This way of teaching EFL or ESL students to name numbers in English, though heavily influenced by Caleb Gattegno‘s work on teaching people to count, is not in fact intended to teach counting skills: it is assumed the students will already know how to do this in their native language. It is also assumed that they are literate in the Latin alphabet and “Arabic” numerals. It’s obvious to most language teachers that being able to name numbers in a foreign language has many practical uses: telling the time, giving dates, going shopping, doing arithmetic, etc. Silent Way teachers, as well as having these practical objectives, also see learning to say numbers as a way for beginners to practice saying long utterances, with reasonably correct pronunciation and intonation, while understanding the meaning of what is being said with no effort. Silent Way teachers also aim for their students to acquire mastery of the English number system in the most economical way, that is with a minimum of effort in the shortest time.
As far as I know, Caleb Gattegno was the first to do two things:
- consider that each new word learnt has an energy cost, roughly the same for all words, which he named an “ogden”. However, the return in usefulness to the learner in exchange for the energy spent is not the same. The energy efficiency of choosing to learn high frequency words first is obvious : a learner can be sure of an opportunity of soon reusing “seven” but they might pass a lifetime without the need to use “andiron”.
- count the number of ogdens need to be spent to be able to count from 1 to, say, 1 000 000 in several languages. Languages vary quite a lot in this respect: English requires more ogdens than Chinese but fewer than French.
The number of ogdens needed in English to count to a million
Let’s count them:
12 ogdens from 1 – 12. Each word is different so the cost is high.
2 ogdens for “thirteen”: 1 for “thir-” + 1 for “-teen”. In a compound word each element has to be paid for.
14 is free because “four” and “teen” have already been paid for.
1 ogden for “fifteen” because the “fif-” is different from “five”.
16 – 19 are free.
2 ogdens for “twenty”: 1 for “twen-” + 1 for “-ty”
21 – 99 are free – there are no new words to be learnt.
2 ogdens for “a hundred”: 1 for “a” and 1 for “hundred”.
1 ogden for “a hundred and one”: “and” is new.
102 – 999 are free.
1 ogden for “thousand”.
1001 to 99 999 are free.
1 ogden for “million”.
Which makes 22 ogdens.
The criteria needed to count to a million
Of course you need more than just the words: you also need to understand the conventions for combining them. These are not so easy to count and to be quite sure we haven’t missed any. I’ll try, but first I’d like to distinguish between “rules” and “criteria” for doing something.
Rules are “out there”: you can read them in books; you can learn them by heart: but you don’t necessarily understand them.
Criteria are inside you. You can’t learn them by heart: you gain them by experience leading to awareness and then, through practice, to automatic functionings. That’s a bit of Gattegno jargon that may not mean much at first, but bear with me and I hope it will.
So what criteria do you need to integrate to be able to count to a million in English? In no particular order:
- In units, 1 is said/written: “one”
10 + 1 is said/written: “eleven’.
- In units, 2 is said/written: “two”
10 + 2 is said/written: “twelve”.
- In units, hundreds, thousands, billions, etc., 3 is said/written: “three”
But in 10 + 3, and 10 x 3, 3 is is said/written: “thir-“
- In units, hundreds, thousands, billions, etc., 5 is said/written: “five”
But in 10 + 5, and 10 x 5, 5 is is said/written: “fif-“
- 10 + most units is said/written: “-teen”.
- 10 + 4 is said/written with the unit first and this is the same for all of the “teens” (except 11 and 12).
- 10 as a multiplier of a unit is said/written: “-ty”.
- 20 + 4 is said with the unit in second place. this is true for all the “-tys”. (“Four and twenty” is also possible but rare and old fashioned.)
- After 100 you need to know where to put “and” (you’ll see how to make this clear later on). Note: It’s not needed in all English dialects – but it is in mine!
- You need to know when to say “a hundred” and when “one hundred”.
Sometimes it’s the same as knowing when to say “a table” or “one table”, for example, “You gave me one hundred euros not two hundred.”
In my dialect, I say, “a hundred and two” and “a thousand and two” but “one thousand, one hundred and two”. This seem to me to be just a convention – but I’m not sure.
- There is no -s when the exact number of hundreds, thousands, millions, etc. is given. For example, we say/write: “four hundred”, “ten million”.
- (If there is no exact number, we do say/write “hundreds of people”, “thousands of cars”, etc. But this is not part of counting from one to a million.)
- Large numbers are said in particular “groups” of words.
As presented above, they’re “rules”. Most native English speakers would be unable to make them explicit even though their speech proves that they’ve mastered the system as a functioning.
How to present students with a series of challenges so that they can attain native-speaker-like mastery in a way that’s both economical and fun? One such way is described below.
It’s possible to get complete beginners to count to a million in an hour to an hour and a half, but though this gives them an undeniable feeling of achievement, I find they retain the number words better in the long term if the work is spread over several days.
A set of challenges for beginner students
I’ll describe one of the ways Silent Way teachers can do it. Please note that it’s just one of the ways: there are lots of variations depending on what the students already know and the teacher’s sensitivity to the needs of a particular group. Some students, even though they’ve never formally studied English, are less “beginners” than others because they’ve picked up words and phrases from films, songs, television, the Internet, etc.
On the white/blackboard write the figure 1. If the students have already learnt the sounds of English with The Silent Way: Sound/Color Rectangles Chart :
use it to show how “one” is pronounced. If not, the teacher says the word clearly just once and then invites, with a gesture, students to say the word. The teacher indicates which students are close to the correct pronunciation and indicates to the others, again with gestures, how to modify their pronunciation to come closer to the English. This is not an article on teaching pronunciation with the Silent Way – it is described elsewhere. It is assumed pronunciation of all the new words will be introduced in a similar way.
When about half the students can manage to produce a reasonable approximation to the pronunciation of the word “one”, write the figure 2 to the right of the 1. Elicit the pronunciation as above.
Then write 3 and proceed as above. The sound “th” doesn’t exist in many languages so it’s not reasonable to expect anything like immediate success. When half the students can say something approximating to “three” – a new game can be proposed. The teacher points to the three figures in various orders, faster and faster and the students have to say them quicker and quicker. This always produces fun and laughter and gives the slower students time to assimilate while adding a challenge for the stronger ones.
Continue up to 9 in the same way. That is, it should look like this:
1 2 3 4 5 6 7 8 9
Some other “games”:
- A student comes to the front of the class and points to the figures they’re not sure how to say. The student at the front says nothing. The other members of the class say the words. The student at the front checks if they are correct or not.
- Two students come to the front of the class. One points to figures and the other says the words. They exchange roles.
- A student holds up a certain number of fingers. Another student says the number.
- A student comes to the front of the class and says a number. The others show the number with their fingers. The student at the front checks who is correct or not.
- Two students come to the front. One student says a number. The other student writes the figure. They change roles.
If you have a large class, after being demonstrated, these games can be done in pairs or small groups – using paper and pencils where necessary.
It’s not necessary to continue until all the students are perfect. In fact, it’s a good idea to stop well before that and continue with a different activity. Come back to numbers the next or another day and, having slept, the students will have “miraculously” improved.
Under the first line of figures, leave a space, then write the hundreds like this:
It’s a good idea not to start with 100, but with one of the others because only one new ogden has to be spent: hundred. It is however quite a difficult word to pronounce. When they are reasonably comfortable with saying the other hundreds, then get them to spend the ogden for “a”. Their curiosity will be roused as to why you don’t point to 100. You can make a game of it by almost pointing to 100, shaking your head and choosing another one. When eventually you do point to it, they will naturally say, “one hundred” and when you make a gesture indicating it’s not completely wrong but it’s better to say, “a hundred”, they’ll be surprised and pay the ogden very easily.
Working on the hundreds they’re also getting more practice with the units. Knowing this, a teacher can feel comfortable moving on from just units even when it’s obvious that many students still have problems with them.
Under the hundreds, write the row of thousands. I often don’t write it out in full: just put a dash in the appropriate column.
This usually goes very fast. Just one new ogden to pay, “thousand”; a student will usually suggest “a” thousand.
Under the thousands, leave two empty rows, and then write the millions. This goes even faster than the thousands.
I hope it’s clear now why it’s not necessary to spend too much time on the units initially: they get lots more practice with the hundreds, thousands and millions.
This is another good place to take a break and come back to numbers a few days later.
If you’re coming back to numbers after a break, get the students to recreate the table on the board exactly as it was.
Then, in the space left for it, write the tens: 10, 20, 30 etc. It can be a good idea to start with the regular ones: 40 (for the pronunciation at least), 60, 70, 80, 90, and then do the irregular ones.
Play the fast pointing game, alternating between the regular and irregular words.
Point to 40 and 4 for the students to say, 44; 60 + 6, 70 + 7, etc. and then the irregular 20 + 2, etc. The memory load is very low. Then go on to 60 + 5, 80 + 2, etc. Keep the very irregular 10 pluses until the end. It will take them more time than the others, but much less than if they’d gone on to it immediately after the units in the traditional way.
A good place to take a break.
Continue to build up the table which will eventually look something like this (you can go up to billions and trillions if the students feel like it):
I replace most of the large numbers by dashes: to save space and to force the students to create mental images.
The table has numerous advantages:
- The teacher can quickly point numbers for the students to say.
- Students can come and point numbers for other students to say.
- A student can come and point a number for another to say.
- Saying a number such as 222, 222 the students can see it’s all in the same column so the memory load is low.
- Saying a number such as 222, 222 the students can realise that if they can say 222 they only need one extra word, “thousand”, to say 222, 222.
- Saying a number such as 222, 222, 222, 222 is easy because only two extra words are needed: “million” and “billion”.
- Saying a number such as 222, 222, 222, 222 students can practice making their voices go up on the “before the comma words”, that is “billion”, “million” and thousand and down on the last word. This is typical of English affirmative sentences but with numbers students don’t have to think about vocabulary or grammar: they can concentrate on the music of the utterance.
- When students start to be fluent with the “all the same” numbers, they can be varied: 486, 933.
- They can see where to say “and”.
Interactive on-line exercises
If you can’t work out what the “xxx” is, these interactive exercises can help you: Find the numbers. Or you can take the easy option and look at this video tutorial:
In fact I’ve created a whole series of interactive exercises: Numbers to give students extra practice out of class.
Having read this article, I hope the reasons for the order of the exercises will be obvious. If they’re not or if you have any questions please leave a message in the comments field below.
Some more games using the Silent Way numbers chart
- Two students come to the front. One writes a number in figures on the board. The other points to the words for the number on the chart. The class says the number.
- The teacher hides a word with her hand. The students say the number.
- The student hides a word with his hand. The other students say the number.
- The teacher hides a word with her hand and asks the class to say how the word is coloured. (This can be said in the native language if students are beginners or low level.)
- Two students come to the front. One points to a word on the numbers chart. The other points to the corresponding rectangles on the Sound/Color Rectangles Chart or on the Fidel (spelling charts).
- Simple arithmetic. For example, a student comes to the front and points to the words, “three” “and” “four”. The other students say the answer, “seven”.
- Two students come to the front. One points a large number on the Numbers table on the board. The other points to the corresponding words on the Numbers chart. The class says the number.
© Glenys Hanson 2015. An earlier version was published on the Une Education Pour Demain website in 2012.
“Teaching English numbers the Silent Way”by Glenys Hanson” is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.