The short answer

A book a week at their level.

The long answer

It’s very complex. The answer involves knowing how frequently words appear in English and how much text one has to read in order to meet a given word. It also involves knowing how many times it takes to meet a word before it is ‘known’. The same applies to grammar too of course.  It also means we need to know how frequent collocations appear and how much text one has to read in order to meet it. We also need to know how quick the forgetting of words is.

We know that the most common word in English is the. It appears so frequently that it appears on average every 17th word and covers about 5.83% of the total volume of English (1). The next most frequent word is the be verb and its inflections (was, were, are, am, is etc). be appears once every 20 words (you would have also met the of course). If you want to meet all the top 25 most frequent words in English statistically speaking (but of course not in reality) you’d have to read about 225 of text. To meet the first 1000 most frequent words in English you’d need to read 8533. The and be would have been repeated hundreds of times in this volume of text but it would take you 8553 words just to meet the 1000th word once. To meet the 2,000th which occupies 0.00432% of the volume of English or occurs once every 23,1003 words.  However, you are only meeting the 2000th word once. If you want to meet it again, you’d have to read another 23,103 words. Statistically of course. The table illustrates this for varying levels of word frequency.

A statistical analysis of the number of English words you need to meet (at given recurrence rates) to ‘learn’ that number of words

A B C (= 100 / B) D (= x times C ) E (= D / Book length)
Word rank Percentage of general English that this word covers Number of running words needed to be met to meet all these words Volume of text you need to read to meet
the words at these recurrence rates 		Number of books to cover this volume given these recurrence rates
5 times 10 times 20 times 50 times Book length 5 times 10 times 20 times 50 times
1st most frequent (the) 5.83898% 17 (1) 86 171 343 856 4,500 0.0 0.0 0.1 0.2
2nd most frequent (be) 5.12332% 20 98 195 390 976 4,500 0.0 0.0 0.1 0.2
25th (as) 0.44382% 225 1,127 2,253 4,506 11,266 4,500 0.3 0.5 1.0 2.5
50th (like) 0.24109% 415 2,074 4,148 8,296 20,739 4,500 0.5 0.9 1.8 4.6
100th (hear) 0.10505% 952 4,759 9,519 19,038 47,595 4,500 1.1 2.1 4.2 10.6
500th (present) 0.02477% 4,037 20,183 40,366 80,732 (4) 201,829 4,500 4.5 9.0 17.9 44.9
1000th (blood) 0.01172% 8,533 (3) 42,665 85,329 170,658 426,645 10,000 4.3 8.5 17.1 42.7
1500th (intent) 0.00677% 14,773 73,864 147,727 295,455 738,636 15,000 4.9 9.8 19.7 49.2
2000th (stumble) 0.00432% (2) 23,103 115,625 231,250 462,500 1,156,250 20,000 5.8 11.6 23.1 57.8
3000th (sergeant) 0.00211% 47,343 236,713 473,425 946,850 2,367,126 30,000 7.9 15.8 31.6 78.9
5000th (satellite) 0.00076% 132,143 660,714 1,321,429 2,642,857 6,607,143 80,000 8.3 16.5 33.0 82.6
10,000th (relativity) 0.00016% 632,895 3,164,474 6,328,947 12,657,895 31,644,733 80,000 39.6 79.1 (5) 158.2 395.6

But of course meeting a word once is not enough for acquisition to take place. To really learn a word you’d have to meet it say 20-30 times. So all the above figures need to be multiplied by this learning factor. So to meet all the 500 most frequent words in English 20 times (4) you’d need to read 80,732 words. To meet all the 10,000 most frequent words in English 10 times, you’d need to read 79.1 books that are 80,000 words long (5).

To get to Intermediate level you’d need a vocabulary of about 2000 words. If we assume it takes each word 20 meetings (recent research suggests up to 50 or more) you’d need to read 462,500 words. Statistically. If you know all the 1- 2,000 most frequent words you can’t read native texts well – you’d be intermediate level and would need another 6000, 7000 words to do this or you’d need to read about 20-25,000,000 words.

But that’s not the only factor.

The above figures are based on an analysis of a corpus of 100m words on English and are based on word forms (different spellings) and word families. This means the 1500th word (intend) also includes intended, intending and intends, and it’s derivatives intention, intentional. The 500th word includes  bloods, bloodied, bloodless etc. But the above figures are based on only meet ONE of these words from each family group one. It does not include the family members.

This table does NOT INCLUDE collocations and colligations, lexical phrases (I’d like a …, How about —ing?  We got a quick bite to eat) phrasal verbs (take up, go along with) and idioms and metaphor.

This also doesn’t include forgetting.

How much reading do students typically do?

A typical course book has about 40,000-50,000 words in it. If an average student completes say 6 books by intermediate level, s/he would have met say 300,000 words and can be expected to have met the top 2700 words at least once, the top 1000 words about 30 times and the top 500 words 70 or more times.

A vocabulary analysis of course books though shows that they tend to select words by topic and do not cover all the most important words. Some topics are almost never dealt within course books and therefore the vocabulary for these topics won’t be learnt in class (war, religion, sex,  etc.)

Clearly this is not enough reading to build a big vocabulary. The only way to build this vocabulary is to read lots and lots and lots.

How much should they read?

As a low level graded reader has about 3000-4000 words they only need to read a book at week before forgetting takes hold.

An intermediate graded reader may have 12,000-15000 words and as most of the words will already be known, they won’t meet many new words often but as the book is longer, a book a week at their level is still fine.

Advanced learners need 2-3 books of longer length at their level because they have to read so much more to meet words they don’t know.