe 1 followed by a hundred zeros.
 
 

Make a million

Each pupil enters a six-digit number in the calculator without the other seeing.
 
Pupils then take turns to ask for a digit at random, for example:

The value of the digit (in this case 70 000) is subtracted from Player B’s total and added to Player A’s calculator total.

 
The game continues until one player goes beyond 999 999 or the other player goes below zero.
 
 

Calculator constants

Organisation: pairs or groups
 
Pupils take turns to use the constant x 10 on the calculator by inputting 10 x x = and another input, such as 58. The partner predicts what the display will show when the equals key is pressed repeatedly.
 
This can be repeated for other starting numbers and developed by changing the constant to x 100.

Arrow cards

Counting stick