Number - Number and Place Value
KS2MA-Y4-D001
Understanding place value in four-digit numbers, counting in larger multiples (6, 7, 9, 25, 1000), negative numbers in context, rounding to nearest 10 and 100, and Roman numerals to 100.
National Curriculum context
In Year 4, pupils extend place value understanding from three-digit numbers to four-digit numbers (thousands, hundreds, tens, ones), significantly expanding the range of numbers they can work with. The non-statutory guidance specifies that pupils should practise reading Roman numerals to 100 (I to C) and begin to understand the year written in Roman numerals. Pupils work with negative numbers in contexts such as temperature and debt, and with rounding — to the nearest 10, 100 and 1000 — which develops estimation skills and understanding of approximation. This domain forms the essential prerequisite for place value work with numbers up to a million in Year 5, and the rounding skills introduced here are used throughout the upper key stage.
5
Concepts
3
Clusters
5
Prerequisites
5
With difficulty levels
Lesson Clusters
Understand place value and count in multiples with four-digit numbers
introduction CuratedFour-digit place value is the foundational concept; counting in multiples of 6, 7, 9, 25 and 1000 extends skip-counting to match the new times table demands. C002 co-teaches with C004.
Round to the nearest 10, 100 and 1000 and use negative numbers in context
practice CuratedRounding and negative numbers both extend the number line concept beyond the positive integers. C004 co-teaches with C002.
Read Roman numerals to 100
practice CuratedRoman numerals is a discrete knowledge strand within NC Number that does not co-teach with other Year 4 number concepts. Standalone practice cluster.
Teaching Suggestions (1)
Study units and activities that deliver concepts in this domain.
Place Value in Four-Digit Numbers and Negative Numbers
Mathematics Pattern SeekingPedagogical rationale
Y4 extends place value to four digits and introduces negative numbers and rounding. The thousands column is best understood through physical place value counters on an expanded chart, making the 10:1 relationship between adjacent columns visible. Negative numbers are introduced through temperature contexts, which give children a meaningful real-world anchor. Rounding is a new skill that requires understanding the midpoint on a number line, not just a mechanical rule.
Access and Inclusion
2 of 5 concepts have identified access barriers.
Barrier types in this domain
Recommended support strategies
Prerequisites
Concepts from other domains that pupils should know before this domain.
Concepts (5)
Place value in four-digit numbers
knowledge AI DirectMA-Y4-C001
Four-digit numbers have digits in the thousands, hundreds, tens and ones positions (e.g. 3,472 = 3000 + 400 + 70 + 2). Understanding this extends the place value system one column to the left. Mastery means pupils can identify the value of any digit in a four-digit number, partition it in standard and flexible ways, and use this understanding as the basis for all four-digit calculations.
Teaching guidance
Extend the Dienes blocks to include thousands cubes (a 10 × 10 × 10 block). Use place value mats with Th, H, T, O columns. Arrow cards now include 1000, 2000, 3000... cards. Place value charts and number lines up to 10,000 provide pictorial support. Key: the thousands digit value is always a multiple of 1000, not simply the digit read as a single number. Practise partitioning in multiple ways (3472 = 3000 + 472 = 2000 + 1472 etc.).
Common misconceptions
Pupils sometimes say 3,472 has a 3 'worth 3' rather than 3000. In four-digit numbers, the zero placeholder causes confusion in numbers like 3,072 (no hundreds) — pupils may write this as 372 or 3720. Writing numbers in words becomes more complex (three thousand, four hundred and seventy-two — note 'and' placement).
Difficulty levels
Identifying the value of each digit in a four-digit number using Dienes blocks (thousands cube, hundreds flat, tens rod, ones cube) on a place value mat.
Example task
Build 2,365 with Dienes blocks on the place value mat. How many thousands, hundreds, tens and ones?
Model response: 2 thousands, 3 hundreds, 6 tens, 5 ones. The 2 is worth 2000, the 3 is worth 300, the 6 is worth 60, the 5 is worth 5.
Partitioning four-digit numbers into standard form (Th + H + T + O) using arrow cards, including numbers with zero placeholders.
Example task
Partition 4,073 into thousands, hundreds, tens and ones. What does the 0 mean?
Model response: 4,073 = 4000 + 0 + 70 + 3. The 0 means there are no hundreds.
Stating the value of any digit in any four-digit number instantly, comparing and ordering four-digit numbers, and partitioning flexibly.
Example task
What is the value of the 8 in 5,831? Order these: 3,456; 3,465; 3,546; 3,564.
Model response: The 8 is worth 800. In order: 3,456; 3,465; 3,546; 3,564.
Explaining how the place value system works multiplicatively — each column is 10 times the column to its right — and using this to reason about numbers up to 10,000.
Example task
Why is 3,000 the same as 300 tens? Explain using place value.
Model response: 3,000 = 3 × 1000. Since 1000 = 100 × 10, that means 3,000 = 300 × 10 = 300 tens. Each column is worth 10 times the column to its right.
CPA Stages
concrete
Using Dienes blocks (thousands cube, hundreds flat, tens rod, ones cube) on a four-column place value mat to build, partition and exchange four-digit numbers
Transition: Child identifies the value of each digit in any four-digit number and partitions flexibly without needing blocks or cards
pictorial
Drawing place value charts and using number lines to 10,000 to represent, compare and order four-digit numbers
Transition: Child reads, writes, compares and orders any four-digit number without a chart, explaining place value reasoning verbally
abstract
Working with four-digit numbers mentally: identifying digit values, partitioning flexibly, comparing and ordering, and solving problems involving place value
Transition: Child answers any four-digit place value question within 3 seconds and uses place value reasoning to justify comparisons
Delivery rationale
Upper primary maths (Y4) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.
Access barriers (1)
Place value to 10,000 extends the positional system to thousands. Each additional place represents a x10 multiplicative relationship that is increasingly difficult to ground in concrete experience — you cannot easily handle 10,000 physical objects.
Counting in multiples of 6, 7, 9, 25 and 1000
skill AI DirectMA-Y4-C002
Year 4 extends skip-counting to the six, seven, nine, twenty-five and one thousand times tables. Counting in 6s, 7s and 9s consolidates the corresponding multiplication tables; counting in 25s connects to money and measurement; counting in 1000s extends place value. Mastery means pupils can count fluently in all these multiples from different starting points and in both directions.
Teaching guidance
For 6s and 9s, use the connection to the 3 times table (6 = 2 × 3; 9 = 3 × 3). The '9 times table finger trick' helps some pupils. For 25s, connect to money: 25p, 50p, 75p, £1.00 — four 25ps make £1. For 1000s, extend the place value understanding to counting in thousands on a number line up to 10,000. Practise all multiples with a mix of 'continue the sequence' and 'what comes after/before?' questions.
Common misconceptions
The 7 times table is the hardest for most pupils and has no obvious pattern to aid memorisation. Counting in 25s causes errors at 100 (some pupils say 100, 125, 150... but then say 275, 300, 325... — correct — having been unsure at 200 and 225). Counting backwards in 9s is particularly challenging.
Difficulty levels
Counting in 25s from 0 to 200 using 25p coins as concrete support.
Example task
Place 25p coins in a line. Count the total: 25, 50, 75... Continue to 200.
Model response: 25, 50, 75, 100, 125, 150, 175, 200
Counting in 6s, 7s and 9s from 0, using a hundred square or known facts as support.
Example task
Count in 7s from 0 to 70.
Model response: 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70
Counting fluently in 6s, 7s, 9s, 25s and 1000s from any starting multiple, forwards and backwards.
Example task
Start at 36. Count in 9s to 72. Count in 1000s from 3000 to 9000.
Model response: 36, 45, 54, 63, 72. 3000, 4000, 5000, 6000, 7000, 8000, 9000.
CPA Stages
concrete
Using bead strings, Cuisenaire rods and hundred squares to count in multiples of 6, 7, 9, 25 and 1000, marking each multiple physically
Transition: Child counts in all five multiples fluently from any starting point without highlighting or stacking
pictorial
Recording multiples as sequences on number lines, circling patterns on number grids, and connecting skip-counting patterns to multiplication tables
Transition: Child generates any sequence of multiples from memory, identifies the nth multiple, and connects skip-counting directly to multiplication facts
abstract
Counting in multiples mentally from any starting point in both directions, and using the sequences to derive multiplication and division facts
Transition: Child counts in all multiples fluently forwards and backwards from any starting point and connects sequences to times table facts instantly
Delivery rationale
Upper primary maths (Y4) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.
Negative numbers in context
knowledge AI DirectMA-Y4-C003
Negative numbers extend the number line below zero. In Year 4, pupils encounter them in contexts such as temperature below freezing, below sea level, and financial debt. Pupils must be able to count through zero in both directions and compare negative numbers. Mastery means pupils can read and record negative numbers in context, compare negative numbers (e.g. –3 > –7), count through zero, and calculate intervals crossing zero.
Teaching guidance
Use a vertical number line (like a thermometer) as the primary visual tool — the physical analogy of temperature falling below zero is highly effective. Number lines on the floor (walk below zero) and horizontal number lines that extend left of zero both help. Practise reading temperatures on a thermometer scale. Compare pairs of temperatures: 'Which is colder, –3°C or –7°C?' Establish: numbers get smaller the further left (or down) you go, even below zero.
Common misconceptions
Pupils commonly think –7 is greater than –3 because 7 > 3 — they apply the absolute value comparison rather than the signed comparison. The language 'minus seven' is confused with 'take away seven', so some pupils treat –7 as a subtraction instruction rather than a number. The word 'negative' itself is important to use alongside 'minus' to make the distinction clear.
Difficulty levels
Reading temperatures below zero on a large vertical number line (thermometer) and counting through zero.
Example task
The temperature is 3°C. It drops by 5 degrees. Use the thermometer to count back. What is the new temperature?
Model response: 3, 2, 1, 0, –1, –2. The new temperature is –2°C.
Ordering negative numbers and comparing them, including recognising that –7 is less than –3.
Example task
Which is colder, –3°C or –7°C? Put these in order from coldest to warmest: 5°C, –2°C, 0°C, –6°C.
Model response: –7°C is colder. Order: –6°C, –2°C, 0°C, 5°C.
Calculating intervals that cross zero and using negative numbers in real-world contexts without a number line.
Example task
The temperature at midnight was –4°C. By midday it was 9°C. What was the temperature rise?
Model response: From –4 to 0 is 4 degrees, from 0 to 9 is 9 degrees. Total rise = 4 + 9 = 13 degrees.
Solving multi-step problems involving negative numbers and explaining the reasoning.
Example task
The temperature was –3°C. It rose by 8 degrees, then dropped by 12 degrees. What is the final temperature?
Model response: –3 + 8 = 5°C. Then 5 – 12 = –7°C. The final temperature is –7°C.
CPA Stages
concrete
Using a vertical number line (thermometer model), a horizontal floor number line extending below zero, and temperature displays to count through zero and locate negative numbers
Transition: Child counts through zero in both directions and compares negative numbers correctly, explaining that -7 is less than -3 because it is further below zero
pictorial
Drawing vertical and horizontal number lines that extend below zero, marking and comparing negative numbers, and calculating intervals across zero
Transition: Child calculates intervals crossing zero on paper and compares negative numbers without needing to count on the number line
abstract
Working with negative numbers mentally: comparing, ordering, and calculating temperature changes and intervals across zero
Transition: Child compares and orders negative numbers instantly and calculates intervals across zero mentally without drawing a number line
Delivery rationale
Upper primary maths (Y4) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.
Rounding to nearest 10, 100 and 1000
skill AI DirectMA-Y4-C004
Rounding is the process of approximating a number to the nearest multiple of 10, 100 or 1000. The rule is: if the digit in the column to the right of the target column is 5 or more, round up; if it is 4 or less, round down. Mastery means pupils can round any number to the specified degree of accuracy, explain the rule with reference to the number line, and use rounding as a checking and estimation tool.
Teaching guidance
Use a number line to show rounding as finding the nearer of the two bounding multiples. For rounding 347 to the nearest 100: it is between 300 and 400, closer to 300, so it rounds to 300. The 'five is on the right side of the hill' mnemonic helps establish the convention for 5. Practise rounding to different degrees of accuracy on the same number. Connect to estimation: before computing 347 + 256, round both to nearest 100 to estimate 300 + 300 = 600.
Common misconceptions
Pupils frequently look at the wrong digit when rounding (rounding to nearest 100, they look at the ones digit rather than the tens digit). The midpoint convention (when the digit is exactly 5, round up) is not understood conceptually, only as a rule. Rounding to the nearest 1000 can produce 0 for numbers less than 500, which surprises pupils.
Difficulty levels
Rounding two-digit numbers to the nearest 10 using a number line showing the two bounding multiples.
Example task
Round 47 to the nearest 10. Is it closer to 40 or 50?
Model response: 47 rounds to 50 because 47 is closer to 50 than to 40 (it is only 3 away from 50 but 7 away from 40).
Rounding three-digit numbers to the nearest 10 and 100, using the 'look at the next digit' rule.
Example task
Round 463 to the nearest 10. Round 463 to the nearest 100.
Model response: To nearest 10: 460 (the ones digit 3 is less than 5). To nearest 100: 500 (the tens digit 6 is 5 or more).
Rounding any number to the nearest 10, 100 or 1000, and using rounding to estimate answers to calculations.
Example task
Round 7,549 to the nearest 1000. Estimate 3,782 + 5,109 by rounding each to the nearest 1000.
Model response: 7,549 rounds to 8,000. Estimate: 4,000 + 5,000 = 9,000.
CPA Stages
concrete
Using number lines marked in 10s, 100s and 1000s to physically locate numbers between two bounding multiples, determining which multiple is nearer
Transition: Child identifies the two bounding multiples and chooses the nearer one without the number line, including the convention that 5 rounds up
pictorial
Drawing number lines to show the rounding process, marking the midpoint and the decision, and recording rounding in a structured format
Transition: Child rounds any number to the nearest 10, 100 or 1000 by identifying the key digit, without needing to draw a number line
abstract
Rounding any number to the nearest 10, 100 or 1000 using the digit-checking rule, and applying rounding to estimate calculations
Transition: Child rounds any four-digit number to any degree of accuracy within 3 seconds and routinely uses rounding to check calculations
Delivery rationale
Upper primary maths (Y4) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.
Roman numerals to 100 (I to C)
knowledge AI DirectMA-Y4-C005
Roman numerals use letters to represent values: I=1, V=5, X=10, L=50, C=100. The system uses additive (VI = 5+1 = 6) and subtractive (IV = 5-1 = 4) principles. In Year 4, pupils read Roman numerals to 100 and understand historically how this differs from our place value system. Mastery means pupils can convert any number from 1-100 to and from Roman numerals and explain why the Roman system does not have place value.
Teaching guidance
Display the seven basic Roman numeral symbols prominently (I, V, X, L, C, D, M — though D and M are not required until later). Teach the subtractive rule: when a smaller numeral precedes a larger one, it is subtracted (IV = 4, IX = 9, XL = 40, XC = 90). Practise conversions in both directions. Connect to history: discuss why the Roman system had no zero and how that limited mathematical development. Contrast with our positional/place value system.
Common misconceptions
Pupils frequently forget the subtractive rule and read IV as 6 (I + V) rather than 4 (V – I). They may apply the subtractive rule incorrectly: IIX is not a valid Roman numeral (the convention is that only one smaller numeral precedes a larger one). Some pupils confuse Roman numeral C (100) with the letter and assign it other values.
Difficulty levels
Reading and writing Roman numerals I to X and matching them to Hindu-Arabic numerals.
Example task
Write these in Roman numerals: 3, 7, 10.
Model response: 3 = III, 7 = VII, 10 = X.
Reading and writing Roman numerals using I, V, X, L and C, applying the subtractive rule for 4, 9, 40, 90.
Example task
Write 49 in Roman numerals. What number is XCIV?
Model response: 49 = XLIX. XCIV = 94.
Converting any number from 1 to 100 between Roman numerals and Hindu-Arabic, and explaining why the Roman system has no place value.
Example task
Write 87 in Roman numerals. Why did the Roman system need separate symbols for 50 (L) and 100 (C)?
Model response: 87 = LXXXVII. The Roman system has no place value — the position of a digit does not change its value. So they needed different symbols for different amounts: L for 50 and C for 100. Our system uses position instead.
CPA Stages
concrete
Using Roman numeral cards, building numbers with individual letter tiles, and converting between Roman and Hindu-Arabic numerals using a reference chart and matching activities
Transition: Child builds and reads Roman numerals to 100, applying both additive and subtractive rules without the reference chart
pictorial
Writing Roman numeral conversion tables, drawing comparison charts showing the Roman system alongside our place value system, and recording conversions on paper
Transition: Child converts any number 1-100 to and from Roman numerals on paper without a reference table
abstract
Converting between Roman and Hindu-Arabic numerals mentally, explaining why the Roman system differs from our place value system, and reading Roman numerals in real-world contexts
Transition: Child converts any number to 100 (and common larger numbers) mentally and articulates the key difference: 'Our system uses position; Roman uses letter values'
Delivery rationale
Upper primary maths (Y4) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.
Access barriers (2)
Formal written methods for addition and subtraction of 4-digit numbers involve the same column procedure as Y3 but with more columns and more opportunities for carrying/exchanging. The procedure has 8+ sequential steps.
Four-digit column methods require tracking carries across 4 columns while maintaining digit alignment. The cumulative working memory load is substantial.