Australia · Years 1 to 6 · Checked at each organiser

Maths competitions for primary kids

Maths competitions can give primary children something school maths rarely does: problems with no obvious method, where the fun is in working out how to start. Australia has a strong set of them, from the Australian Mathematics Competition, first run in 1978, to the APSMO Maths Olympiad for Years 5 and 6 and a brand-new paper for Years 1 and 2. This page lists them by year level, with every detail checked at the organiser, and works through one problem-solving strategy that helps on almost every paper. We are independent of every organiser named, and we never reproduce their questions.

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Checked at each organiser on 7 October 2026 · Independent of all of them · Problem solving, not drilling

In short

Australian primary students can sit the Australian Mathematics Competition from Year 3 (60 minutes for primary), Kangourou sans Frontières, ICAS Mathematics from Year 2, the APSMO Maths Olympiad in Years 5 and 6, and the AJMO up to Year 8. The Maths Challenge program runs over 3 to 4 weeks. Years 1 and 2 can try the free AMC Early Primary pilot from 12 to 23 October 2026.

Where to start

Three courses for young problem solvers

Number sense and problem solving first; competitions reward both.

Mental Maths for Kids course thumbnail

MPK / 01

Mental maths for kids

Number sense rather than tricks, for ages 5 to 10: the base every primary paper builds on.

Open the syllabus →
Maths Olympiad & Competition Course course thumbnail

MPK / 02

Competition maths

Problem-solving strategies for the AMC and APSMO style of question, and beyond.

Open the syllabus →
Elementary Maths for Grades 1-5 course thumbnail

MPK / 03

Primary maths

Live classes that place each child by level, so competition work rests on secure basics.

Open the syllabus →

The competitions

Maths competitions open to primary students, by year level

Year levels and 2026 dates are as each organiser publishes them. Most competitions are entered through schools.

Maths competitions and programs for Australian primary students, 2026
CompetitionOrganiserPrimary years2026 timing
AMC Early Primary (free pilot)Australian Maths TrustYears 1 and 212 to 23 October, online
ICAS MathematicsICAS AssessmentsYears 2 to 6 (and to Year 12)24 to 28 August sitting window
Kangourou sans Frontières (KSF)Australian Maths TrustYears 3 to 6 (and secondary)24 to 26 March
Maths ChallengeAustralian Maths TrustYears 3 to 6 (and to Year 10)A 3 to 4 week program between 2 March and 26 June
Australian Mathematics Competition (AMC)Australian Maths TrustYears 3 to 6 (and secondary)4 to 6 August
Maths EnrichmentAustralian Maths TrustCapable students from Year 412 to 16 weeks between 30 March and 16 October
Maths Olympiad Years 5-6APSMOYears 5 and 66 May, 10 June, 29 July, 9 September
Australian Junior Mathematics Olympiad (AJMO)Australian Maths TrustUp to Year 8Thursday 10 September

Coding and computational thinking contests for the same age group are gathered in our guide to coding competitions for primary kids, and the full year appears month by month on the Australian competitions calendar. Entry fees are set by the organisers and are not shown here.

Sources: AMT AMC; AMT Maths Challenge; AMT AJMO; AMT 2026 key dates; APSMO Maths Olympiad Years 5-6; ICAS 2026 dates. Read 7 October 2026.

Formats

What each one actually involves

Competitions differ more in format than in difficulty. Knowing the format helps a child prepare calmly.

Formats for primary students, from the organisers
CompetitionPrimary formatWorth knowing
AMC60 minutes; Middle Primary (Years 3 and 4) and Upper Primary (Years 5 and 6) divisionsTopics may include arithmetic, fractions and ratios, pre-algebra, geometry, measurement, statistics and probability, and problem solving
AMC Early Primary pilot25 questions (20 multiple choice, 5 integer answer), 50 minutes, online onlyFree in 2026; the AMT says it will join the standard AMC from 2027
Maths ChallengeAbout 1 hour of class time and 2 to 3 hours of study a weekPrimary students work in groups of three; problems vary each year, based on the national curriculum
APSMO Maths OlympiadFour contests about six weeks apart; each has 5 questions worth 1 mark, in 30 minutesSchool entry only; teams of up to 30 students; running in Australia since 1987
ICAS MathematicsYear 2: 30 questions in 35 minutes; Years 3 to 5: 40 in 45 minutes; Year 6: 40 in 1 hourOne paper per year level, sat at school or a testing centre
AJMO10 problems, 90 minutes, online, single integer answers from 0 to 999A first olympiad-style paper; schools choose the AJMO or the AIMO for each student

The AMC, according to the AMT, is Australia's longest running, largest and best-known maths competition for school students. Kangourou sans Frontières, which the AMT says was inspired by the AMC, now has more than 6 million participants worldwide each year.

Maths Enrichment is a different kind of program: an extension course for capable students from Year 4, run over 12 to 16 weeks with printed notes students keep, in divisions named after mathematicians from Ramanujan to Pólya.

APSMO describes its Maths Olympiad as an inter-school competition for high-achieving and high-potential Years 5 and 6 students, completed individually under exam conditions, with solutions reviewed as a group afterwards.

The AJMO is new: the AMT pitches it at students up to Year 8 who enjoy challenging problems but are not yet ready for the Australian Intermediate Mathematics Olympiad.

Strategy lesson

Solve a simpler problem first

Competition problems often look too big to start. One reliable strategy is to shrink the problem, solve small versions, and look for the pattern. The problem below is ours.

The problem

How many squares of any size can you find in a 6 by 6 grid? Not just the 36 small ones: 2 by 2 squares, 3 by 3 squares, all the way up to the whole grid.

Make it smaller

Start with a 1 by 1 grid: 1 square. A 2 by 2 grid has 4 small squares and 1 big one: 5. A 3 by 3 grid has 9, 4 and 1: 14.

Find the pattern

The counts are 1, then 1 plus 4, then 1 plus 4 plus 9. Each grid adds the next square number. So a 6 by 6 grid has 1 plus 4 plus 9 plus 16 plus 25 plus 36.

Squares of any size in an n by n grid, counted by size
Grid1 by 12 by 23 by 34 by 45 by 56 by 6Total
1 by 111
2 by 2415
3 by 394114
4 by 41694130
5 by 5251694155
6 by 636251694191

The answer for the 6 by 6 grid is 91. The table also shows why the pattern works, which matters as much as the number: in a 6 by 6 grid, a 2 by 2 square can start in any of 5 positions across and 5 down, giving 25; a 3 by 3 square in 4 positions each way, giving 16; and so on, until the single 6 by 6 square. Children who can explain that reason have done more than spot a pattern, they have shown why it must continue. This is exactly the habit the harder competition questions reward, and it carries all the way to olympiad level.

Trying it at home

Draw the small grids on squared paper and colour each size of square in a different colour. Counting by colour keeps the work organised and makes the pattern visible.

Then ask a follow-up: what about a 6 by 4 rectangle? The same shrinking strategy works, and the answer is a good test of whether the reason was really understood.

Other places it helps

Problems about handshakes, paths through a grid, or numbers in a growing pattern all yield to the same move: try the small cases, record them in a table, and look for what changes each time.

It also builds patience. A child who knows that small cases lead somewhere is far less likely to give up on a question that looks impossible at first.

Choosing

Picking a first competition, and preparing for it

For most children, the right first competition is a short one that feels like a game. Here is a gentle starting guide.

A starting guide for primary maths competitions
Year levelA gentle first stepWhen ready for more
Years 1 and 2AMC Early Primary (free pilot), puzzles at homeICAS Mathematics in Year 2
Years 3 and 4Maths Challenge with friends, KSFThe AMC Middle Primary division
Year 5The AMC Upper Primary divisionAPSMO Maths Olympiad, Maths Enrichment
Year 6APSMO Maths OlympiadThe AJMO, or Maths Enrichment at a higher division

Our classes build number sense and problem-solving strategies: drawing a picture, making a table, working backwards, solving a simpler problem, checking an answer makes sense. Children explain their thinking out loud, because explaining is how the strategies stick.

Practice uses problems we write ourselves in a similar spirit; organisers' past papers belong to them and we never reproduce them.

We are independent of the Australian Maths Trust, APSMO and ICAS, and do not enter children or handle results. Entries normally go through schools, and each organiser explains how families can take part.

We do not promise a score, a certificate level or a medal. For a primary child, a competition is a chance to enjoy hard thinking, and the result is simply one day's snapshot.

Growing as a problem solver

Four rungs through primary maths competitions

Children grow at different speeds; the order is usually this one.

From confident counting to explained solutions
AroundRungThe sign it is secure
Years 1 and 21. Confident with numberCounts, adds and compares quickly and accurately
Years 3 and 42. Has strategiesChooses to draw, list or act out a problem without being told
Years 4 and 53. Organises workRecords small cases in a table and spots the pattern
Years 5 and 64. Explains whySays why a pattern must continue, not only that it does

After a competition

Look at one question your child found hardest and solve it together slowly. That single conversation teaches more than another practice paper.

Praise the strategy, not the score. Strategies are what carry forward.

Coding contests too

For coding and computational thinking contests, see coding competitions for primary kids.

Older students can read our Australian Mathematical Olympiad guide.

The catalogue

Nine courses for primary mathematicians

From number sense to competition strategy. Each card opens its syllabus.

I

Number sense

Years 1 to 4

MPK / NS / 02

Early maths foundations

Secure first steps in number.

Open the syllabus

MPK / NS / 03

Abacus mental maths

Visual calculation for young learners.

Open the syllabus
II

Problem solving

Years 3 to 6
III

Stretch

Upper primary and beyond

How lessons run

Friendly online maths classes after school

Our maths teachers teach live from India. Australian clocks run ahead: Darwin by four hours all year, Melbourne by four and a half in winter and five and a half in summer. So an Australian after-school maths class takes place in the Indian afternoon, at a comfortable hour for young children.

After school

Number sense and a strategy of the week.

Saturday morning

A longer set of puzzles, solved together.

Before a competition

Calm practice with our own problems.

Strategies taught

Draw it, list it, shrink it, check it.

Thinking out loud

Children explain how they solved each problem.

Original problems

Never copied from competition papers.

Classes of fifteen to twenty

Children at a similar level, learning from each other.

One-to-one option

For a child who needs a different pace or more stretch.

No medal promised

Organisers set and mark; we build the thinking.

Student work

Work our students have shared

Made for the love of it, apart from any competition. See the student labs.

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Fees

Fees

Maths classes are charged per month in US dollars, our international rate, with no enrolment fee and no fixed term. Competition entries are arranged with the organisers, usually through schools, and are separate from our fees.

Free first class

USD 0

no card required

  • A free first maths class
  • A short check of number sense and strategies
  • No payment details
Book it

Group batch

USD 100

a month, billed in US dollars

  • Fifteen to twenty children at one level
  • The same teacher each week
  • Problems solved and discussed together
  • A certificate on completion
Start here

One to one

USD 150

a month, billed in US dollars

  • A teacher for one child
  • Work pitched exactly at the child's level
  • Times arranged around family life
Enquire

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Questions about primary maths competitions

What parents and teachers ask

What maths competitions can primary students enter in Australia?

The AMC from Year 3, Kangourou sans Frontières, the Maths Challenge program, ICAS Mathematics from Year 2, the APSMO Maths Olympiad in Years 5 and 6, the AJMO up to Year 8, and Maths Enrichment for capable students from Year 4.

Is there anything for Years 1 and 2?

Yes. The AMT is running a free AMC Early Primary pilot for Years 1 and 2 from 12 to 23 October 2026: 25 questions in 50 minutes, online only. ICAS Mathematics also has an Introductory paper for Year 2.

What is the APSMO Maths Olympiad?

An inter-school competition for Years 5 and 6 run by APSMO since 1987: four contests a year, each of 5 questions in 30 minutes, entered by schools in teams of up to 30 students.

How long is the AMC for primary students?

Sixty minutes for the Middle Primary (Years 3 and 4) and Upper Primary (Years 5 and 6) divisions. In 2026 it ran from 4 to 6 August.

What does "solve a simpler problem first" mean?

A problem-solving strategy: shrink a big problem to small versions, solve those, record the answers in a table and look for the pattern, then explain why it holds.

Can my child enter without their school?

APSMO says individual registration is not possible; it is school entry only. For other competitions, each organiser's site explains whether families can enter through testing centres or other routes.

Is Maths Challenge a test?

Not in the usual sense. The AMT runs it as a 3 to 4 week problem-solving program, with primary students working in groups of three alongside teacher discussion.

Do you use past competition papers?

No. Past papers belong to the organisers. We teach strategies with problems written by us in a similar spirit.

Will classes guarantee a High Distinction or medal?

No. Organisers set and mark their own competitions. We build number sense and problem-solving strategies, which is what the papers reward.

What happens in the free class?

Your child tries a few problems with a teacher, including one that uses a strategy like solving a simpler case first, and you get honest advice on a suitable first competition.

Related pages

More for primary families

Coding contests, maths support and the national picture.

Coding competitions for primary kids

Bebras, the CAT and more.

Competitions calendar

Every contest by month.

AMC practice by year

Divisions and question style.

Maths Challenge practice

Problems marked with a rubric.

APSMO practice

Five questions, thirty minutes.

ICAS Maths practice

Papers and entry routes.

NAPLAN numeracy

How the tailored test works.

AMT competitions

The AMC, CAT and AIO in depth.

Maths tutoring online

Weekly maths for Australian students.

Maths olympiad tutoring

For children ready for more.

Start here

Book a free maths class

Tell us your child's year level and how they feel about maths puzzles. The free class tries a few competition-style problems together and ends with a suggestion for a first competition.

Would you like to see the courses first? Every syllabus is on the course atlas, and how we teach explains our classes.

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

WhatsApp is generally the quickest way to hear back. Our number is Indian because our teachers work from India; we have no Australian office.

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