Munich · Maths help in English · Klasse 1 to Abitur
A maths tutor in Munich who teaches in English
Bavarian maths has more fixed checkpoints than most families expect: a transfer report in Klasse 4, comparison tests in Klasse 3 and 8, at least three Schulaufgaben a year in the Gymnasium middle school, central tests in grades 8 and 10, and from this school year a new digital test in grade 11. Here is each one by school type, with the 2027 dates, the German words your child will read in them, and a real Munich task that shows how we teach: slowly, in English, with the reasoning written down.
Live online since 2020 · 10,000+ students worldwide · Bavarian maths explained in English
In short
Modern Age Coders is a maths tutor for Munich pupils that teaches live online in English, with mentors who match your child's pace and accent. We follow the Bavarian school year from Grundschule and the Übertritt in Klasse 4, through Schulaufgaben and Jahrgangsstufentests, to the Realschule final exam and the Abitur, and we teach the German maths words alongside. Lessons run one to one or in a batch of fifteen to twenty.
Where to start
Three maths courses for Munich pupils
One for the middle years where most gaps open, one for the Oberstufe, and one for Grundschule children before the Übertritt. The mentor maps each to your child's school type.
Which maths tests does a pupil in Munich sit, and when?
Some are national, some Bavarian, some belong to one school type. This table puts them in the order a child meets them.
Maths checkpoints for pupils at Bavarian schools, with dates for 2027 where published
Klasse
Checkpoint
School type
What we know for 2027
3
VERA-3 in maths, a comparison test
Grundschule
Test window 12 April to 26 May 2027; not graded
4
Übertrittszeugnis, the transfer report
Grundschule
Early May; average of German, maths and Heimat- und Sachunterricht
Mittelstufe
At least three Schulaufgaben in maths each year
Gymnasium
Grade 9 reduced from four to three
8
VERA-8 in maths
Secondary schools
Test window 8 February to 25 March 2027; not graded
8 and 10
Jahrgangsstufentest in maths
Gymnasium
Continues in the usual form
10
Abschlussprüfung in maths
Realschule
Part of the final exam with German, English and the profile subject
11
Central digital test of basic skills
Gymnasium
New from 2026/27, in the second half-year, counts as a small assessment
Q12 and Q13
Abitur
Gymnasium
Five subjects: three written exams and two oral
Sources: IQB, VERA-3 and VERA-8 pages (2027 windows); Bayerisches Staatsministerium für Unterricht und Kultus, pages on the Grundschule, the Realschule, the Gymnasium and Prüfungskultur am Gymnasium. Read 2 and 3 November 2026. According to the IQB, VERA produces no marks and no ranking of schools or Länder.
The ministry's page on assessment at the Gymnasium explains the newest change. From the school year 2026/27, a central digital test of Grundkompetenzen, the basic skills, is provided for grade 11. Pupils take it in a digital exam environment in the second half of the year, it counts as a small assessment, a kleiner Leistungsnachweis, and in the first step schools may choose whether to take part. The grade 8 and grade 10 Jahrgangsstufentests in maths carry on as before.
The same page also allows modular maths systems, MMS, as a digital aid in assessments from grade 8. For a pupil who learned maths in English with a graphing app, that is good news, but it also means the written working around the tool is what earns the marks. We practise both: using the tool and explaining in words what it showed.
School types
How does maths differ between Mittelschule, Realschule and Gymnasium in Bavaria?
The topics overlap far more than the school names suggest. What changes is the pace, the exam at the end, and how much written reasoning is expected.
Mittelschule
Runs to grade 9, or 10 in the M-Zug. The ministry describes a qualifizierender Abschluss for strong results and the option of the mittlerer Schulabschluss in grade 10 through the M-Zug. Maths help here is about secure arithmetic, percentages and everyday modelling.
Realschule
Ends after grade 10 with the Abschlussprüfung in German, English, maths and the profile subject of the chosen branch. Help focuses on algebra, functions and geometry, and on writing a solution that a marker can follow step by step.
Gymnasium
Nine years again, with the Oberstufe from grade 11 to 13 and the Abitur after Q13. Maths moves fastest here; the Schulaufgaben, the two Jahrgangsstufentests and the new grade 11 test are where gaps first show.
Across all three, the KMK's national standards set the same big ideas. The standards for the Abitur name five Leitideen, among them Funktionaler Zusammenhang, functions and how one quantity depends on another, and Daten und Zufall, data and chance. The trend-line task further down sits right where those two meet.
German maths words an English-speaking pupil meets first (our list)
German
English
Where it usually appears
Dreisatz
Rule of three, scaling a ratio
Klasse 6 and 7
Zuordnung, proportional
Direct proportion
Klasse 7
Term, Gleichung
Expression, equation
Klasse 7 and 8
Gleichungssystem
Simultaneous equations
Klasse 8 to 9
Wahrscheinlichkeit
Probability
Klasse 7 onward
Mittelwert, Median
Mean, median
Klasse 6 onward
Ausgleichsgerade
Line of best fit
Data work, Oberstufe
Ableitung
Derivative
Grade 11 onward
The word list and the usual grades are our own teaching notes, not an official syllabus; Bavarian schools set the exact order in their own plans.
A pupil who moved to Munich from an English-language school often knows the mathematics and loses marks on the wording. "Begründe" asks for a reason, "berechne" for a calculation, "skizziere" for a sketch, and a correct number without the requested reason earns only part of the marks. Our mentors teach in English and show the German instruction word next to each task, so the pupil learns to read the question the way the teacher wrote it.
A Munich data task
Is Munich getting warmer? Fitting a trend line by hand
The Deutscher Wetterdienst publishes one mean temperature per year for its station München-Stadt, from 1955 to 2025, as open data. With it, a pupil in grade 10 or the Oberstufe can do a least-squares regression from the formula, then check the answer against the DWD's own figures.
The data
The annual file for station 3379 has 71 years, each with a mean temperature in degrees Celsius; no year is missing. We give the pupil munich_years.csv with three columns: the year, the mean temperature and the year's rain.
One warning sits in the metadata, not in the numbers: the station stood at 520 metres until 7 July 1997 and has been at a site at 515 metres since 8 July 1997. A good analysis mentions that, because a move can shift readings a little.
The method
For a line y = mx + c through points (x, y), least squares gives the slope m as the sum of (x minus the mean of x) times (y minus the mean of y), divided by the sum of (x minus the mean of x) squared. The line then passes through the point of means, so c is the mean of y minus m times the mean of x.
Pupils first do it by hand for five years to see how it works, then let Python do all 71.
Version 1: the least-squares line through 71 yearsPython
import csv
years = []
temps = []
with open("munich_years.csv") as source:
for line in csv.DictReader(source):
years.append(int(line["year"]))
temps.append(float(line["mean_temp"]))
n = len(years)
x_bar = sum(years) / n
y_bar = sum(temps) / n
top = sum((x - x_bar) * (y - y_bar) for x, y in zip(years, temps))
bottom = sum((x - x_bar) ** 2 for x in years)
m = top / bottom
c = y_bar - m * x_bar
print("Years:", n, "from", years[0], "to", years[-1])
print(f"Mean of all years: {y_bar:.2f} C")
print(f"Slope: {m:.4f} C per year, {10 * m:.2f} C per decade")
print(f"Line at 1960: {m * 1960 + c:.2f} C, at 2025: {m * 2025 + c:.2f} C")
It prints: Years: 71 from 1955 to 2025, Mean of all years: 9.63 C, Slope: 0.0345 C per year, 0.34 C per decade and Line at 1960: 8.60 C, at 2025: 10.84 C.
The slope is about 0.034 degrees a year, so the fitted line rises by roughly 0.34 degrees per decade and by more than two degrees between 1960 and 2025. That is a description of the past 71 years at one station. It is not a forecast: nothing in the method knows about the future, and a pupil who extends the line to 2100 has only drawn a longer ruler.
Version 2 asks the question in another way. Instead of one line, it compares two thirty-year averages, the kind of figure meteorologists call a climate normal.
Version 2: two thirty-year meansPython
import csv
temp = {}
with open("munich_years.csv") as source:
for line in csv.DictReader(source):
temp[int(line["year"])] = float(line["mean_temp"])
def period_mean(first, last):
values = [temp[y] for y in range(first, last + 1)]
return sum(values) / len(values)
old = period_mean(1961, 1990)
new = period_mean(1991, 2020)
print(f"1961 to 1990: {old:.2f} C")
print(f"1991 to 2020: {new:.2f} C")
print(f"Difference: {new - old:+.2f} C")
It prints: 1961 to 1990: 9.14 C, 1991 to 2020: 10.11 C and Difference: +0.96 C.
Our averages for München-Stadt against the DWD's published climate normals
Period
Our mean from the annual file
DWD normal for station 3379
1961 to 1990
9.14 °C
9.1 °C
1991 to 2020
10.11 °C
10.1 °C
Difference
+0.96 °C
+1.0 °C
Data: Deutscher Wetterdienst, Climate Data Center, annual climate values for station 3379 München-Stadt (1955 to 2025) and the multi-annual means 1961 to 1990 and 1991 to 2020, licence CC BY 4.0, downloaded 3 November 2026. The regression, the period means and the differences are our own calculations. The DWD marks its 1961 to 1990 figure as referred to the current station site.
Klasse 5 and 6. The means for 2023, 2024 and 2025 were 11.57, 11.58 and 10.66 °C. Find their average. (Answer: 11.27 °C.)
Klasse 7. Rain fell from 1,126.8 mm in 2024 to 738.5 mm in 2025. Find the percentage change to one decimal place. (Answer: a fall of 34.5 percent.)
Klasse 8 to 10. The line gives 10.84 °C for 2025, the station measured 10.66 °C. Find the residual and say what its sign means. (Answer: minus 0.18; 2025 was a little cooler than the trend.)
Klasse 10 and Oberstufe. Our program finds the largest residuals in 1994, 1.41 above the line, and 1996, 1.56 below it. Explain why one cool year next to one warm year does not change the slope much.
Oberstufe. Write two sentences for a report: one that the data supports, one that it does not. Use the words Ausgleichsgerade and Prognose correctly.
Practice set written by Modern Age Coders; the answers come from our own runs on the DWD annual file.
Class times
When can a Munich pupil take a maths lesson?
After the school day and before dinner, or on a quiet Sunday morning, with the mentor in the Indian evening or afternoon.
Sample Munich lesson times and the mentor's time in India
Munich time
India, until 28 March 2027
India, from 28 March 2027
16:45
21:15
20:15
18:15
22:45
21:45
Sunday 10:15
14:45
13:45
Under the Einheitenzeitgesetz, Germany runs on UTC+1 in winter and UTC+2 in summer. Clocks went back on 25 October 2026 and go forward on 28 March 2027. India stays on UTC+5:30, four and a half hours ahead of Munich in winter, three and a half in summer. Example rows only, not set batch times.
Families usually plan the heavier weeks around the Bavarian calendar: Christmas holidays from 24 December 2026 to 8 January 2027, Easter from 22 March to 2 April 2027, and Whitsun from 18 to 28 May 2027, according to the KMK holiday table. Many pupils add a second weekly lesson in the four weeks before a Schulaufgabe or the Realschule final exam.
How we work
From a lost mark to a secure method
Our own sequence for a pupil who comes to us with a weak result, used in every school type.
Five stages of a tutoring plan (ours)
Stage
What happens
How you see it
1. Read the paper
We go through the last test with your child, question by question
A short list of what went wrong and why
2. Fix the base
The missing earlier topic is taught again, in English, with the German terms
Small checks your child passes
3. Write it out
Solutions in full sentences and steps, as markers expect
Neat worked solutions in the notebook
4. Mixed practice
Questions in the style of a Schulaufgabe, timed
A score your child records
5. Explain back
Your child teaches one method to the mentor
Confidence you can hear
For parents
We never promise a grade. We show you what changed in your child's work, in their notebook, week by week.
The school's marks are the ones that count; our job is to make the method secure behind them.
For pupils
A number on its own is half an answer. Write down how you got there.
If a line fits the points, ask what it does not tell you before you trust it.
More maths
Nine more maths courses for Munich pupils
All taught live, in English, by a mentor who stays with your child, in a batch or privately.
Two live lessons a week with one mentor, built around what is due at school next. 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
After the school day, from about 16:45 Munich time.
Sundays
A quiet morning slot before the school week.
1-on-1
Times agreed around Schulaufgaben and exams.
One mentor
The same tutor follows your child through the year.
English, with German terms
Explained in English, labelled in German.
Written working
Every answer comes with its steps.
School first
We start from the next test, not from a fixed book.
Short reports
What was covered and what to practise.
Batch or private
Fifteen to twenty pupils, or one to one.
Student work
Projects from our students
Maths and code meet in many of our students' projects. A few are below; the student labs page has more.
AI and ML
NutriLife
An AI nutrition coach that reads what you eat and works you toward a target.
A weather forecasting site with live conditions for any location.
by Krish
Fees
Maths tutoring fees for Munich families
A monthly fee for eight live lessons. The page displays it in euro, worked out at the European Central Bank reference rate; your card is charged in US dollars and your bank converts it, so the booked amount can differ slightly.
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Munich families ask
Maths tutoring in Munich in English: common questions
Are the classes in German?
No. Every lesson is live and in English only. The mentor adapts to your child's pace and accent and writes the German maths terms next to the English ones, so your child can read the Schulaufgabe in German and still follow the explanation in English.
Can you help with the Übertritt in Klasse 4?
We help with the maths behind it: place value, the four operations, measuring and word problems. The Übertrittszeugnis itself is based on the school's marks in German, maths and Heimat- und Sachunterricht, so we work alongside the class teacher, never instead of the school.
Do you prepare for the Realschule final exam in maths?
Yes. The Bavarian Realschule ends after grade 10 with an Abschlussprüfung in German, English, maths and the profile subject. We cover the maths with practice questions we write ourselves, timed, and we teach how to set out each step.
What is the new grade 11 test at the Gymnasium?
From 2026/27 the Bavarian ministry provides a central digital test of basic skills in maths for grade 11. It is taken in the second half-year in a digital exam environment and counts as a small assessment; at first, schools may choose whether to use it.
Can you help with the Abitur in Bavaria?
Yes, alongside school. The Bavarian Abitur has three written and two oral exams across five subjects, after Q12 and Q13. We teach Analysis, Geometrie and Stochastik in English. The school course and the exam are what count; we do not award grades.
My child is at an international school in Munich. Can you help?
Yes. The international schools near Munich listed by the AGIS teach IB programmes, and we run separate courses for IB and IGCSE maths. The mentor first checks which programme and level your child follows, then plans from their next assessment.
When are lessons in Munich 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. Most Munich pupils pick a slot between about 16:45 and 19:00, or a Sunday morning.
Who are the tutors?
Our mentors are based in India and teach live over video in English. Your child keeps the same mentor, who learns where they tend to slip and how they like to work.
How big are the groups?
A batch has fifteen to twenty pupils at a similar level. For exam preparation or a large gap, most Munich families choose one to one, with two private lessons a week.
How are fees paid?
Monthly. We show the fee in euro at the European Central Bank reference rate; the payment is made in US dollars and your bank converts it, so the amount on your statement may differ a little. The first lesson is free and needs no card.
Bring a recent Schulaufgabe, a homework sheet or simply a topic that feels shaky. The mentor works through it with your child, sees where the difficulty really starts, and proposes a plan.
Lessons are live online with mentors in India, in English only. Write to us on WhatsApp, in English, with any question.
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.
