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In Key Stage 2 you work with much bigger numbers than before — all the way up to ten million (10,000,000). You also meet negative numbers and Roman numerals. In this lesson you will learn to read, write, order, compare, and round large numbers with confidence.
Every digit in a number has a place value — its position tells you exactly how much it is worth.
Here are the seven place value columns:
| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|---|
| M | HTh | TTh | Th | H | T | O |
Example: 3,456,789
| M | HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|---|
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
So 3,456,789 = 3,000,000 + 400,000 + 50,000 + 6,000 + 700 + 80 + 9.
Commas are written every three digits from the right to make large numbers easier to read.
Each column to the LEFT is ten times bigger than its neighbour. Each column to the RIGHT is ten times smaller. This is true for whole numbers and decimals together:
flowchart LR
A["Millions<br/>1,000,000"] -->|/ 10| B["Hundred<br/>Thousands<br/>100,000"]
B -->|/ 10| C["Ten<br/>Thousands<br/>10,000"]
C -->|/ 10| D["Thousands<br/>1,000"]
D -->|/ 10| E["Hundreds<br/>100"]
E -->|/ 10| F["Tens<br/>10"]
F -->|/ 10| G["Ones<br/>1"]
G -->|/ 10| H["Tenths<br/>0.1"]
H -->|/ 10| I["Hundredths<br/>0.01"]
I -->|/ 10| J["Thousandths<br/>0.001"]
Reading left to right, each step divides by 10; reading right to left, each step multiplies by 10.
To compare two numbers, look at the highest place value first. Move right until you find a difference.
Example: Compare 4,283,100 and 4,289,000
Example: Order from smallest to largest: 23,450 | 23,045 | 24,350 | 23,540
Rounding replaces a number with a nearby round number that is easier to use — for example when estimating.
The rule: Look at the digit immediately to the right of the place you are rounding to.
Rounding to the nearest 10:
Rounding to the nearest 1,000:
Rounding to the nearest 1,000,000:
Negative numbers are less than zero. They sit to the left of zero on a number line.
... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ...
Key rule: The further left from zero, the smaller the number.
Real-life uses: temperature below zero, depths below sea level, bank overdrafts.
Calculating with negative numbers:
Counting in multiples means skip-counting — jumping by the same number each time.
Year 3 multiples you must know:
Year 4 multiples you must also know:
Using multiples to count in steps:
Tip: A multiple of 4 is always even. A multiple of 9 has digits that add up to 9 (or a multiple of 9) — for example, 63: 6 + 3 = 9.
Roman numerals use letters to represent numbers. You need to know these up to 1,000.
| Roman | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1,000 |
The subtraction rule: when a smaller numeral appears directly before a larger one, subtract it.
The addition rule: when a smaller numeral appears after a larger one, add it.
Examples:
A geography lesson in Year 6 introduces the population of London, recorded as 8,982,256 in a recent census. The pupils are asked to read, write, partition, round, and compare this number.
Step 1 — Read the number. Identify the place value of each digit:
| M | HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|---|
| 8 | 9 | 8 | 2 | 2 | 5 | 6 |
In words: eight million, nine hundred and eighty-two thousand, two hundred and fifty-six.
Step 2 — Partition the number into place values.
8,000,000 + 900,000 + 80,000 + 2,000 + 200 + 50 + 6
That is the value of each digit added together.
Step 3 — Round to the nearest hundred. Look at the tens digit (5). 5 ≥ 5, so round up.
8,982,256 → 8,982,300
Step 4 — Round to the nearest thousand. Look at the hundreds digit (2). 2 < 5, so round down.
8,982,256 → 8,982,000
Step 5 — Round to the nearest ten thousand. Look at the thousands digit (2). 2 < 5, so round down.
8,982,256 → 8,980,000
Step 6 — Round to the nearest hundred thousand. Look at the ten-thousands digit (8). 8 ≥ 5, so round up.
8,982,256 → 9,000,000
Step 7 — Round to the nearest million. Look at the hundred-thousands digit (9). 9 ≥ 5, so round up.
8,982,256 → 9,000,000
Step 8 — Compare with another city. Birmingham's population is recorded as 1,144,919. Order from smallest to largest:
1,144,919 < 8,982,256
The difference between the two: 8,982,256 - 1,144,919 = 7,837,337 (using column subtraction with exchanges).
Step 9 — Calculate ten times bigger. What if London had ten times as many people?
8,982,256 x 10 = **89,822,560**
Each digit moves one place to the LEFT — the millions digit becomes the ten-millions digit, and so on.
Step 10 — Convert a Roman numeral context. The original census year was MMXXI. Decode this Roman numeral: M (1,000) + M (1,000) + XX (20) + I (1) = 2,021. The 2021 census recorded London's population.
Step 11 — Negative numbers in temperature. On the day of the census, London's temperature was -3 degrees Celsius and Manchester's was -8 degrees. Which was warmer? London — because -3 is to the right of -8 on the number line, so -3 > -8. The difference is 5 degrees.
Step 12 — Counting in multiples. From the rounded population 9,000,000, count down in 100,000s for 6 steps:
9,000,000 → 8,900,000 → 8,800,000 → 8,700,000 → 8,600,000 → 8,500,000 → 8,400,000
Each step is a subtraction of 100,000. This is direct application of place value — the hundred-thousands digit decreases by 1 each step.
Step 13 — Find 1,000 more and 100,000 less. Starting from 8,982,256:
1,000 more = 8,983,256 (the thousands digit increases by 1)
100,000 less = 8,882,256 (the hundred-thousands digit decreases by 1)
This worked example uses every key skill of place value: reading, writing, partitioning, rounding to multiple place values, comparing, calculating differences, multiplying by 10, decoding Roman numerals, counting in multiples, finding more or less by a power of 10, and reasoning about negative numbers — all essential for Year 6 SATs.
A common error is reading numbers from right to left or omitting place values where digits are zero. The number 8,902,256 is "eight million, nine hundred and TWO thousand" — the zero in the ten-thousands column matters. Pupils sometimes also confuse rounding rules — when rounding to the nearest 1,000, they look at the WRONG digit (the tens or ones), not the hundreds. Always look at the digit one place to the right of the target. With negative numbers, pupils often think -8 is greater than -3 because 8 is greater than 3 — but the further left of zero, the SMALLER the number.
Working towards (around 85 marks). Pupils read and write numbers up to 1,000 and identify the value of each digit (hundreds, tens, ones). They count forwards and backwards in 10s and 100s, and order three-digit numbers from smallest to largest. They round to the nearest 10 or 100. They recognise positive and negative numbers in everyday contexts (temperature, lift floors below ground). SATs questions at this level give clear prompts such as "What is the value of the 4 in 247?" or "Order these numbers."
Expected standard (around 100 marks). Pupils read and write numbers up to 1,000,000 and identify the value of each digit. They round to the nearest 10, 100, 1,000, 10,000, 100,000, and 1,000,000 fluently. They count forwards and backwards through zero with negative numbers (for example, 3, 2, 1, 0, -1, -2, -3). They use Roman numerals up to 1,000 (M) and decode common dates such as MCMXCIX (1999) or MMXXIV (2024). They identify multiples of 4, 6, 7, 8, 9, 25, 50, and 1,000.
Greater depth (around 110 marks). Pupils read, write, and order numbers up to 10,000,000 and beyond. They round large numbers to any specified place value, including problems like "round 8,982,256 to the nearest 10,000". They reason about negative numbers in calculation problems (for example, "find the difference between -7 and 12 on a number line" — answer: 19). They solve multi-step problems combining rounding and estimation: "A factory produces 7,283 items per week. Estimate how many items in a year by rounding to the nearest 1,000, then explain whether your estimate is too high or too low." Greater depth pupils use precise vocabulary fluently: digit, place value, partition, round, multiple, factor, integer, negative, positive.
Year 6 SATs-style reasoning question. The number 5,8,2_6 is missing three digits (one in the hundred-thousands column, one in the thousands column and one in the tens column). The number is between 5,400,000 and 5,500,000, and when rounded to the nearest 100,000 it rounds to 5,500,000. The thousands digit is greater than the hundred-thousands digit. The tens digit is half of the thousands digit. Find every possible value of the full number.
Worked solution.
Step 1 — Hundred-thousands digit. The number is between 5,400,000 and 5,500,000, so the hundred-thousands digit is 4.
Step 2 — Check rounding. Round 5,4_8_,2_6 to the nearest 100,000. We look at the ten-thousands digit (the 8). Because 8 ≥ 5, we round UP — so 5,4XX,XXX becomes 5,500,000. Confirmed.
Step 3 — Thousands digit. It must be greater than 4 (the hundred-thousands digit). Possible values: 5, 6, 7, 8, 9.
Step 4 — Tens digit. It must be HALF the thousands digit. Half of 5 = 2.5 (not a digit). Half of 6 = 3. Half of 7 = 3.5 (not a digit). Half of 8 = 4. Half of 9 = 4.5 (not a digit). So the valid pairs are (thousands, tens) = (6, 3) or (8, 4).
Step 5 — Final possible numbers.
Thousands = 6, tens = 3: 5,486,236
Thousands = 8, tens = 4: 5,488,246
There are two possible numbers: 5,486,236 and 5,488,246.
Suggested manipulatives and scaffolds for working-towards learners.
Misconception scenario. Theo is asked, "Round 4,562 to the nearest 1,000." He writes: "The ones digit is 2, which is less than 5, so I round down. Answer: 4,000."
Why this is wrong. Theo has looked at the WRONG digit. To round to the nearest 1,000, you must look at the hundreds digit (the digit one place to the right of the thousands), not the ones. The hundreds digit here is 5, so we round UP.
Worked correction. Identify the target column (thousands = 4). Look at the digit immediately to the right (hundreds = 5). Because 5 ≥ 5, round up:
4,562 -> **5,000**
A reliable scaffold: draw an arrow above the digit you are rounding to, and circle the digit immediately to its right — that circled digit is the only one that decides up or down. Practise on a rounding number line with 4,000 and 5,000 at the ends and 4,500 marked in the middle, so pupils can see that 4,562 sits past the halfway point.
Number and place value spans the full KS2 ability range, from reading three-digit numbers in Year 3 to comparing seven-digit numbers and negative integers in Year 6. The descriptors below show Level 3, Level 4, and Level 5 mastery.
Working towards (Level 3 / Grade 1-2). A Year 5 or Year 6 child working below age-related expectations reads, writes, and orders three-digit numbers (up to 1,000) using a place-value chart with HTO columns labelled. They need scaffolds: base-ten blocks (hundreds flats, tens rods, ones cubes), a printed thousand square, and digit cards to physically swap into columns. They confuse 4,205 with 4,025 because zeros as placeholders are not yet secure, and they round only to the nearest 10 with the support of a number line.
Expected (Level 4 / Grade 3-4 — working at the standard). A child meeting end-of-KS2 expectations reads, writes, orders, and compares numbers up to 10,000,000 using place value, rounds any whole number to the nearest 10, 100, 1,000, 10,000, 100,000, or 1,000,000, counts forwards and backwards through zero with negative numbers, and reads Roman numerals up to 1,000 (M). They use the symbols < and > correctly, and identify the value of any digit in a seven-digit number.
Greater depth (Level 5 / Grade 5-6 — mastery). A confident KS2 child solves multi-step reasoning problems involving rounding (e.g. "A number rounds to 5,500,000 to the nearest 100,000. The hundred-thousands digit is 4. The thousands digit is greater than the hundred-thousands digit. Find all possible values."), calculates intervals across zero with negative numbers in real-world contexts (temperature, sea level, bank balance), reads and writes Roman numerals beyond 1,000, and explains place-value reasoning in full sentences ("The 5 in 5,486,236 is worth 5,000 because it is in the thousands column"). They check answers using estimation and recognise unreasonable outcomes from misplaced commas or zeros.
This content is aligned with the UK National Curriculum for Key Stage 2 Mathematics (Years 3-6, programmes of study) and the end-of-key-stage SATs assessments. For the most accurate and up-to-date information, please refer to the Department for Education National Curriculum framework and Standards & Testing Agency materials.