Number - Number and Place Value
KS2MA-Y6-D001
Reading, writing, ordering and comparing numbers to 10,000,000; understanding place value; negative numbers and intervals across zero; rounding to any degree of accuracy.
National Curriculum context
Year 6 number and place value work consolidates and extends the progression from thousands (Year 4) through 1,000,000 (Year 5) to 10,000,000, ensuring pupils have a secure understanding of our base-10 number system at its upper primary limit. Mastery of place value to 10 million is foundational for the formal written methods, mental calculations, and estimation skills that pervade all other Year 6 domains. Work on negative numbers extends from the introductory contexts of temperature and debt encountered in Year 5 to more formal number-line reasoning and calculation across zero, which underpins algebraic thinking and prepares pupils for the directed number work of KS3. Rounding to any degree of accuracy is a transferable skill that pupils apply throughout measurement, statistics, and problem-solving contexts in Year 6 and beyond. This domain also develops the language and symbolic representation of very large numbers, an important outcome for numeracy in everyday life.
3
Concepts
2
Clusters
3
Prerequisites
3
With difficulty levels
Lesson Clusters
Read, write and order whole numbers to 10,000,000
introduction CuratedSeven-digit place value is the Year 6 extension of place value and is the entry point for the domain before rounding and negative numbers.
Round to any degree of accuracy and calculate intervals across zero
practice CuratedRounding to any degree of accuracy and negative numbers/intervals across zero are co-taught (C002 co-teaches with C003) and together complete the Year 6 number system coverage.
Teaching Suggestions (1)
Study units and activities that deliver concepts in this domain.
Place Value to 10,000,000
Mathematics Pattern SeekingPrerequisites
Concepts from other domains that pupils should know before this domain.
Domain Vocabulary
25 terms across 3 concepts (25 domain-specific)
above zero(phrase)
A value greater than zero; a positive number, often used when discussing temperatures.
approximate(adjective)
Close to but not exact; a value estimated rather than precisely calculated.
below zero(phrase)
A value less than zero, indicating a negative number; commonly encountered in temperature contexts.
compare(verb)
To look at two or more numbers or objects to find which is bigger, smaller, longer, shorter, etc.
degree of accuracy(noun)
How precisely a number has been rounded, stated as the nearest whole number, ten, hundred, or decimal place.
difference(noun)
The result of subtracting one number from another; how much more or less one number is than another.
digit(noun)
A single number symbol from 0 to 9.
estimate(noun)
A sensible guess at an amount or answer, close to the actual value but not exact.
greater than(phrase)
Having a higher value; shown by the > symbol.
inequality(noun)
A mathematical statement showing that two values are not equal, using symbols such as <, >, ≤, or ≥.
interval(noun)
The regular gap between values on a number line or scale, or between marked points on a measuring instrument.
less than(phrase)
Having a smaller value; shown by the < symbol.
millions(noun)
The place-value column representing groups of one million (1,000,000); numbers in the millions.
multiple(noun)
A number that can be divided by another number with no remainder; a result of a times table.
nearest(adjective)
The closest value to a given number when rounding, estimating, or measuring.
negative number(noun)
A number less than zero, written with a minus sign, representing values below zero on a number line.
number line(noun)
A straight line marked with numbers at equal intervals, used for counting, adding, and subtracting.
order(verb)
To arrange numbers from smallest to largest or largest to smallest.
place value(noun)
The value of a digit determined by its position in a number (ones, tens, hundreds, etc.).
positive number(noun)
A number greater than zero.
round(adjective)
Having a curved shape like a circle or sphere.
ten millions(noun)
The place-value column for 10,000,000; ten groups of one million.
thermometer(noun)
An instrument for measuring temperature, marked with a scale in degrees.
value of a digit(noun)
The worth of a digit based on its position in a number (e.g. the 3 in 350 has a value of 300).
zero(noun)
The number 0; the starting point on a number line, representing nothing or no quantity.
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Concepts (3)
Place Value to 10,000,000
knowledge AI DirectMA-Y6-C001
A pupil who has mastered place value to 10,000,000 can confidently read and write any whole number in this range in digits and words, identify the value of any digit by its position, and use this understanding to order and compare numbers. Mastery is demonstrated when pupils can apply place value flexibly — for example, recognising that 4,000,000 is the same as 40 hundred-thousands — and when they can use this understanding to support estimation, mental calculation, and formal written methods without error.
Teaching guidance
Use extended place value charts showing columns from ones to millions, and ask pupils to represent numbers by placing digit cards. Physical representations such as large-format 'millions strips' help bridge understanding from 100,000. Emphasise the pattern of grouping in threes (ones, thousands, millions) which reflects the way large numbers are written with commas. Progress from reading and writing to ordering, using inequality symbols, and then to application in context. Calculator investigations exploring what happens to a digit when a number is multiplied by 10 repeatedly are very effective.
Vocabulary (10 terms)
Common misconceptions
Pupils often misread multi-digit numbers, especially those with zeros as placeholders (e.g., reading 4,006,050 as 'four million sixty-five'). When writing numbers from words, pupils may omit placeholder zeros. Some pupils confuse the face value of a digit (e.g., 4) with its place value (e.g., 4,000,000). Reinforce the role of each zero as a place-holder with explicit examples.
Difficulty levels
Reading and writing numbers to 1,000,000 using a place value chart, identifying the value of each digit.
Example task
Write in digits: two million, three hundred and four thousand and fifty. What is the value of the 3?
Model response: 2,304,050. The 3 is worth 300,000 (three hundred thousand).
Reading, writing and ordering numbers to 10,000,000, including numbers with multiple zero placeholders.
Example task
Order these from smallest to largest: 4,006,050; 4,060,500; 4,600,005; 4,005,060.
Model response: 4,005,060; 4,006,050; 4,060,500; 4,600,005.
Identifying the value of any digit in numbers up to 10,000,000, partitioning flexibly, and applying the ones-thousands-millions grouping pattern.
Example task
In 7,482,319, what is the value of the 4? Partition 5,600,000 in two different ways.
Model response: The 4 is worth 400,000. 5,600,000 = 5,000,000 + 600,000 = 4,000,000 + 1,600,000.
Explaining the multiplicative structure of the place value system across non-adjacent columns and using it to reason about equivalences involving millions.
Example task
How many thousands are there in 10,000,000? Explain why 3,500,000 is the same as 35 hundred-thousands.
Model response: 10,000,000 ÷ 1,000 = 10,000 thousands. 3,500,000 = 35 × 100,000, so it is 35 hundred-thousands. Each column is 10 times the one to its right, so moving two columns left multiplies by 100.
CPA Stages
concrete
Using place value counters on a seven-column mat (M, HTh, TTh, Th, H, T, O) and large-format 'millions strips' to build, partition and compare numbers to 10,000,000
Transition: Child reads and writes numbers to 10,000,000 including those with zero placeholders, identifying the value of every digit without counters
pictorial
Using place value charts, Gattegno charts and number lines to represent and compare numbers to 10,000,000, connecting to real-world contexts (populations, distances)
Transition: Child works with any number to 10,000,000 on paper, partitioning flexibly and comparing column-by-column
abstract
Working with numbers to 10,000,000 mentally: reading, writing, partitioning, comparing and applying in context
Transition: Child handles any number to 10,000,000 with instant confidence, explaining place value patterns in the ones-thousands-millions grouping
Delivery rationale
Upper primary maths (Y6) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.
Rounding to Any Degree of Accuracy
skill AI DirectMA-Y6-C002
Mastery of rounding means pupils can round any whole number or decimal to any specified degree of accuracy — including to the nearest 10, 100, 1,000, 10,000, 100,000, 1,000,000, or to any number of decimal places — and can select the appropriate degree of accuracy for a given context. A fully secure pupil understands rounding as a process of finding the nearest named value and applies the rounding rule (5 or more rounds up) consistently, including for numbers ending in exactly 5.
Teaching guidance
Use number lines to develop conceptual understanding before moving to procedural rules. Place the number on a number line between the two nearest multiples and identify which is closer. Gradually increase the scale of number lines from tens to thousands to millions. Connect rounding to real-world contexts: money (to the nearest pound), distance (to the nearest kilometre), and population (to the nearest thousand). Address boundary cases (e.g., 350 to the nearest hundred) explicitly. Later, connect to decimal rounding by extending the number line to tenths and hundredths.
Vocabulary (6 terms)
Common misconceptions
When rounding to a large unit (e.g., nearest 100,000), pupils often round only the digit in the required column, ignoring whether subsequent digits cause the number to be closer to the upper or lower value. Pupils frequently round 'down' when they should round up at the 5-boundary. Some pupils truncate rather than round when working with large numbers. Explicit number-line work addresses all these errors.
Difficulty levels
Rounding whole numbers to the nearest 10, 100, 1,000 and 10,000 (consolidating Year 5 skills).
Example task
Round 456,789 to the nearest 10,000.
Model response: 460,000. The thousands digit is 6 (≥ 5), so round up.
Rounding to the nearest 100,000 and 1,000,000, and rounding decimals to the nearest whole number and to 1 decimal place.
Example task
Round 3.456 to 1 decimal place. Round 2,750,000 to the nearest million.
Model response: 3.456 rounds to 3.5 (the hundredths digit 5 rounds up). 2,750,000 rounds to 3,000,000.
Rounding any number to any degree of accuracy and selecting appropriate rounding for estimation and context.
Example task
A charity raised £3,847,291. Round this to the nearest million for a headline and to the nearest £100,000 for a report.
Model response: Headline: approximately £4,000,000. Report: approximately £3,800,000.
CPA Stages
concrete
Using number lines at various scales (tens, thousands, millions, tenths) to locate numbers and determine which bounding multiple is nearer, for both whole numbers and decimals
Transition: Child rounds any number — whole or decimal — to any degree of accuracy without the number line, using the digit-checking rule
pictorial
Drawing number line segments for rounding decisions, recording rounding to multiple degrees of accuracy, and using rounding to estimate calculations
Transition: Child rounds to any degree of accuracy instantly and uses rounding to estimate answers before calculating
abstract
Rounding any number to any specified accuracy mentally, selecting appropriate accuracy for context, and using rounding for estimation and reasonableness checking
Transition: Child selects the appropriate degree of rounding for any context and explains the range of values that round to a given number
Delivery rationale
Upper primary maths (Y6) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.
Negative Numbers and Calculating Intervals Across Zero
knowledge AI DirectMA-Y6-C003
Mastery means pupils can use negative numbers fluently in context (temperature, bank balances, sea level, coordinates) and calculate the interval between a negative and a positive number by reasoning on a number line rather than by applying a rule. A fully secure pupil understands that subtracting a negative number increases the value and can calculate multi-step problems involving both negative and positive quantities, explaining their reasoning clearly.
Teaching guidance
Contexts should drive initial understanding: temperature is the most intuitive starting point, as pupils can visualise rising and falling. Use a vertical number line (like a thermometer) to make the direction of change concrete. Progress to horizontal number lines and then to abstract calculations. Explicitly connect negative numbers to the coordinate grid work pupils will meet in the geometry domains. The key calculation to practise is finding the difference between a negative and a positive number (e.g., the difference between -4 and +6 is 10), which pupils can model by counting steps on the number line.
Vocabulary (9 terms)
Common misconceptions
Pupils commonly think -8 is greater than -3 because 8 is greater than 3. When calculating the difference between -3 and +5, pupils often compute 5 - 3 = 2 rather than 5 - (-3) = 8. The number line is the essential tool for overcoming both misconceptions. Some pupils resist the idea that the result of subtracting a larger positive number from a smaller one can be negative, reflecting over-generalisation from whole number arithmetic.
Difficulty levels
Counting through zero in both directions on a number line, reading negative numbers in the context of temperature.
Example task
The temperature is –3°C. It rises by 7 degrees. What is the new temperature? Use the number line.
Model response: –3 + 7 = 4°C. Counting up: –3, –2, –1, 0, 1, 2, 3, 4.
Calculating intervals across zero between a negative and a positive number without a number line.
Example task
The temperature fell from 5°C to –8°C overnight. What was the temperature drop?
Model response: From 5 to 0 is 5 degrees. From 0 to –8 is 8 degrees. Total drop: 5 + 8 = 13 degrees.
Solving multi-step problems with negative numbers in context, including ordering negative numbers and calculating with them fluently.
Example task
At 6 am the temperature was –5°C. By noon it was 8°C. By midnight it had dropped 14°C from noon. What was the midnight temperature? Order all three temperatures.
Model response: Midnight: 8 – 14 = –6°C. Order (coldest to warmest): –6°C, –5°C, 8°C.
CPA Stages
concrete
Using vertical number lines (thermometer models) and horizontal floor number lines extending well below zero to count, compare and calculate intervals involving negative numbers
Transition: Child calculates intervals across zero without the number line, explaining: 'I add the distance from the negative number to zero and from zero to the positive number'
pictorial
Drawing number lines to show calculations with negative numbers, recording intervals, and solving problems involving negative numbers in context on paper
Transition: Child calculates with negative numbers on paper using the additive model and solves context problems without drawing
abstract
Working with negative numbers mentally in all contexts: temperature, coordinates, bank balances, sea level, and abstract calculations
Transition: Child performs calculations with negative numbers mentally, selecting the most efficient strategy and applying in unfamiliar contexts
Delivery rationale
Upper primary maths (Y6) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.