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Number and place value is the foundation of all mathematics. Understanding what digits mean, how numbers are ordered, and how our number system works gives children the tools they need for every other area of maths.
The National Curriculum for Key Stage 1 develops children's number sense in two stages:
Children learn to count forwards and backwards to and across 100, starting from any number — not just from 1.
Examples:
Children read and write numbers in numerals and in words up to 20, and in numerals up to 100.
| Numeral | Word |
|---|---|
| 1 | one |
| 2 | two |
| 5 | five |
| 10 | ten |
| 11 | eleven |
| 12 | twelve |
| 13 | thirteen |
| 20 | twenty |
Note: Numbers 11-19 have irregular names that children must memorise. "Eleven" and "twelve" give no clues about their value — unlike "twenty-one" which clearly shows 2 tens and 1 one.
Given any number, children should be able to find one more and one less quickly and confidently.
| Number | 1 less | 1 more |
|---|---|---|
| 10 | 9 | 11 |
| 29 | 28 | 30 |
| 49 | 48 | 50 |
| 99 | 98 | 100 |
Teaching tip: Pay extra attention to numbers that cross a tens boundary (e.g. 1 more than 39 is 40, not 310).
Children represent and locate numbers on a number line. This helps them visualise the relationship between numbers.
0 10 20 30 40 50 60 70 80 90 100
|----|----|----|----|----|----|----|----|----|----|
Language to use: equal to, more than, less than, fewer, most, least
In Year 2, children formally learn that every two-digit number is made up of tens and ones (also called units).
| Number | Tens | Ones |
|---|---|---|
| 23 | 2 | 3 |
| 45 | 4 | 5 |
| 70 | 7 | 0 |
| 9 | 0 | 9 |
Partitioning:
Understanding place value is crucial. The digit 3 in 30 means 3 tens (= 30), while the digit 3 in 13 means 3 ones (= 3). Same digit, very different value!
flowchart TD
N[The number 47]
N --> T["Tens column<br/>digit 4 = 40"]
N --> O["Ones column<br/>digit 7 = 7"]
T --> Sum[40 + 7 = 47]
O --> Sum
Children use the symbols < (less than), > (greater than) and = (equal to) to compare numbers.
| Symbol | Meaning | Example |
|---|---|---|
| < | less than | 34 < 56 |
| > | greater than | 72 > 27 |
| = | equal to | 40 = 40 |
Memory trick: The open end of the symbol always faces the bigger number. Think of it as a hungry crocodile — it always eats the larger number!
| Count in | Example sequence |
|---|---|
| 2s | 0, 2, 4, 6, 8, 10, 12... |
| 3s | 0, 3, 6, 9, 12, 15... |
| 5s | 0, 5, 10, 15, 20, 25... |
| 10s from any number | 7, 17, 27, 37, 47... |
Counting in 3s prepares children for understanding a third (1/3) in fractions.
| Term | Meaning |
|---|---|
| digit | A single number symbol (0-9) |
| numeral | A written number (e.g. 47) |
| place value | The value of a digit based on its position |
| tens | Groups of ten |
| ones / units | Single values |
| partition | Split a number into parts (e.g. 45 = 40 + 5) |
| estimate | Make a sensible guess at a value |
| more than / greater than | Larger in value |
| less than / fewer than | Smaller in value |
| equal to | The same value |
Place value is the most important idea in primary mathematics — it underpins every calculation children will ever perform. In Year 2, the expected target is that children can partition a two-digit number into tens and ones with full understanding. Imagine teaching a lesson with the objective: "Children will partition the number 47 into tens and ones and show this with manipulatives."
Step 1 — Concrete with Dienes (base-10) blocks. Place 4 ten-rods on the desk, then 7 unit cubes. Say, "How many tens?" (4) "How many ones?" (7) "How many altogether?" Count: 10, 20, 30, 40, 41, 42, 43, 44, 45, 46, 47. The crucial step is the count: one ten, two tens, three tens, four tens — and then forty-one, forty-two…. This explicit verbalisation builds the link between counting in tens and place value.
Step 2 — Place value counters. Replace the Dienes with place value counters — small discs labelled with 10 or 1. Children place 4 tens-counters in the tens column and 7 ones-counters in the ones column of a place value chart:
Tens | Ones
4 | 7
This is more abstract because a single small disc represents 10 — children must trust that the disc value comes from its label and column, not its size. This shift is significant.
Step 3 — Numicon or ten-frames. Use Numicon shapes or two ten-frames to show 47 as 4 full tens and a frame with 7 counters. This gives children another image of how big 47 actually is — useful for comparing two numbers later.
Step 4 — Abstract notation. Write 47 = 40 + 7 and ask children to read it aloud. Then introduce non-standard partitioning: 47 = 30 + 17 (3 tens and 17 ones). Show this with the Dienes by exchanging one ten-rod for 10 unit cubes. The same number, partitioned differently. Non-standard partition matters because it underpins regrouping in subtraction next year.
Verbal prompts to use:
Common errors to watch for:
End with reasoning: "The number has a 5 in the tens place and a 2 in the ones place. What number is it? How do you know?" (52). Then reverse: "My number is 38. What is in the tens place? What is in the ones place?"
The deepest KS1 misconception in this topic is the belief that "the digit is the value" — children read 47 and think the 4 means four, not forty. This breaks every subsequent calculation. Use the language "the value of the 4 is 40" relentlessly. Show the same digit in different positions: in 24 the 2 is worth 20; in 42 the 2 is worth 2. Same digit, very different value. Layered place value cards (also called arrow cards) make this visible — pull the card apart to reveal 40 under the 47, then 7 behind. The number is not the digits; the number is the digits in their places.
Place value can be approached at three clear levels of abstraction in the same classroom.
Working towards (concrete and counting). These children focus on counting accurately to 100 in 1s, 2s, 5s and 10s. They use Numicon, ten-frames, hundred squares and Dienes. They find 1 more and 1 less of any number to 50 using a number line or hundred square. They sequence numbers up to 30. Example tasks: "Place these number cards in order: 12, 4, 19, 7, 25." "What is 1 more than 18? What is 1 less than 30?" Vocabulary stays simple: more, less, bigger, smaller.
Expected (pictorial and structured). Children at the expected standard partition any two-digit number into tens and ones. They compare numbers using <, > and =. They count in 2s, 3s, 5s and 10s. They identify the value of each digit. Example task: "Use < or > to compare 47 and 74. Partition each number into tens and ones. Explain how you know which is greater."
Greater depth (reasoning and problem-solving). These children solve problems involving missing digits, non-standard partitioning and reasoning about digit value. Example tasks:
This three-tier structure builds place value as a deep, reasoned concept — the foundation of every calculation method in KS2 and beyond. Children who finish KS1 with secure place value tend to flourish in KS2; children who do not, struggle with everything from column addition to decimals. Time spent on this topic is never wasted, and the use of varied manipulatives — Dienes, place value counters, Numicon, ten-frames, hundred squares — gives children many different mental images to draw on when calculating.
A final practical note for parents: number sense is built at home as well as at school. Counting objects in real situations — stairs, plates, cars on a journey — builds fluency far better than worksheets. Talking about numbers everywhere they appear (door numbers, prices, phone numbers, ages) makes place value feel natural rather than abstract. By the end of Year 2, a child who has counted thousands of real things, in many different ways, has a much stronger foundation than one who has only worked through textbook exercises.
Place value rewards daily, varied, real-world counting more than any other primary maths topic. The activities below set out a clear progression, with practical support for children who find the work tricky, easy at-home games and stretch tasks for greater-depth learners.
If your child finds it tricky. Return to a hundred square and a set of base-10 blocks every time. Practise one more, one less and ten more, ten less for any number on the square. Use the rhyme "down a row is ten more, up a row is ten less". For numbers crossing a boundary (1 more than 39, 1 less than 50), slow right down and use base-10 blocks to exchange physically: 39 = 3 tens and 9 ones; add one more one — that is 10 ones — exchange for a ten-rod — now 4 tens and 0 ones = 40. Practise reading two-digit numbers aloud in partitioned form: 47 is forty-seven, which is 4 tens and 7 ones, or 40 + 7. The reading-aloud is half the battle.
At-home games and routines. Number plate hunt: on a journey, look at car number plates and find the largest number, the smallest, one more, one less. Shop receipts: circle every two-digit number on a receipt; ask which has the most tens. Stair counting: count up the stairs in 1s; coming down, count in 2s. Once secure, count up in 5s and down in 10s starting from any number. Dice place value: roll two dice; the first is tens, the second is ones — what is the number? Find one more, one less, ten more, ten less. Hundred-square hide-and-seek: cover a number on a hundred square and ask the child to work out what it is from its neighbours.
Stretch tasks for greater depth. Set missing-digit puzzles: "I am thinking of a 2-digit number. The tens digit is double the ones digit. The ones digit is 4. What is my number?" (84). Introduce non-standard partition explicitly: "Show 36 in three different ways using tens and ones." (3 tens 6 ones; 2 tens 16 ones; 1 ten 26 ones). Push reasoning about digit value: "Aimee says 19 is greater than 91 because 9 is greater than 1. Is she right? Explain." Ask digit-arrangement problems: "Use the digits 3, 5 and 8 to make all the 2-digit numbers you can. Order them from smallest to largest."
The scenario. Mr O'Brien is teaching place value to his Year 2 class. He asks Lily, aged 6, to write the number "forty-seven" on her whiteboard. Lily writes 407. She has heard "forty" (and written 40) and "seven" (and written 7) and joined them as a string of digits. When Mr O'Brien reads back her answer as "four hundred and seven", Lily is confused — "That is what you said!"
What to do. Mr O'Brien does not correct in writing first. He places 4 ten-rods and 7 unit cubes in front of Lily. "This is your number. Tell me what it is." Lily counts: 10, 20, 30, 40, 41, 42, 43, 44, 45, 46, 47 — and says "forty-seven". Mr O'Brien then introduces place value cards (also called arrow cards) — a card showing 40 with the 0 in the ones column, and a separate card showing 7. He overlays the 7 card on top of the 0 of the 40 card — and Lily sees how forty-seven is written: the 7 hides the 0 in the ones place. They practise with thirty-two, sixty-five and twenty-nine. Lily now writes 47, not 407. Mr O'Brien adds a place value chart to her tray, with Tens and Ones columns labelled, so she has a permanent reference until the convention is automatic.
Scenario question. "What is the value of the digit 4 in the number 47? Compare 47 and 74 using < or >. Then find a 2-digit number where the tens digit is double the ones digit and the ones digit is 4."
At a Grade 1 / Working towards (Year 1) level. The child shows 47 with 4 ten-rods and 7 unit cubes, counting 10, 20, 30, 40, 41, 42, 43, 44, 45, 46, 47. With prompting they say "the 4 means 40". To compare 47 and 74 they build both with Dienes and physically see which pile is taller. They are not yet ready for the missing-digit puzzle; instead they sequence the numbers 10 to 30 on cards and find one more / one less.
At a Grade 2 / Expected (Year 2) level. The child partitions any 2-digit number into tens and ones in symbols: 47 = 40 + 7. They write 47 < 74 confidently, explaining that 74 has more tens. They count in 2s, 3s, 5s and 10s. For the puzzle they reason: "Ones digit is 4, tens digit is double, so tens digit is 8. The number is 84." They identify the value of each digit in any 2-digit number.
At a Grade 3 / Greater depth level. The child uses non-standard partitioning fluently ("36 = 30 + 6, or 20 + 16, or 10 + 26") and explains why all three are equivalent. They spot and correct misconceptions: "Aimee says 19 > 91 because 9 > 1. Why is she wrong?" They generate every 2-digit number whose digits sum to 5 (14, 23, 32, 41, 50) and prove the list is complete. They reason about how many numbers between 20 and 50 contain a 4, listing them systematically.
This content is aligned with the UK National Curriculum for Key Stage 1 Mathematics (Years 1-2, programmes of study). For the most accurate and up-to-date information, please refer to the Department for Education National Curriculum framework.