Chatswood · Kindergarten to Year 12 and adults · Maths taught live online

Maths tutor in Chatswood

Chatswood's Lunar New Year festival has just finished the Year of the Horse, and its organisers say they will see everyone "in February 2027 for Year of the Goat". The animal years come round every 12 years; leap years every 4. So here is a question for a Year 7 student: will a Year of the Goat ever be a leap year? The answer is no, never, and the reason is a lowest common multiple. Because 12 is a multiple of 4, every Goat year leaves the same remainder when divided by 4. The festival's Celebration Day on 13 February 2027 opens a second puzzle about weekdays, worked through below. That is how we teach maths in Chatswood, from Kindergarten counting to HSC Extension 2.

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Maths only on this page · Kindergarten to adult · Independent of every Chatswood school and the festival

Maths tutor in Chatswood, in brief

For Chatswood, Modern Age Coders provides live online maths teaching to anyone from 6 to 67: Kindergarten to Year 10 under the NSW syllabus, all four HSC maths courses up to Extension 2, and adult maths. Teaching happens over video at Sydney times, either privately or with up to twenty classmates at the same stage. Our Chatswood example uses lowest common multiples to show why a Year of the Goat is never a leap year. The first lesson is free.

Where Chatswood learners start

Number sense, junior algebra and HSC maths

Three courses for the most common Chatswood requests; the full list is below.

Mental Maths for Kids course thumbnail

CHW / 1

Number sense for young learners

Multiples, factors and patterns, the ideas behind every later cycle puzzle.

Open the syllabus →
Middle School Mathematics Mastery course thumbnail

CHW / 2

Years 7 to 10 maths

Factors and multiples, algebra and geometry, with reasoning written out.

Open the syllabus →
High School Mathematics course thumbnail

CHW / 3

HSC maths

Functions, calculus and proof for Advanced, Extension 1 and Extension 2.

Open the syllabus →

A Chatswood worked example

Will a Year of the Goat ever be a leap year?

Two repeating cycles, a 12-year cycle of animal years and a 4-year cycle of leap years, line up in a fixed pattern. The lowest common multiple tells us the pattern.

Chatswood's festival page says "Thank you for a fantastic Year of the Horse celebration. See you in February 2027 for Year of the Goat!"; it also shows pictures from "Chatswood's Year of the Dragon". The Goat years are 2027, 2039, 2051 and so on, 12 apart. Leap years are, almost always, the years divisible by 4. Since LCM(12, 4) = 12, adding 12 never changes a year's remainder on division by 4, so the pattern locks in.

Animal years and leap years (our calculation with the Gregorian calendar rules)
Animal yearsExample yearsRemainder when divided by 4Leap years?
Dragon2024, 2036, 20480Always, until the century rule
Horse2026, 2038, 20502Never
Goat2027, 2039, 20513Never
The weekday of 13 February in each Goat year (our calculation)
YearWeekday of 13 FebruaryLeap days since the previous Goat year
2027Saturdayn/a
2039Sunday3
2051Monday3
2063Tuesday3
2075Wednesday3
2087Thursday3
2099Friday3
2111Friday2 (2100 is not a leap year)

One weekday per cycle

Twelve years with three leap days are 4,383 days, which is 626 weeks and 1 day. So 13 February slides one weekday later every Goat year, from Saturday in 2027 to Friday in 2099.

The simple rule wins, for a while

Counting "one day per year plus one per leap day" predicts every row correctly until 2099. No calendar software is needed for most of this century.

Then the century rule bites

The year 2100 is divisible by 4 but not by 400, so it is not a leap year. That cycle has only 2 leap days and 4,382 days, exactly 626 weeks, so 2111 is a Friday again.

What students practise

Multiples, factors, remainders, the lowest common multiple and the greatest common divisor, and reasoning about repeating patterns rather than listing every case.

Years 7 and 8 students handle the leap-year table; senior students can prove that a 12-year shift preserves the remainder modulo 4.

Why a festival calendar

The festival is a real Chatswood event with real dates: Willoughby City Council lists the Chatswood Year of the Horse Festival among its sites. Neither the festival nor the council is connected with us; we only use the published years and dates.

The calendar arithmetic is ours, checked with the standard Gregorian rules.

Sources: Visit Chatswood, Lunar New Year festival and Willoughby City Council, read 14 October 2026. Calendar calculations are our own.

More cycle puzzles

The same idea in everyday questions

Once students see that repeating cycles meet at the lowest common multiple, they find the pattern everywhere.

Cycles that meet, and when (our worked answers)
Two cyclesLengthsThey line up again after
A weekly class and a fortnightly test7 days and 14 days14 days
Buses every 4 minutes and every 6 minutes4 and 612 minutes
A 12-year animal cycle and the 7-day week, ignoring leap days12 and 784 (LCM of 12 and 7)
Lights flashing every 3, 4 and 5 seconds3, 4 and 560 seconds

LCM and HCF together

For two numbers, the lowest common multiple times the highest common factor equals the product. For 4 and 6 that is 12 times 2, which equals 24. Students check the rule on several pairs before they trust it.

The calendar puzzle uses the LCM; simplifying fractions uses the HCF. They are two sides of the same factor list.

When the simple model breaks

Real calendars carry exceptions, like the year 2100. Good maths students learn to state the model, use it, and then ask where it stops being true.

That habit matters far beyond calendars, from timetables to physics.

HSC mathematics

Choosing HSC maths in Chatswood

NSW students in Years 11 and 12 choose among the Stage 6 mathematics courses published by NESA.

The main Stage 6 mathematics courses and our pages
CourseSuitsMore detail
Mathematics StandardPractical, applied mathsHSC Standard tutoring
Mathematics AdvancedCalculus-based studyHSC Advanced tutoring
Mathematics Extension 1Strong Advanced studentsHSC Extension 1 tutoring
Mathematics Extension 2Proof and the hardest problemsHSC Extension 2 tutoring

Past papers, used well

NESA encourages students to "Look at past HSC exam papers for Mathematics courses with marking guidelines and feedback to help you get ready for your exams."

We use them that way: one paper at a time, marked against the guidelines, with the mistakes turned into the next lesson.

No band promises

Tutoring improves understanding and exam habits; it cannot promise a band, a mark or an ATAR, and we never suggest otherwise.

Schools set assessment tasks for students to complete themselves, and we keep it that way.

Quoted from the NESA Stage 6 Mathematics page as it read on 14 October 2026.

Kindergarten to Year 10

Patterns and multiples from Kindergarten up

The calendar puzzle rests on ideas that start in the first years of school and grow every year.

Multiples and patterns through the years
YearsIdeaA Chatswood-style task
Kindergarten to 2Repeating patternsContinue a pattern of red and gold lanterns
3 to 6Multiples and times tablesWhich years between 2024 and 2060 are leap years?
7 and 8Factors, multiples, LCM and HCFWhen do a 12-year and a 4-year cycle line up?
9 and 10Remainders and simple proofShow that adding 12 keeps the remainder on division by 4

Tests along the way

Families with OC and selective tests in mind can read OC test maths and selective test mathematical reasoning. Problem solvers may enjoy the Australian Mathematics Competition practice.

Everything else on this page is about ordinary week-to-week maths.

Chatswood learners

The 2021 Census counted 1,979 Chatswood residents at primary school and 1,592 at secondary school, with 719 in vocational education and 1,836 at university. There were 1,227 residents aged 15 to 19.

Every one of them could join a lesson from home.

Source: ABS, 2021 Census QuickStats, Chatswood, read 14 October 2026.

Sydney time

Lessons through the 2027 NSW school year

Lessons follow the NSW terms on the Sydney clock, which moves for daylight saving in October and April.

The 2027 calendar

NSW public schools in the Eastern division start Term 1 on Thursday 28 January 2027, and Term 4 runs from Monday 11 October to Monday 20 December.

Revision blocks before the HSC exams are planned around those dates.

The teacher's side of the clock

Our teachers work in India, which has no daylight saving. A 6:30pm Chatswood lesson is 2pm for the teacher in winter and 1pm in summer.

Families keep the same lesson time all year.

Private lessons

One teacher, one learner: ideal for a gap, a deadline or a learner who prefers it.

Classes

Fifteen to twenty learners at one level, with questions that help everyone.

Working on show

Each line of reasoning goes up on a shared whiteboard for the teacher to follow.

Source: NSW Department of Education, term dates, read 14 October 2026.

Adult learners

Maths for adults in Chatswood

Adults study in their own classes or privately, usually for practical reasons.

Back to basics

Fractions, percentages and ratio, rebuilt calmly with time for every question.

For work

Estimating, checking figures and reading charts, with an eye for numbers that do not add up.

For the family

Understanding how schools teach methods now, so homework help agrees with class.

The calendar puzzle is a good first lesson for adults too: it needs only multiples and remainders, and it ends with a genuine surprise in the year 2100.

Progress

From patterns to proof

A learner moves to the next stage when the skill works on a fresh problem.

Stages and their checks
TypicallyStageChecked by
Kindergarten to Year 21. PatternsContinuing and describing a repeating pattern
Years 3 to 62. MultiplesListing multiples and spotting common ones
Years 7 to 103. LCM and remaindersExplaining when two cycles line up
Years 11 and 124. ProofProving a pattern holds for every case

Arriving in Year 11

Late starters usually need algebra and functions strengthened first; we say how long that should take.

It makes Stage 6 far more manageable.

Adults

Adults often enjoy pattern and number puzzles more than they expect.

Adult classes are kept separate from school students.

Course list

Maths courses for Chatswood

By stage. Cards use our international course names; lessons follow the NSW stages and HSC courses.

I

Kindergarten to Year 6

Primary
II

Years 7 to 10

Stages 4 and 5
III

Stage 6 and adults

Senior and beyond

How it works

A maths week for Chatswood families

Lessons sit at fixed Sydney times, with the October and April clock changes absorbed on our side.

After school

Kindergarten to Year 10.

Evenings

HSC students and adults.

Weekends

Longer lessons by request.

A steady teacher

The same teacher week after week.

Notes home

Brief, honest updates for parents.

Levelled classes

Grouped by skill, not just age.

Real puzzles

Local dates and data alongside textbook work.

HSC run-up

Private lessons can be added before trials.

Reasoning aloud

Learners explain before practising.

Student work

Projects our learners built

Things made by students who began with maths like this. More in the student labs.

NutriLife AI nutrition coach project screenshot

AI and ML

NutriLife

An AI nutrition coach that reads what you eat and works you toward a target.

by Bhavya · Open it

Misti AI chatbot for maths and coding screenshot

AI and ML

Misti

A chatbot that answers mathematics and programming questions, built and deployed by a student.

by Harshit · Open it

GuardianX AI internet safety assistant screenshot

AI and ML

GuardianX

An assistant that helps a young person recognise unsafe situations online.

by Vivaan · Open it

SkyCast weather forecast application screenshot

Web app

SkyCast

A weather forecasting site with live conditions for any location.

by Krish

Fees

Fees for Chatswood maths lessons

Outside India, lessons are billed once a month in US dollars. Joining is free and you can stop whenever a month ends.

Free first class

USD 0

no card required

  • A real lesson at the right level
  • Straight advice afterwards
  • No card needed
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Group batch

USD 100

a month, billed in US dollars

  • Fifteen to twenty learners at one level
  • One teacher across the term
  • Marked practice
  • Stop at any month end
Start here

One to one

USD 150

a month, billed in US dollars

  • Private teaching
  • One goal at a time
  • Helpful before HSC trials
Enquire

What families say

Rated 4.9 across 547 Google reviews

Families reviewing us on Google, verbatim.

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"Modern Age Coders has been a game-changer for me. I struggled to grasp IT concepts and coding before joining, but their classes transformed everything. I can now confidently write complex programs with ease."

Samriddha Mondal

Student

★★★★★

"One of the most wonderful education centres out there. Education is not limited to school syllabus but focuses on skill development."

Vansh Agarwal

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★★★★★

"My child Dhairya is really enjoying the Modern Age Coders classes. This is his first online class and he eagerly looks forward to it. I can already see his improvement, and the teachers are very cooperative."

Sonam Oswal

Parent of Dhairya

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"Modern Age Coders have wonderful teachers who teach in a clear, easy and practical way. The teacher boosts students' confidence and inspires them to learn without hesitation."

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Chatswood maths questions

Questions about a maths tutor in Chatswood

Can Chatswood students have maths lessons with you?

Yes. Lessons are online and scheduled on Sydney time, for Kindergarten to Year 12 and adults, as private lessons or level-matched classes.

Which of the HSC maths courses can you help with?

All four: Standard for applied maths, Advanced for calculus, and Extension 1 and Extension 2 for students who want more depth.

Is a Year of the Goat ever a leap year?

No. Goat years are 12 apart and 12 is a multiple of 4, so every Goat year leaves remainder 3 on division by 4. 2027, 2039 and 2051 are all ordinary years.

What is a lowest common multiple?

The smallest number that is a multiple of two or more numbers. LCM(12, 4) is 12, which is why the animal-year and leap-year cycles line up the same way every time.

What weekday is 13 February 2027?

A Saturday. In each later Goat year it moves one weekday on, reaching Friday in 2099; because 2100 is not a leap year, it is Friday again in 2111.

Can you guarantee an HSC band?

No tutor can. We aim for real understanding and tell you frankly how it is going; the band and the ATAR are earned in the exams.

Do lessons move when the clocks change?

No. Lessons stay at the same Sydney time; we adjust the teacher's schedule.

Do you teach adults?

Yes, in adult classes or one to one.

Why is 2100 not a leap year?

Under the Gregorian rules, a year divisible by 100 is a leap year only if it is also divisible by 400. 2000 was a leap year; 2100 will not be.

Is there a charge for the first lesson?

No. It is free; monthly fees after that are shown in the fees panel.

Also on this site

More for Chatswood families

NSW maths pages and our Chatswood coding page.

HSC Extension 2

Proof and complex numbers.

HSC Advanced

Calculus-based senior maths.

Selective test maths

For Year 6 applicants.

Maths tutor in Parramatta

Another Sydney suburb page.

Maths tutor in Sydney

The citywide page.

Coding in Chatswood

Programming and AI classes.

Start here

Book a free Chatswood lesson

Let us know the year level and the topic causing trouble. The free lesson is taught properly, and afterwards you get our honest recommendation.

Background reading: our teaching approach, and online maths lessons across Australia.

WhatsApp us · +91 91233 66161 · connect@modernagecoders.com

Replies come from India, where our teachers are based, so the number has a +91 code. We do not have a Chatswood office. WhatsApp is usually quickest.

Free, no card, no obligation.

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