Five columns are official curricula. The first is what one real Frankfurt classroom actually did, week by week. Every other cell is badged against it: ▲ ahead, ● level, ▼ behind.
Six concepts, six systems. The spread inside a single row is the story.
| Concept | FIS FrankfurtActual classroom artifacts | SingaporeMOE syllabus | United StatesCommon Core | United KingdomNational Curriculum, Year 4 / 6 | IndiaNCERT / CBSE | AustraliaACARA v9 | KumonReference point: mastery levels, self-paced |
|---|---|---|---|---|---|---|---|
| Place value | ★ Sep 2026: 3-digit numbers | ▲ Ahead Numbers up to 10,000 | ● Level Within 1,000 | ▲ Ahead 4-digit numbers, negatives, Roman numerals | ● Level Staged to 1,000 across the year | ▲ Ahead Beyond 10,000 | ▼ Behind No standalone place-value unit: number writing runs to 220 at Level 4A, and place value is then carried inside the addition levels (A and B) |
| Addition & subtraction | ★ Within 1,000; strategies Sep, algorithm Oct | ▲ Ahead Algorithms up to 4 digits | ● Level Fluent within 1,000, strategy-based | ▲ Ahead 4 digits, formal column methods | ● Level 2-3 digits, composing and decomposing | ● Level 2-3 digits, regrouping named | ● Level Level A: horizontal addition and subtraction, heavily mental. Level B: vertical addition and subtraction, with carrying and borrowing |
| Rounding & estimation | ★ Oct 2026: nearest 10, on a number line | ▼ Behind Not taught until Primary 4 | ▲ Ahead Nearest 10 and 100, core standard | ▲ Ahead Nearest 10, 100 or 1,000 | ▼ Behind Estimation only, no rounding rules | ▼ Behind Estimation only; rounding from Year 4 | ▼ Behind No rounding in the early levels; estimation first appears at Level D, as a tool for long division and fractions |
| Multiplication | ★ Introduced late Oct 2026, as groups | ▲ Ahead Tables 6-9; 3-digit by 1-digit | ▲ Ahead All 1-digit facts memorised by year end | ▲ Ahead Recall all tables to 12 x 12 | ● Level Introduced: tables 2, 3, 4, 5, 10 | ▲ Ahead Recall facts for 3, 4, 5, 10 | ▲ Ahead Level C: the tables are drilled to instant recall, then multiplication up to 4-digit by 1-digit |
| Division | ★ Introduced Nov 2026 | ▲ Ahead Within tables, remainders, 3-digit by 1-digit | ● Level Introduced: fluent within 100 | ▲ Ahead Facts to 12 x 12, short division | ● Level Introduced: sharing, repeated subtraction | ● Level Facts linked to 3, 4, 5, 10 tables | ● Level Introduced in Level C (by one digit, straight after multiplication); long division is Level D |
| Fractions | ★ Not yet (Nov 2026) | ▲ Ahead Equivalence, comparing, adding related fractions | ▲ Ahead Introduced: unit fractions, number line | ▲ Ahead Equivalence, hundredths, decimal equivalents | ▲ Ahead Introduced Oct-Nov: halves and quarters only | ▲ Ahead Unit fractions; equivalence from Year 4 | ▼ Behind Begin only at the end of Level D: reducing with the greatest common factor, improper and mixed conversions |
By Grade 5 the systems have quietly chosen different destinations, most visibly in fractions and decimals.
| Concept | FIS FrankfurtActual classroom artifacts | SingaporeMOE syllabus | United StatesCommon Core | United KingdomNational Curriculum, Year 4 / 6 | IndiaNCERT / CBSE | AustraliaACARA v9 | KumonReference point: mastery levels, self-paced |
|---|---|---|---|---|---|---|---|
| Place value & decimals | ★ Not yet seen in Grade 5 class materials (as of Nov 2026) | ▲ Ahead Whole numbers up to 10 million; decimals to 3 places handled under operations | ▲ Ahead Decimals to thousandths; powers of 10 and exponents | ▲ Ahead Numbers up to 10,000,000; value of digits to 3 decimal places | ● Level Large numbers in the Indian system (lakh, crore); no decimals chapter at all in Class 5 | ▲ Ahead Decimals with more than 2 places on the number line; no whole-number range such as millions is set | ▼ Behind Decimals arrive late, in Levels E and F, and only after fractions (fraction-decimal conversions close Level E) |
| Multi-digit multiplication & division | ★ Not yet seen in Grade 5 class materials (as of Nov 2026) | ▲ Ahead No new limits at Primary 5 (set at Primary 4: 4-digit by 1-digit, 3-digit by 2-digit); focus on x and / by 10, 100, 1000 and order of operations | ▲ Ahead Standard algorithm for multiplication is required; division to 4-digit dividends by 2-digit divisors, strategy-based | ▲ Ahead Long multiplication (4-digit by 2-digit) and long division, remainders read as whole numbers, fractions or rounded | ● Level Large-number operations inside travel and farm contexts; no formal long-division algorithm is stated | ▲ Ahead Multiply larger numbers by one- or two-digit numbers with chosen strategies; remainders interpreted as whole, decimal or fraction | ● Level Level C: up to 4-digit by 1-digit. Level D: 2-digit by 2-digit multiplication, then long division |
| Fractions as division | ★ Oct 2026: the core of the current unit (family support pack, 15 Oct) | ● Level Yes: dividing a whole number by a whole number gives a fraction; fractions expressed as decimals | ● Level Yes: a/b = a / b is an explicit standard (5.NF.B.3) | ● Level Yes: a fraction is associated with division; decimal equivalents such as 3/8 = 0.375 | ● Level Yes: fractions represented as divisions of whole numbers (Class 5, fractions chapter, Jul-Sep) | ▼ Behind Not stated in that form; division results may be expressed as a fraction | ▼ Behind Not framed as division: fractions are taught as a pure computation strand (Levels D to F) |
| Fraction x whole number, fraction x fraction | ★ Oct 2026: the second half of the current unit (whole number x fraction and mixed numbers) | ▲ Ahead Yes: fraction x whole, mixed number x whole, and fraction x fraction | ▲ Ahead Yes: fraction x whole and fraction x fraction, including mixed numbers in word problems | ● Level Fraction x whole is set in Year 5; Year 6 adds multiplying pairs of proper fractions and dividing fractions by whole numbers | ▼ Behind Not stated in the Class 5 syllabus or textbook outcomes | ▼ Behind Not a Year 5 item in the current curriculum | ● Level Level E: students add, subtract, multiply and divide fractions; Level F continues with the order of operations |
| Adding fractions, unlike denominators | ★ Not part of the Oct 2026 unit, which covers fractions as quotients and fraction multiplication | ▲ Ahead Adding and subtracting mixed numbers (unlike denominators, to 12, were set at Primary 4) | ▲ Ahead Yes: unlike denominators including mixed numbers are an explicit standard (5.NF.A.1) | ▲ Ahead Yes: different denominators and mixed numbers, using equivalent fractions | ● Level Only as a fraction-strips activity; no unlike-denominator method is stated | ● Level Only fractions with the same or related denominators | ▲ Ahead Level E, including borrowing from integers to subtract fractions |
| Decimal operations | ★ Not yet seen in Grade 5 class materials (as of Nov 2026) | ▲ Ahead Multiply and divide decimals (to 3 places) by 10, 100, 1000; general decimal addition and subtraction were Primary 4 | ▲ Ahead All four operations with decimals to hundredths | ▲ Ahead Multiply decimals by whole numbers; written division giving answers to 2 decimal places; x and / by 10, 100, 1000 to 3 places | ● Level None: the Class 5 maths book has no decimals chapter among its 15 chapters | ● Level Place value and comparison only; multiplying and dividing decimals by powers of 10 waits until Year 6 | ▼ Behind Level F: decimal work follows fraction mastery; fraction calculations with the order of operations sit alongside |
Rounding to the nearest 10 first appears in Singapore's Primary 4, while Primary 3 pupils are comparing unlike fractions and adding related ones. In the US and UK, rounding is a Grade 3 staple the same year.
Common Core expects all products of two one-digit numbers from memory by the end of Grade 3. India's Class 3 builds tables of 2, 3, 4, 5 and 10, as repeated addition. The UK goes furthest: recall to 12 x 12 by Year 4.
All 15 chapters of NCERT's Maths Mela for Class 5 skip decimals. The same year, US fifth graders operate on decimals to hundredths and UK Year 6 pupils divide to two decimal places.
FIS Frankfurt, Singapore, the US, the UK and India all treat a/b as a divided by b at this level. Australia's current curriculum does not state it even at Year 5, and does not include fraction x whole number either.
In Kumon's sequence, vertical addition and subtraction with carrying and borrowing is Level B, the multiplication tables are Level C, and fractions do not begin until the end of Level D, after all four operations are secure. A Kumon child can sit two levels ahead of their school year, or behind it, by design: the level, not the birthday, decides.
FIS Grade 3 followed the strategies-first pattern of the US and Australian curricula rather than formal algorithms, and reached multiplication in late October, weeks after India's syllabus introduces it in the same term. Only dated classroom artifacts show this; a syllabus never will.
The official columns above took an afternoon to assemble from published syllabi. The starred column is the hard one: it exists only because a parent in Frankfurt handed over a class feed. Every classroom that joins adds one more dated, honest column: what was actually taught, in the month it was taught.
Two ways in: run a class hub for your child's classroom (a parent volunteer connects their own class app account, read-only; the class gets a documents page like the FIS hub), or simply forward the worksheets and unit guides your school sends home. No children's names, photos or schoolwork are ever collected; the atlas publishes concepts and timing, the documents stay with the class.
This is a prototype. One school is live. The goal is a hundred.