There are some basic classes that all elements are in together and specific element classes as well. You're required to take normal classes such as math and writing as well as your magic classes.
If two elements are listed together with a '/' that means the two houses take that class together. When taking required classes, be sure to pay attention to who they'd be in class with. For example, Fire students take elemental history with Water students, but would not be attending with Earth or Air students. However, they're given the same work, so it would be possible to study for.
As for optional classes, any student that wants to attend would take it together.

Year 1 Classes:

Required:
Dueling, Professor Trilily (All together)
Elemental History, Mister Berk (A/E & F/W)
Community, Professor Anderson (All together)
General [Element] Studies, HofH
General Education, Carl (A/F & E/W)
Language Arts, Professor Hart (A/W & E/F)
Physical Education, Mister Butch (All together)

Optional:
Animal Care, Professor Henwen
Art, Professor Octavia
Astronomy, Madame Helen
Blacksmithing, Mister Smith
Culinary, Chef Midnight
Divination, Madame Helen
Geography, Mister Berk (required for E/W)
Herbology, Miss Alice (required for E/W)
Home Ec, Chef Midnight
Journalism, Professor Hart
Music, Madame Fairweather
Weapon Wielding, Mister Smith

Schedule
Monday:
Elemental History (A/E) 7am-10am
Elemental History (F/W) 10:30am-1:30pm
Community 2pm-4pm
General Education (A/F) 4:30pm-5:30pm
Astronomy 6pm-8pm

Tuesday:
General Education (E/W) 7am-8am
Language Arts (A/W) 8am-9am
Language Arts (E/F) 9am-10am
Weapon Wielding 10:30am-Noon
No classes noon-1pm
Music 1pm-4pm
Divination 4:30pm-6:30pm

Wednesday:
Physical Education 8am-9am
No classes 9am-10am
General [Element] Studies 10am-Noon
Lunch Break Noon-1pm
General [Element] Studies (con.) 1pm-3pm
Herbology/Geography 3:15pm-5:45pm

Thursday:
Dueling 7am-9am
Home Ec 9:30am-11:30am
Culinary Noon-2pm
Art 2:30pm-4:30pm
Journalism 5pm-7pm

Friday:
Animal Care 6am-10am
Blacksmithing 10am-Noon
Open Hours for All Classrooms Noon-5pm

Year 2 Classes:

Required:
Dueling, Professor Trilily (All together)
History, Mister Anderson (A/E & F/W)
Etiquette, Professor Anderson (All together)
General [Element] Studies, HofH
General Education, Carl (A/F & E/W)
Language Arts, Professor Hart (A/W & E/F)

Optional:
Animal Care, Professor Henwen
Art, Professor Octavia
Art History, Professor Octavia
Astronomy, Madame Helen
Blacksmithing, Mister Smith
Childcare, Chef Midnight
Culinary Arts, Chef Midnight
Divination, Madame Helen
Herbology, Miss Alice
Investigative Journalism, Professor Hart
Music, Madame Fairweather
Swordsmanship, Mister Smith

Schedule
Monday:
General Education (A/F) 6am-7am
General Education (E/W) 7am-8am
Language Arts (A/W) 8am-9am
Language Arts (E/F) 9am-10am
No classes 10am-11am
Herbology 11am-2pm
History (A/E) 2:30pm-5:30pm

Tuesday:
History (F/W) 8am-11am
Art 11:30am-1:30pm
Music 1pm-4pm
Art History 2pm-4pm
Childcare 4:15pm-6:15pm
Astronomy 6:30pm-8:30pm

Wednesday:
Dueling 6am-9am
No classes 9am-11am
Etiquette 11am-1pm
Blacksmithing 1:30pm-3:30pm
Culinary Arts 3:45pm-6pm

Thursday:
General [Element] Studies 6am-Noon
Animal Care 12:30pm-2:30pm
Swordsmanship 3pm-4pm
Divination 4:30pm-6pm

Friday:
Investigative Journalism 8am-10am
Open Hours for all Classrooms Noon-5pm

Year 3:

Required:
Dueling & Defense, Professor Trilily
Dawn of Elementals, Professor Backwater (A/E & F/W)
Etiquette & Community, Professor Anderson
General [Element] Studies, HofH
General Education, Carl (A/F & E/W)
The Language of Elements, Professor Hart (A/W & E/F)

Optional:
Creature Care, Professor Henwen
Art, Professor Octavia
Elemental Art, Professor Octavia
Astronomy, Madame Helen
Blacksmithing, Mister Smith
Home Mathematics, Chef Midnight
Culinary Arts, Chef Midnight
Divination, Madame Helen
Herbology & Botany, Miss Alice
Journaling, Professor Hart
Music, Madame Fairweather
Archery, Mister Smith

Schedule
Monday:
Creature Care 6am-9am
Herbology & Botany 9:30am-11am
Dawn of Elementals (A/E) 11:30am-1:30pm
General [Element] Studies 2pm-5pm

Tuesday:
Dawn of Elementals (F/W) 6am-8am
Culinary Arts 8am-10am
Home Mathematics 10am-noon
General Education (E/W) noon-1pm
Music 1pm-4pm
Journaling 3:30pm-5pm
Generals Education (A/F) 5:15pm-6:15pm

Wednesday:
Astronomy 6am-8am
Divination 8:30am-10:30am
Dueling & Defense 11am-1pm
No classes 1pm-2pm
Etiquette & Community 2pm-4pm
Archery 4:30pm-5:30pm

Thursday:
Blacksmithing 8am-9am
Language of Elements (A/W) 9:30am-10:30am
Language of Elements (E/F) 11am-noon
Art 12:30pm-2:30pm
Herbology & Botany 3pm-5pm
Astronomy 5pm-7pm

Friday:
Elemental Art 8am-10am
Open Hours for all Classrooms noon-5pm

Year 4:

Required:
Dueling & Defense, Professor Trilily
Modern Elemental, Professor Anderson
Dual Elementing, HofH

Optional:
Advanced Animal Care, Professor Henwen
Art & Culture, Professor Octavia
Elemental Art History, Professor Trilily
Real Vs. Myth, Mister Berk
Advanced Blacksmithing, Mister Smith
Advanced Culinary, Chef Midnight
Advanced Divination, Madame Helen
Herbology & Botany, Miss Alice
Advanced Journalism, Professor Hart
Defined Music, Madame Fairweather
Shield Work, Mister Smith

Schedule
Monday:
Dueling & Defense 8am-11am
No classes 11am-noon
Modern Elemental noon-2pm
No classes 2pm-3pm
Advanced Animal Care 3pm-5pm

Tuesday:
Dual Elementing 8am-noon
No classes noon-3pm
Elemental Art History 3pm-4pm
Real vs. Myth 4:30pm-5:30pm

Wednesday:
Advanced Blacksmithing 8am-10am
Advanced Culinary 10:30am-12:30pm
Advanced Divination 1pm-3pm
Advanced Journalism 3:30pm-5:30pm
Herbology & Botany 6pm-8pm

Thursday:
Art & Culture 8am-10am
Shield Work 10am-11am
No classes 11am-1pm
Defined Music 1pm-3pm

Friday:
Open Hours for all Classrooms noon-5pm

Year 5:

*Starting year 5, you begin specializing and advancing your magic. You have two required classes, but mainly you spend time with your private instructor(s) to further your power.*
Required:
Elemental Magic, Professor Trilily
[Element], HoH

Optional:
Advanced Animal Care, Professor Henwen
Art & Culture, Professor Octavia
Real vs. Myth, Mister Berk
Advanced Blacksmithing, Mister Smith
Advanced Culinary Arts, Chef Midnight
Advanced Divination, Madame Helen
Advanced Herbology, Miss Alice
Newspaper, Professor Hart
Advanced Music, Madame Fairweather
Weapons, Mister Smith
Career Pathway, Carl

Schedule
Monday:
Weapons 8am-9am
Advanced Music 9:30am-12:30pm
Career Pathway 1pm-2pm
Newspaper 2:15pm-4:15pm

Tuesday:
Advanced Divination 8am-10am
No classes 10am-1pm
Advanced Animal Care 1pm-3pm
Advanced Herbology 3pm-5pm

Wednesday:
Advanced Culinary Arts 6am-8am
Art & Culture 8:30am-10am
Advanced Blacksmithing 10am-noon

Thursday:
Elemental Magic 10am-noon
Air 1pm-3pm
Earth 1pm-3pm
Water 2pm-4pm
Fire 3pm-5pm

Friday:
Real vs. Myth 7am-8am
Open Hours for all Classrooms noon-5pm

Year 6:

Required:
Elemental Magic, Professor Trilily
Advanced [Element], HofH

Optional:
Advanced Creature Care, Professor Henwen
Art & Culture, Professor Octavia
Practical Magic, Professor Anderson
Practical Blacksmithing, Mister Smith
Elemental Culinary, Chef Midnight
Advanced Divination, Madame Helen
Advanced Herbology, Miss Alice
Advanced Newspaper, Professor Hart
Advanced Music, Madame Fairweather
Combat, Mister Butch

Schedule
Monday
Advanced Herbology 7am-9am
Advanced Music 9:30am-12:30pm
Advanced Divination 1pm-3pm

Tuesday
Advanced Newspaper 10am-noon
Elemental Culinary noon-2pm
Practical Blacksmithing 2:30pm-4:30pm

Wednesday
Advanced [Element] 6am-10am
Art & Culture 10:30am-12:30pm
Advanced Creature Care 1pm-4pm

Thursday
Practical Magic 12:30pm-2:30pm
Combat 3pm-4pm

Friday
Elemental Magic 8am-11am
Open Hours for all Classrooms noon-5pm

Year 7:

Required:
Elemental Magic, Professor Trilily
Advanced [Element], HofH
Career Pathway, Chef Midnight

Optional:
Creature Career Paths, Professor Henwen
Art Career Paths, Professor Octavia
Home Ec, Professor Octavia
Enforcement Careers, Mister Butch
Culinary Careers, Chef Midnight
Science Careers, Madame Helen
Divination Careers, Madame Helen
Herbology & Medical Careers, Miss Alice
Skills & Crafting Career Paths, Mister Smith
Music Pathways, Madame Fairweather
Desk and Other Careers, Carl
Media Careers, Professor Hart

Schedule
Monday
Career Pathway 6am-8am
Home Ec 8am-10am
Elemental Magic 11am-1pm
Culinary Careers 1:30pm-3:30pm
Skills & Crafting Career Paths 4pm-6pm

Tuesday:
Art Careers 8am-10am
No classes 10am-noon
Herbology & Medical Careers noon-2pm
No classes 2pm-3pm
Enforcement Careers 3pm-5pm

Wednesday:
Desk and Other Careers 8am-10am
No classes 10am-11am
Media Careers 11am-1pm
No classes 1pm-3pm
Music Careers 3pm-5pm

Thursday:
Science Careers 6am-8am
No classes 8am-10am
Divination Careers 10am-noon
No classes noon-3pm
Creature Career Paths 3pm-5pm

Friday:
Advanced [Element] 8am-noon
Open Hours for all Classrooms noon-5pm