Five of these columns are official curricula: what Singapore, the United States, the United Kingdom, India and Australia say children should learn. The first column is different. It is what one real classroom in Frankfurt actually did, week by week, taken from the worksheets and family guides the school sent home. Official intentions on one side, dated reality on the other.
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 |
|---|---|---|---|---|---|---|
| Place value | ★ Sep 2026: 3-digit numbers (building and representing 423) | Numbers up to 10,000 | Works within 1,000; place value underpins rounding and algorithms | 4-digit numbers; order beyond 1,000; negative numbers; Roman numerals to 100 | Staged across the year: to 99 (Apr), 200 (Jul), 500, then 1,000 | Numbers beyond 10,000 |
| Addition & subtraction | ★ Sep-Oct 2026: within 1,000; strategies first (25 Sep), written algorithm with regrouping by 16 Oct | Algorithms up to 4 digits | Fluent within 1,000 using place-value strategies; no single mandated algorithm | Up to 4 digits with formal column methods; estimate and check with inverse operations | Two- and three-digit numbers fluently via composing and decomposing; money with and without regrouping | Two- and three-digit numbers; partitioning, rearranging and regrouping are named explicitly |
| Rounding & estimation | ★ Oct 2026: rounding to the nearest 10 on a number line (2 Oct sheet) | Not taught in Primary 3 (rounding starts in Primary 4) | Core requirement: round to the nearest 10 or 100 | Round any number to the nearest 10, 100 or 1,000 | Estimation only: 'estimate the answer to the nearest hundred'; no formal rounding rules | Estimation and checking reasonableness; rounding is not named until Year 4 |
| Multiplication | ★ Introduced Oct 2026: as groups of objects, with diagrams (19 and 30 Oct) | Tables of 6, 7, 8, 9 this year (2, 3, 4, 5, 10 in Primary 2); 3-digit by 1-digit algorithms | Introduced this year; by the end of Grade 3, all products of two one-digit numbers from memory | Recall all tables up to 12 x 12; multiply 2- and 3-digit numbers by 1 digit in formal layout | Introduced this year as repeated addition; tables of 2, 3, 4, 5, 10 | Recall facts for 3, 4, 5 and 10; multiply one- and two-digit numbers with strategies |
| Division | ★ Nov 2026: the class moved on from multiplication into division this month | Within the tables, with remainders; algorithms up to 3 digits by 1 digit | Introduced this year: quotients as sharing and grouping; fluent within 100 | Division facts to 12 x 12; short division in official guidance | Introduced this year: equal sharing; facts found by repeated subtraction | Division facts linked to the 3, 4, 5, 10 tables; divide one- and two-digit numbers |
| Fractions | ★ Not yet seen in Grade 3 class materials (as of Nov 2026) | Equivalent fractions, simplest form, comparing unlike fractions (denominators to 12), adding related fractions | Introduced this year: unit fractions, the number line, simple equivalence, comparing | Equivalent fraction families, hundredths, adding same-denominator fractions, first decimal equivalents | Introduced Oct-Nov: halves and quarters only, as parts of wholes and on number lines | Unit fractions (1/2, 1/3, 1/4, 1/5, 1/10) and their multiples; equivalence waits until Year 4 |
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 |
|---|---|---|---|---|---|---|
| Place value & decimals | ★ Not yet seen in Grade 5 class materials (as of Nov 2026) | Whole numbers up to 10 million; decimals to 3 places handled under operations | Decimals to thousandths; powers of 10 and exponents | Numbers up to 10,000,000; value of digits to 3 decimal places | Large numbers in the Indian system (lakh, crore); no decimals chapter at all in Class 5 | Decimals with more than 2 places on the number line; no whole-number range such as millions is set |
| Multi-digit multiplication & division | ★ Not yet seen in Grade 5 class materials (as of Nov 2026) | 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 | Standard algorithm for multiplication is required; division to 4-digit dividends by 2-digit divisors, strategy-based | Long multiplication (4-digit by 2-digit) and long division, remainders read as whole numbers, fractions or rounded | Large-number operations inside travel and farm contexts; no formal long-division algorithm is stated | Multiply larger numbers by one- or two-digit numbers with chosen strategies; remainders interpreted as whole, decimal or fraction |
| Fractions as division | ★ Oct 2026: the core of the current unit (family support pack, 15 Oct) | Yes: dividing a whole number by a whole number gives a fraction; fractions expressed as decimals | Yes: a/b = a / b is an explicit standard (5.NF.B.3) | Yes: a fraction is associated with division; decimal equivalents such as 3/8 = 0.375 | Yes: fractions represented as divisions of whole numbers (Class 5, fractions chapter, Jul-Sep) | Not stated in that form; division results may be expressed as a fraction |
| Fraction x whole number, fraction x fraction | ★ Oct 2026: the second half of the current unit (whole number x fraction and mixed numbers) | Yes: fraction x whole, mixed number x whole, and fraction x fraction | Yes: fraction x whole and fraction x fraction, including mixed numbers in word problems | Fraction x whole is set in Year 5; Year 6 adds multiplying pairs of proper fractions and dividing fractions by whole numbers | Not stated in the Class 5 syllabus or textbook outcomes | Not a Year 5 item in the current curriculum |
| Adding fractions, unlike denominators | ★ Not part of the Oct 2026 unit, which covers fractions as quotients and fraction multiplication | Adding and subtracting mixed numbers (unlike denominators, to 12, were set at Primary 4) | Yes: unlike denominators including mixed numbers are an explicit standard (5.NF.A.1) | Yes: different denominators and mixed numbers, using equivalent fractions | Only as a fraction-strips activity; no unlike-denominator method is stated | Only fractions with the same or related denominators |
| Decimal operations | ★ Not yet seen in Grade 5 class materials (as of Nov 2026) | Multiply and divide decimals (to 3 places) by 10, 100, 1000; general decimal addition and subtraction were Primary 4 | All four operations with decimals to hundredths | Multiply decimals by whole numbers; written division giving answers to 2 decimal places; x and / by 10, 100, 1000 to 3 places | None: the Class 5 maths book has no decimals chapter among its 15 chapters | Place value and comparison only; multiplying and dividing decimals by powers of 10 waits until Year 6 |
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.
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.