Number & the four operations

Subitize small quantities (≤ 4–5 without counting); one-to-one counting; cardinality; compare “more/fewer”.

Compose/decompose teen numbers 11–19 as “ten ones and some further ones” (18 = 10 + 8) — the bridge to place value.

Count, read, write & order whole numbers to ~100; “1 more / 1 less”; place on a number line.

Ordinal numbers & rank (“twentieth”; identify a position in an ordered list).

Place value of a two-digit number (tens & ones); compose/decompose (30 + 5); use =, <, >.

Count, read, write & order to ~1000; skip-count (2s, 3s, 5s, 10s).

Place value to ~10,000; round to the nearest 10/100; estimation / orders of magnitude as a recurring check (Überschlag).

Roman numerals (via the clock I–XII, then I–C).

Place value to ~1,000,000; round to any place; negative numbers on the number line (count back through 0).

Read/order numbers to ~10,000,000+; Roman numerals to M (EN Y5); the 10× / ⅒ place-value relationship (the basis for decimals).

Standard form A × 10ⁿ (1 ≤ A < 10); rounding to significant figures / an appropriate degree of accuracy; error bounds a < x ≤ b; classify numbers into ℕ, ℤ, ℚ and appreciate their infinitude.

Number bonds within 20; add/subtract within 20 (concrete/pictorial); meaning of +, −, =; missing-number problems.

Know from memory all addition facts to 20; commutativity of +; the inverse relationship of + and −; add/subtract within 100 mentally & with informal written methods.

Column (standard) written addition & subtraction, up to 3–4 digits; estimate the result first & check with the inverse.

Meaning of multiplication (repeated addition, arrays, “groups of”) & division (sharing & grouping); commutativity of ×.

Build & recall the 2, 5, 10 tables (then 3, 4, 8); odd/even.

Recall multiplication & division facts up to 12×12 fluently (single-digit “to 9×9 from memory” is the US/CCSS floor; England’s Y4 MTC assesses to 12×12).

Multiply 2–3-digit by 1-digit (formal written / area model); short/Euclidean division with a 1-digit divisor & remainders; factor pairs; divisibility rules (2, 3, 5, 10); the distributive law.

Long multiplication; long/short/decimal division with 2-digit divisors; factors, multiples, HCF/LCM; prime & composite numbers, prime factorisation; square & cube numbers, powers with natural exponents, powers of ten, roots & reciprocals; order of operations.

Negative numbers: order, add/subtract (and ×/÷ — DE / KS3) integers; absolute value.