each is a school year

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Note added at 11 mins (2017-06-03 17:19:33 GMT)
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e.g. see this school a Jesuit public schoo (i.e.private and expensive) https://en.wikipedia.org/wiki/Clongowes_Wood_College

Each year is known by a name, drawn from the Jesuit Ratio Studiorum: Elements (First year), Rudiments (Second year), Grammar (Third year), Syntax (Fourth year), Poetry (Fifth year), and Rhetoric (Sixth year).[6]


obviously here there are 7 years rather than 6 as they have added "figures" to the list

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Note added at 20 mins (2017-06-03 17:28:35 GMT)
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a Jesuit school that existed in Australia had the same system so it seems like it's probably an international Jesuit thing

http://www.wikiwand.com/en/St._Louis_School,_Claremont,_West...

Until the mid-1960s, the year grades were named after levels in the traditional Jesuit curriculum: Elements, Rudiments, Grammar (I and II)3rd reverse this order, Syntax (I and II)reverse this order, Poetry and Rhetoric.

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Note added at 44 mins (2017-06-03 17:52:24 GMT)
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this is from page 11 of the Belvedere handbook ( a school still very popular and which retains these names)
www.belvederecollege.ie/files/FINAL_HANDBOOK_2016.pdf

YEAR AND CLASS NAMES
The primary aim of Jesuit education is to create the vir eloquens – literally eloquent man who is able
to think and speak for himself. Thus the classes in a Jesuit College are named after the stages in the
learning of a classical language, e.g. Latin. Following the tradition of Jesuit educational institutions
around the world, each year group is assigned a name based on the Renaissance Jesuit tradition.
1st Year – Elements, the basics of the language
2nd Year – Rudiments, enhancing the basics
3rd Year – Grammar, the grammar of the language
4th Year – Syntax, the word order of the language
5th Year – Poetry, the literature of the language
6th Year – Rhetoric, public speaking
There are six classes in each year and each is given individual names: Loyola (St Ignatius Loyola,
founder of the Jesuits), Aylmer, (Fr Charles Aylmer SJ, founder & first Rector of Belvedere College SJ)
Xavier (St Francis Xavier, co-founder of the Society of Jesus and patron of Belvedere College SJ).Kenney (Fr
Peter Kenney SJ, superior of the restored Jesuits in Ireland & provincial when Belvedere was founded),
Finlay (Fr Thomas Finlay SJ, a prolific writer and second Rector of Belvedere College SJ, and Scully
(Fr Thomas Scully SJ, teacher of Physics at Belvedere College SJ with a long association with SVP. The
Scully Science medal is awarded every year in his name)
Each class group retains its name, so a boy in first year, Elements Scully (ES), will graduate in sixth
year in Rhetoric Scully (RS).

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Note added at 2 hrs (2017-06-03 19:24:46 GMT)
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sorry about typo in header. it should read:

each lasts a year
i.e. each school year is given one of these names

It looks like the old man may have made a mistake by adding "figures" to the list but then, maybe there really were 7 years in his school. You can only deal with what you've got anyway.

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Note added at 2 hrs (2017-06-03 19:43:33 GMT)
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scratch my last comment. Mount St mary's, another Jesuit school, in the UK , has 7 years. This is page 9 of their pdf handbook:
msmcollege.com/download/101
MOUNT TERMINOLOGY
There are a number of terms or words that are used at the College that reflect the history and heritage we cherish. The following is a very brief guide to some of the most common names and phrases you may come across:
Our Year Groups
Upper Elements 11-12 year olds (Year 7)
Figures 12-13 year olds (Year 8)
Rudiments 13-14 year olds (Year 9)
Grammar 14-15 year olds (Year 10)
Syntax 15-16 year olds (Year 11)
Poetry 16-17 year olds (Year 12 – Lower Sixth)
Rhetoric 17-18 year olds (Year 13 – Upper Sixth)
...
THE STRUCTURE OF THE COLLEGE
The College is divided into three sections, the Lower School, the Middle School and Higher Line. The
year groups at Mount St Mary’s are known as lines.
Lower School Upper Elements Year 7
Figures Year 8
Rudiments Year 9
Middle School Grammar Year 10
Syntax Year 11
Higher Line Poetry Year 12
(VIth Form) Rhetoric Year 13
These names have their origin in the earliest days of Jesuit education in the sixteenth century when
the Jesuit founder, Ignatius of Loyola, adopted a system of education common in the universities of
Europe at the time. These names may seem old fashioned to us today, but they do serve to remind us of the long-standing Jesuit tradition of education of which we are proud to be a part.


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Note added at 1 day55 mins (2017-06-04 18:03:24 GMT)
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To respond to Tina, obviously these days Jesuit schools follow the national curriculum of whichever country they are in notwithstanding the names they put on year groups or class groups.
Lots of schools put names on year groups, e.g. I taught in one school where all the years were named after scientists, so Newton, Galileo, Einstein etc. another school named after rivers/mountains/writers etc. It's more interesting than saying Year 1 or 6th Form/Grade. But most schools these days are quite large so there can be 4-8 classes within each year group.

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Note added at 8 days (2017-06-12 16:26:58 GMT) Post-grading
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Glad to have helped. Well, I had a vague memory of seeing these names before. Must have been in some James Joyce book (I'm a big fan!) as he went to Clongowes and Belvedere, both Jesuit schools and both still very popular (though fees are high) and also, I was a teacher for years so am aware of names being given to classes and years.