1. Written methods
[N4.1 Extension Starter]
1) Can you explain what happens when you multiply a 3-digit number by 1001?
What do you notice?
2) Is this correct? If not, re-write the statement to make it correct. “To multiply by five, just halve the number and add a zero.”
Why does this rule for multiplication by 21 work? “Double the number, multiply this by ten and add the original number.”
Calculate and investigate pairs of multiplications like these   34
and 28   43
Preamble
Pupils are given the opportunity to use written methods of calculations in an investigative context. They
should be asked to explain their methods and conclusions, so working in small groups would be useful.
Possible content
Using written methods for the addition, subtraction, multiplication and division of integers.
Resources
None.
Solution/Notes
The number abc becomes the number abcabc, this is a result of the original number added to itself multiplied by a thousand. ( 1001 → abc000 + abc)
This is wrong, multiplication by 10 is not always a matter of adding a zero – it is the number that “moves”. It should read “divide by 2 and multiply by 10 by moving the number one “space” to the left”.
If the number is x, double the number, multiply by 10 becomes 20x. By adding the original number you add x, so you have 21x.
What happens is that ab  cd is equal to ba  dc, other pairs of numbers where this occurs are: 93  26 = 39  62 and 84  12 = 48  21. (Put symbolically the condition for ab  cd = ba  dc, is ac = bd – this may be informally explained by more capable pupils.)
Original Material © Cambridge University Press 2010
Original Material © Cambridge University Press 2010