Number - Number and Place Value
KS2MA-Y5-D001
Reading, writing, ordering and comparing numbers to at least 1,000,000; counting forwards and backwards in steps of powers of 10; negative numbers; rounding to any power of 10; Roman numerals to 1000.
National Curriculum context
In upper key stage 2, the principal focus of mathematics teaching is to ensure that pupils extend their understanding of the number system and place value to include larger integers. In Year 5, pupils read, write, order and compare numbers to at least 1,000,000, developing their understanding that the place value system extends indefinitely — each column is ten times the value of the column to its right. The non-statutory guidance specifies that pupils should identify the value of each digit to three decimal places and practise with increasingly large numbers, reading scales and number lines with increasing accuracy. Roman numerals to 1000 (M) are introduced, including the year in Roman numerals. Rounding to any power of 10 — including to the nearest 10,000 and 100,000 — develops estimation skills needed across all upper KS2 domains. This domain underpins the long multiplication, formal division and fraction work that are central to Year 5.
2
Concepts
1
Clusters
2
Prerequisites
2
With difficulty levels
Lesson Clusters
Read, write and order numbers to 1,000,000 and round to any power of 10
practice CuratedSix-digit place value and rounding to any power of 10 (nearest 10,000; 100,000) are the two statutory Year 5 number/PV requirements. Only two concepts; single cluster appropriate.
Teaching Suggestions (1)
Study units and activities that deliver concepts in this domain.
Numbers to 1,000,000
Mathematics Pattern SeekingPrerequisites
Concepts from other domains that pupils should know before this domain.
Concepts (2)
Numbers to 1,000,000 and their place value
knowledge AI DirectMA-Y5-C001
Place value extends to six digits in Year 5, with columns for hundred-thousands, ten-thousands and thousands joining the familiar hundreds, tens and ones. Each column is ten times the value of the column to its right. Mastery means pupils can identify the value of any digit in a number up to 1,000,000, partition such numbers in multiple ways, compare and order them, and read and write them in numerals and words.
Teaching guidance
Extend place value charts to six columns. Use large number cards for the display board (100,000, 200,000... cards alongside the familiar 1,000, 2,000... cards). Connect to real-world contexts: populations of cities, distances in space, stadium capacities. Pupils who understand the repeating pattern (ones, tens, hundreds — then thousands ones, thousands tens, thousands hundreds — then millions...) see the structure clearly. Number lines from 0 to 1,000,000 help with ordering and estimation.
Common misconceptions
Pupils sometimes omit commas in large numbers or place them incorrectly. Numbers with zeros in the middle (e.g. 304,056) cause placeholder confusion. Pupils may read 304,056 as 'three hundred and four thousand and fifty-six' omitting the hundreds of thousands value or collapsing place values.
Difficulty levels
Reading and writing numbers to 100,000 using a place value chart with columns labelled TTh, Th, H, T, O.
Example task
Place digit cards on the place value chart to make 47,302. What is the value of the 7?
Model response: 47,302. The 7 is worth 7,000 (seven thousand).
Reading, writing and ordering numbers to 1,000,000, including numbers with zero placeholders in multiple columns.
Example task
Write in digits: three hundred and four thousand and fifty-six. Order these: 456,000; 465,000; 405,600; 450,600.
Model response: 304,056. Order: 405,600; 450,600; 456,000; 465,000.
Identifying the value of any digit in a number up to 1,000,000, partitioning flexibly, and comparing and ordering such numbers fluently.
Example task
What is the value of the 6 in 862,415? Partition 750,000 in three different ways.
Model response: The 6 is worth 60,000 (sixty thousand). 750,000 = 700,000 + 50,000 = 600,000 + 150,000 = 500,000 + 250,000.
Explaining the multiplicative structure of the place value system: each column is 10 times the one to its right, and using this to reason about equivalences.
Example task
Explain why 400,000 is the same as 4,000 hundreds. How many tens are there in 1,000,000?
Model response: 400,000 = 4,000 × 100, so it is 4,000 hundreds. 1,000,000 ÷ 10 = 100,000, so there are 100,000 tens in 1,000,000.
CPA Stages
concrete
Using place value counters (100,000; 10,000; 1,000; 100; 10; 1) on a six-column place value mat to build, partition and compare numbers up to 1,000,000
Transition: Child reads, writes and partitions six-digit numbers without counters, explaining the value of each digit including zero placeholders
pictorial
Using place value charts, number lines to 1,000,000, and Gattegno charts to represent, compare and order large numbers on paper
Transition: Child reads and compares any number up to 1,000,000 without visual aids, articulating the column-by-column comparison
abstract
Working with numbers to 1,000,000 mentally: identifying digit values, partitioning flexibly, comparing, ordering, and reading/writing in words
Transition: Child works with any number to 1,000,000 fluently, partitioning flexibly and comparing instantly
Delivery rationale
Upper primary maths (Y5) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.
Rounding to any power of 10
skill AI DirectMA-Y5-C002
Rounding in Year 5 extends to the nearest 10,000 and 100,000. The underlying rule is identical to Year 4 (look at the next column right: 5 or more rounds up, 4 or less rounds down), but the range of numbers and the columns involved are much larger. Mastery means pupils can round any number up to 1,000,000 to any specified degree of accuracy and explain why, connecting rounding to the position of the number on a number line.
Teaching guidance
Practise identifying the two bounding multiples of the target rounding unit first: to round 347,500 to the nearest 100,000, identify that it is between 300,000 and 400,000, then determine which it is closer to. Use a number line segment showing just the relevant range. Connect rounding to estimation: before multiplying 4,713 × 23, estimate as 5,000 × 20 = 100,000. Emphasise that rounding does not change the number — it approximates it.
Common misconceptions
When rounding to the nearest 10,000, pupils look at the ones or tens digit (the last digit) rather than the thousands digit. Cascading rounding — rounding 95,000 to the nearest 100,000 gives 100,000 — surprises pupils who may not expect rounding to increase the number of digits.
Difficulty levels
Rounding numbers to the nearest 10, 100 and 1,000 (consolidating Year 4 skills with larger numbers).
Example task
Round 34,567 to the nearest 1,000.
Model response: 35,000. The hundreds digit is 5, so round up.
Rounding to the nearest 10,000 and 100,000 using a number line to identify the bounding multiples.
Example task
Round 347,500 to the nearest 100,000. Round 347,500 to the nearest 10,000.
Model response: To nearest 100,000: 300,000 (4 < 5, round down). To nearest 10,000: 350,000 (7 ≥ 5, round up).
Rounding any number up to 1,000,000 to any specified degree of accuracy, and using rounding for estimation.
Example task
Estimate 47,832 × 6 by rounding to the nearest 10,000 first.
Model response: 47,832 rounds to 50,000. Estimate: 50,000 × 6 = 300,000.
CPA Stages
concrete
Using number lines marked in 10,000s and 100,000s to physically locate numbers and identify which bounding multiple they are nearer to
Transition: Child identifies the bounding multiples and chooses the nearer one without a number line, correctly applying the '5 rounds up' convention
pictorial
Drawing number line segments to show the rounding process, marking midpoints and decisions, and recording rounding to different degrees of accuracy
Transition: Child rounds any number to any power of 10 by identifying the key digit, without drawing a number line
abstract
Rounding any number up to 1,000,000 to any power of 10 using the digit-checking rule, and applying rounding to estimate calculations with large numbers
Transition: Child rounds any large number to any degree of accuracy within 3 seconds and uses rounding to estimate calculations routinely
Delivery rationale
Upper primary maths (Y5) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.