Subtraction by Adding On

This is also sometimes called “subtraction using a blank numberline” and I’ve even heard it called “that nonsensical modern method”. This latter is a real misnomer since it is neither nonsensical nor modern. In fact it’s a method that dates back to before I was born, in days before we had calculators and electronic tills. It’s also a really useful method involving counting forwards, which is always easier than counting backwards – even for maths geniuses!

Let’s return to those old-fashioned little shops. I buy some sweets for 24p and hand over a £5. To work out my change, the shopkeeper needs to calculate £5 – 24p. Now she could count £4.99, £4.98, £4.97 until she had subtracted 24p, but what you actually would have heard is this:

24 and 6 makes 30, and 20 makes 50 and another 50 makes £1. 2, 3, 4, £5. And while doing this they counted the change (£4.76) into your hand.

This is the method that schools have returned to. To begin with, Children use a “blank numberline” – that is, a line that they can write the numbers on themselves. They then write the lower number at one end, and see what they need to add to make the higher number. Here’s an example:



The children first of all use their knowledge of number bonds to add to the next 10 (38 + 2 = 40).
They then use their ability to add multiples of 10. In the example above the child has done 40+10 = 50 and then 50 + 40 = 90. They may have been able to see straight away 40 + 50 = 90 and done this as one step, or they may have needed to do 40 + 10 = 50, 50 + 10 = 60, 60 + 10 = 70 and so on up to 90. The method isn’t about having to complete it in a certain number of steps, it’s about each child breaking it down into the smallest number of steps that they can manage.
When they reach the multiple of 10 before the higher number, they add on whatever units are needed to make the higher number, in this case it was +6 to make 96.
Finally, they add up all the numbers they added on to find the answer: 2+10+40+6 = 58 so 96 – 38 = 58.

When they are confident with this, they move on to jotting down only the numbers they are adding on, and they keep the tally in their head, until eventually they develop their working memory enough to hold all of the numbers in their head and write down just the answer.

Related posts: Teaching the Times Tables, Teaching Sequencing and Column Addition

Learning Chinese

As readers of this blog will know, I love learning new things.  Last summer I spotted an advert for a course in Chinese for primary school teachers, and as MFL (modern foreign languages) is my specialist subject, I decided to sign up.  Throwing myself in at the deep end, I promised my new school that I would set up a lunchtime Chinese club, so I had to make sure I really did learn some!

I must confess, I was a bit worried.  I mean – Chinese is really difficult, right?  It’s doesn’t even have an alphabet, just thousands of characters.  But it actually turned out to be a lot easier than I imagined.  Obviously, it takes years to learn to speak a language fluently, so I have only learnt the basics, but this is what I discovered:

–          It’s a subject-verb-object language, so the word order is the same as English.  This already makes it easier than some languages.

–          The verbs don’t conjugate (i.e. there are no different endings depending on who is doing it – like he lives, they live in English, or il habite, ils habitent in French.

–          There are no articles (English has ‘a’ and ‘the’; French has un, une, des, le, la and les; Spanish has un, una, unos, unas, el, la, los and las; Chinese has nothing)

–          There are no tenses.  In Chinese, the verb remains exactly the same and you know whether it’s past, present or future from the context.

This simplicity actually makes it ideal for primary school children to learn.

Like any language, it does have its peculiarities and difficulties, such as the tones (the way your voice goes up or down for certain words) but this is no more challenging than getting children to understand the concept of nouns having genders (Chinese doesn’t have those) or that ‘you are’ might be ‘tu es’ but might be ‘vous êtes’ depending on who and/or how many people you are talking to.

Of course the characters are tricky but the children in my club really enjoy drawing and practising them, and they have the advantage that children are not influenced by how the word is written, so in general their pronunciation is better right from the start.  The fact that the language isn’t written with an English alphabet doesn’t faze them at all.  (In fact, I also run an Ancient Greek club and the children there are also fascinated by the fact that language can be written using different symbols.)  We all enjoy making up little stories to help remember the characters.  On the course I did, we learned a little about how the characters are made up, with radicals giving an indication of meaning and a phonetic element indicating pronunciation.

And there is far more vocabulary in some topic areas.  For example, English has mum, dad, brother, sister, grandma, granddad, while Chinese has different words depending on whether it’s an older or younger brother, a maternal or paternal grandmother etc.  But for the moment the primary aged children I am teaching only need to learn the ones they require for their own family.

The children and I are really enjoying learning together, and although I will never be fluent in Mandarin, you never know – one of the children I am teaching may be inspired to study it further and become fluent in the future.