Singapore mental math (2) - special numbers

More from this book (see yesterday’s post for background information).

Here is the strategy from Week 33:

Good things: If used like this then there is some mental maths going on and the following of an algorithm.  It could keep mental maths sharp and settle pupils at the start of a lesson.  Vocabulary is used (product, factor, multiple).

Bad things: If used just like this then it seems to me to be very unlikely that anyone will remember what the special number is, or what fraction to use.  It doesn’t make it clear that this is only for 2-digit numbers.

Pupils could be asked to explore why this works (to be fair, perhaps this happens even though it isn’t mentioned in the book).

What is going on?

Multiplying by 429 somehow involves multiplying by 3/7 (and then doing some other jiggery-pokery).  What is the link between 429 and 3/7?

Let’s do 429 divided by 3/7 – we get 1001.  Aha, if we write down a 2-digit number, put a zero in the hundreds place and then write the 2-digit number down for the thousands then that is the same as multiplying by 1001.  This explains the final few steps.

Questions for pupils to consider:

• One of the questions is 7x429.  How does the algorithm need to be tweaked to make this one work?
• What happens if you do this with a 3-digit number?  Or a 4-digit number?
• What would be a better way to explain the algorithm?  (Maybe: “multiply by 3/7 and then multiply by 1001”?)
• What happens if you choose a number that isn’t a multiple of 7? 

The strategy for Week 34 is almost identical, except that the ‘special number’ is 715 and the initial instruction is to multiply by 5/7.

Week 36 has special number 858 and ‘multiply by 6/7’.

Both of these are fractions of 1001 too. 

What other ‘special numbers’ could there be?  Can pupils write an algorithm for those? 

(For example, 1/7 of 1001 is 143…)