Frankfurt am Main · Maths tutoring · Klasse 1 to 13
Maths tutor in Frankfurt, taught in English
Frankfurt pupils sit Hessian maths papers, but many of their families think, read and help with homework in English. This page sets out what maths a Frankfurt child meets in each Klasse and which tests and exams fall in 2027, from VERA-3 in the spring to the Landesabitur on 5 May 2027. It explains what live tutoring in English adds and what it cannot replace, and it ends with a geometry project on the city's own district map, where one wrong division makes the old town larger than a mountain range.
Teaching maths and coding live since 2020 · 10,000+ students worldwide · tutoring in English
In short
A maths tutor in Frankfurt, in English: Modern Age Coders gives live online maths lessons in English to Frankfurt pupils from Klasse 1 to 13, following the Hessen curriculum and its exams, from the central Realschule papers in May 2027 to the Landesabitur, or the IB, IGCSE or AP courses of international schools. One regular mentor explains each method in clear English at your child's pace, in a group or one to one.
Where Frankfurt pupils start
Three maths courses for Frankfurt pupils
A year-long course for the middle Klassen, a course for the Hessian Abitur, and one for children who want harder problems than school gives them.
Which maths tests does a Frankfurt pupil take, Klasse by Klasse?
Hessen follows the national Bildungsstandards, adds its own diagnosis in the primary years, and sets central papers at the end of Realschule and in the Abitur. The table puts the 2026/27 school year in order.
Maths tests and exams for Frankfurt pupils in the 2026/27 school year
Klasse
What happens
When
3
VERA-3 comparison test in maths and German
Test window 12 April to 26 May 2027
4 to 6
MSK-Online-Check, a digital maths diagnosis that schools may use
During the year, at the school's choice
8
VERA-8 comparison test in maths, German and languages
Test window 8 February to 25 March 2027
10, Realschule track
Central Abschlussarbeit in maths, plus German and the first foreign language
10 to 14 May 2027; resits 1 to 3 June 2027
Oberstufe
Written Landesabitur in maths, Leistungskurs and Grundkurs
Wednesday 5 May 2027; resit Thursday 3 June 2027
Sources: IQB, VERA-3 and VERA-8 test windows for 2027; Hessisches Ministerium für Kultus, Bildung und Chancen, pages on the MSK-Online-Check, the Realschulabschluss and the Landesabitur dates for 2027. Read on 2 and 3 November 2026.
Primary and lower secondary
VERA results are not marks. The IQB says no school or Land rankings come out of them; they show a teacher, a year early, where a class stands against the standards for grade 4 or grade 9. A weak VERA-3 result in May 2027 is a reason to look closely, not a verdict.
The MSK-Online-Check ("Mathe sicher können") is Hessen's own tool for Klassen 4 to 6. The ministry describes it as a digital diagnosis of basic maths skills that gives teachers support suggestions, free to every Hessian school since 2025/26. Its training themes are telling: natural numbers in Klasse 4 to 5, fractions and decimals in Klasse 6 to 7.
Where gaps usually open
Fractions and decimals are a common place for a gap to open, usually in Klasse 6 or 7, and the training themes of the Hessian check point at the same stage. A pupil who can add 2/3 and 3/4 without a calculator, and say why the answer is more than 1, has the base for equations in Klasse 7 and 8.
The second gap opens with functions and algebra in Klasse 8 to 10, just before the Realschule papers or the move into the Oberstufe. Tutoring before an exam year works far better than tutoring during one.
Hessen exams in 2027
How do the Hessen maths exams work in 2027?
Two moments matter most: the central papers at the end of the Realschule track in Klasse 10, and the written Landesabitur. Both are set by the ministry, not by the school alone.
Realschulabschluss, Klasse 10
In the Realschule track, the ministry writes the final papers centrally: "Die zentralen Abschlussarbeiten werden in den Fächern Deutsch, Mathematik und der ersten Fremdsprache geschrieben." A presentation based on a portfolio, in another compulsory subject, completes the procedure, and both count towards the overall grade.
The Realschulabschluss is awarded with an overall result of 4,4 or better. The qualifizierender Realschulabschluss, which opens the way to the gymnasiale Oberstufe, needs 3,0 or better including the papers in German, maths and the first foreign language. In 2027 the written papers fall between 10 and 14 May, with resits from 1 to 3 June 2027.
Landesabitur, Oberstufe
The Hessian Landesabitur combines central tasks from the ministry with parts written by the pupils' own teachers. The written exams in 2027 run from 15 April to 5 May 2027, and maths is the last of them: Wednesday 5 May 2027, for Leistungskurs and Grundkurs alike. The resit, with tasks that are also the same across Hessen, is on Thursday 3 June 2027.
On calculators, the ministry says the current rules in the Kerncurriculum hold up to the Abitur year 2029; from the Abitur year 2030, the requirements for extended calculator functions will follow the IQB. A pupil in Klasse 9 today should ask the school which calculator to buy.
The shared IQB task-pool format for Abitur maths, as published by the IQB
Level
Marks (Bewertungseinheiten)
Time, including choice time
Part A (no aids) handed in within
Leistungskurs (erhöhtes Niveau)
100
300 minutes
110 minutes
Grundkurs (grundlegendes Niveau)
80
255 minutes
100 minutes
Source: Institut zur Qualitätsentwicklung im Bildungswesen (IQB), pool documents for mathematics. Each Land decides through its own commission which pool tasks it uses and how many tasks of its own it adds, so a Hessian paper follows this frame but is not identical to another Land's. Exam dates: Hessian ministry, Termine Landesabitur 2027.
We prepare pupils for these papers, but we do not set or mark them, and nothing we do replaces the school course: the grade a Frankfurt pupil gets comes from the school and the ministry. What a tutor can do is make sure the methods are secure months before 5 May 2027, and practise with problems we write in the same style, never with leaked or copied exam tasks.
Maths in English
Does maths tutoring in English help a pupil at a German school?
Often, if it is done carefully. The maths is identical; what changes is the language around it, and we take care that a pupil can say every method in the words their teacher uses.
Only English, said up front
We teach in English and not in German, and we tell families that before the first class. For a child at an international school in or near Frankfurt, English is already the language of maths lessons. For a child at a Hessian Gymnasium or Realschule, it means two languages for one subject, which takes some care.
Both sets of words
Mentors keep a running list of the German terms from the pupil's own worksheets beside the English ones: Nenner and denominator, Bruch and fraction, Steigung and gradient, Ableitung and derivative. Pupils write their working in German when the paper will be German.
Pace, not pressure
The mentor adjusts speed and accent to the pupil, explains one idea in two or three ways, and waits. A pupil who hides confusion in a full classroom often asks freely in a small online group or alone with a tutor.
Our mentors are based in India and teach live over video, so Frankfurt afternoons fall in their evenings. A pupil keeps the same mentor through the school year, which matters in maths more than in most subjects: the tutor who saw the fraction gap in Klasse 6 is the one who notices it again when it comes back inside an algebra problem in Klasse 8.
A Frankfurt maths project
How big is Frankfurt's Altstadt? The shoelace formula on the city's own map
The city publishes the exact boundaries of its 46 Stadtteile as corner coordinates in metres. With one formula from coordinate geometry, a Klasse 9 or 10 pupil can turn those corners into an area, check it against the city's figure, and then fall into the most common unit trap in school maths.
The data
Stadt Frankfurt am Main publishes WFS Stadtgebietsgliederung under the Datenlizenz Deutschland Namensnennung 2.0. Its Stadtteile layer, downloaded on 3 November 2026 in metres (ETRS89, UTM zone 32N), gives each district as one polygon: the Altstadt has 231 corner points, each an east and a north value in metres.
The layer also stores an area for each Stadtteil, which lets a pupil check the answer. We exported the corners to a small file, stadtteile.json.
The formula
For a polygon whose corners (x, y) are listed in order around the edge, multiply each x by the next y, subtract the next x times this y, add everything up, take the absolute value and halve it. In German it is often called the Gaußsche Trapezformel; in English it is the shoelace formula, after the criss-cross pattern of the products.
It works for any polygon without crossings, however many corners it has, which is why a computer can do in a moment what would take a page by hand.
Version 1: test the formula on shapes you can checkPython
It prints: Pitch: 7140.0 m2 and L-shaped garden: 80.0 m2. A 105 m by 68 m pitch is 7,140 m²; the garden is 12 by 9 minus a 7 by 4 corner, 108 minus 28.
Only after the formula passes a test we can do in our heads do we trust it on real data. Version 2 runs straight after the function from Version 1 and also does the conversion two ways: once by dividing by 1,000, the mistake we see most, and once properly.
Version 2: two Stadtteile, and the unit trapPython
import json
with open("stadtteile.json", encoding="utf-8") as f:
parts = json.load(f)
for name in ["Altstadt", "Sachsenhausen-Süd"]:
m2 = shoelace(parts[name])
print(name, round(m2), "m2")
print(" wrong: / 1000 =", round(m2 / 1000, 1), "km2")
print(" right: / 1000000 =", round(m2 / 1000000, 2), "km2 =", round(m2 / 10000, 1), "ha")
It prints: Altstadt 506266 m2, wrong: / 1000 = 506.3 km2, right: / 1000000 = 0.51 km2 = 50.6 ha, then Sachsenhausen-Süd 30520652 m2, wrong: / 1000 = 30520.7 km2 and right: / 1000000 = 30.52 km2 = 3052.1 ha.
The shoelace result for the Altstadt, 506,266 m², matches the city's stored area of 506,265.71 m² to the nearest square metre. For Sachsenhausen-Süd we get 30,520,652 m² against the city's 30,520,651.41; the one square metre comes from our rounding of each corner to the centimetre. The formula is right. The danger is the next line.
A kilometre is 1,000 metres, so a square kilometre is 1,000 times 1,000 square metres: a factor of a million. Dividing by 1,000 makes the Altstadt 506 km², and Sachsenhausen-Süd over 30,000 km². A quick check shows which answer can be true.
Version 3: a box around the AltstadtPython
xs = [x for x, y in parts["Altstadt"]]
ys = [y for x, y in parts["Altstadt"]]
width = max(xs) - min(xs)
depth = max(ys) - min(ys)
print("Box:", round(width), "m by", round(depth), "m =", round(width * depth / 1000000, 2), "km2")
It prints: Box: 961 m by 934 m = 0.9 km2. The whole Altstadt fits in a box under one square kilometre, so 506 km² is impossible and 0.51 km² is believable.
Three Frankfurt Stadtteile by area (our shoelace calculation, city boundaries)
Stadtteil
Square metres
Hectares
Square kilometres
Altstadt
506,266
50.6
0.51
Bahnhofsviertel
532,302
53.2
0.53
Sachsenhausen-Süd
30,520,651
3,052.1
30.52
Data: Stadt Frankfurt am Main, www.frankfurt.de, WFS Stadtgebietsgliederung, layer Stadtteile, Datenlizenz Deutschland Namensnennung 2.0, downloaded 3 November 2026. Areas are our own shoelace results on unrounded corners, which agree with the city's Shape_Area field to the square metre; the conversions and the box check are ours. Of the 46 Stadtteile, the Altstadt is the smallest and Sachsenhausen-Süd the largest.
Klasse 5 and 6, on squared paper. Draw an L-shaped room, count the squares, then split it into two rectangles and check that both ways agree.
Klasse 7 and 8, by hand. Use the shoelace formula on a triangle with corners (0, 0), (6, 0) and (2, 5). Compare with one half times base times height.
Klasse 9 and 10, in Python. Run Version 1, then find the area of Bahnhofsviertel from the file and convert it to hectares without looking at the table.
Oberstufe. List the corners of a square clockwise instead of anticlockwise and print the sum before abs(). What does the sign tell you, and why does the formula need abs()?
Beyond the school course
Which maths competitions can a Frankfurt pupil enter in 2026/27?
Two national contests reach most schools, and both welcome pupils who simply enjoy problems.
Känguru der Mathematik
In 2027 the Känguru takes place on 8 April, later than its usual third Thursday in March, because that date would fall just before the Easter holidays in almost every Land. Schools register their pupils online from 1 December 2026 to 31 January 2027.
It lasts 75 minutes: 24 problems for Klassen 3 to 6 and 30 from Klasse 7. More than 920,000 pupils from over 13,000 schools took part in 2026.
Mathematik-Olympiade
The 66th Mathematik-Olympiade began with a school round in the autumn of 2026. The regional round is on 11 November 2026 and the Land round from 26 to 28 February 2027; the national final runs from 30 May to 2 June 2027 in Kaiserslautern.
Both contests enter through the school, so a pupil should ask the maths teacher. We are not connected with either organiser, and we train with original problems of our own.
Lesson times
When do maths lessons run in Frankfurt time?
Lessons sit after school on weekdays or on weekend mornings. The times below are examples in Frankfurt time with the matching clock in India.
Example Frankfurt lesson times and the mentor's clock
Frankfurt
India, winter (until 28 March 2027)
India, summer (from 28 March 2027)
16:50
21:20
20:20
18:10
22:40
21:40
Sunday 10:20
14:50
13:50
Under the Einheitenzeitgesetz, German time is UTC+1 in winter and UTC+2 in summer; summer time ended on 25 October 2026 and resumes on 28 March 2027. India keeps UTC+5:30 the whole year, which puts it four and a half hours ahead of Frankfurt now and three and a half hours ahead from late March.
Lessons continue through Hessian school holidays. Abitur pupils can use the Easter break, 22 March to 2 April 2027, for a block of extra practice before the written exams start on 15 April 2027.
Our maths ladder
What a pupil should be able to do before each step
Our own checkpoints, used to place a new pupil and to plan the year. They follow the order of the Hessian curriculum, not its wording.
Maths checkpoints from Klasse 3 to the Abitur (ours)
Before
Checkpoint
Typical warning sign
Klasse 5
Times tables and written division without hesitation
Counting on fingers for 7 times 8
Klasse 7
Fractions, decimals and percentages as one idea
Adding numerators and denominators
Klasse 9
Solve and check a linear equation; read a graph
Moving terms across the equals sign by habit
Klasse 10 papers
Area, volume, Pythagoras and units, with a sanity check
Answers that cannot be true, left unchecked
Abitur
Functions, derivatives and probability, explained in words
Correct method, wrong operator
For parents
The unit trap in the project above is the warning sign in row four. Pupils who check the size of an answer catch it; pupils who do not, lose marks in every exam year.
Reports to you say what your child can now do alone, and what is next.
For pupils
Square units grow by the square. Metres to kilometres is a thousand; square metres to square kilometres is a million.
Before you write the answer, ask whether it could fit inside a box you can picture.
More maths
Nine more maths courses for Frankfurt pupils
All taught live in English by one regular mentor, in a group or alone.
I
Primary years
Klasse 1 to 4
MTF / PRIM / 01
Primary maths
Counting to fractions, placed by grade, Klasse 1 to 5.
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Fees
Maths tutoring fees for Frankfurt families
Fees are monthly, for eight live lessons. The page lists them in euro, worked out at the European Central Bank reference rate; your card or bank is charged in US dollars and converts the amount, so the euro figure on the statement can be a little different.
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Frankfurt families ask
Maths tutor in Frankfurt in English: common questions
Are the classes in German?
No. All lessons are live and in English only. The tutor speaks clearly, adjusts to your child's pace and accent, and keeps the German terms from school worksheets alongside the English ones, so your child can still write answers in German for a Hessian paper.
When is the Abitur maths exam in Hessen in 2027?
The Hessian ministry has set the written Abitur in Mathematik, Leistungskurs and Grundkurs, for Wednesday 5 May 2027, the last day of the written exams that start on 15 April 2027. The resit is on Thursday 3 June 2027.
When are the Realschule final papers in 2027?
In the Hessian Realschule track, the central written papers in German, maths and the first foreign language run from 10 to 14 May 2027, with resits from 1 to 3 June 2027. A portfolio presentation in another subject completes the final grade.
Can you help my child in Klasse 4 or 5?
Yes. Our Primary maths course places children by grade, and many Frankfurt families start around Klasse 4 or 5, before fractions and decimals arrive. The free first lesson includes a short check on a recent worksheet so we start in the right place.
Does an English-speaking tutor confuse a pupil at a German school?
Not if the tutor keeps both sets of words. Our mentors write the German term from the worksheet next to the English one, and pupils practise writing their working in German when the test will be in German. The methods themselves do not change.
Do you tutor IB, IGCSE or AP maths?
Yes, for pupils at international schools in and around Frankfurt. We have courses for IB Mathematics AA and AI, IGCSE Mathematics and AP Calculus, alongside the Hessian school course and the Abitur.
When are lessons in Frankfurt time?
Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. Late afternoons are a common choice, or a weekend morning for a longer session.
Can you guarantee a better grade?
No, and nobody honestly can. The grade comes from the school and from the Hessian papers. What we promise is regular, careful teaching: secure methods, practice with problems we write ourselves, and an honest report on what your child can do.
What are the fees, and which currency do I pay in?
Lessons are paid monthly. Prices on this page are shown in euro at the European Central Bank reference rate, while the payment is taken in US dollars and converted by your bank, so your statement may differ slightly. The first lesson is free and needs no card.
Where are the tutors based?
In India. They teach live over video, so a 16:50 lesson in Frankfurt is 21:20 for the tutor in winter. Your child keeps the same tutor through the school year.
Bring a recent worksheet or test. The tutor works through part of it with your child, finds where the method breaks down, and suggests a course and a level.
To read more first: how we teach describes a live lesson, and all courses lists our maths syllabuses.
Lessons are live online with tutors based in India and are taught in English only. The quickest way to ask us something is WhatsApp, in English.
Want a class sooner? Book a priority demo
A priority demo is a full class of about 45 to 60 minutes. After the class the mentor sends a written skill report and a personal learning roadmap on WhatsApp. If you enrol, the demo fee is adjusted against your first month's fee. Share your demo Order ID with us on WhatsApp and we take it off.
