📋 In This Article
Ask most children what the digit 4 in 47 is worth and they'll say "four." Ask them why it's actually worth 40, and many will shrug. That gap — between knowing a digit and understanding its value — is the place value problem. And it's the root of most arithmetic struggles all the way into secondary school.
This guide gives you a clear, step-by-step approach to close that gap, whether you're a parent helping at home or a teacher working with a whole class.
What is place value — and why does it matter?
Place value is the idea that a digit's value depends on its position in a number. The digit 4 in 47 is worth 40 (four tens). The digit 4 in 74 is worth only 4 (four ones). Same digit, completely different value.
This seems simple, but children as old as 9 or 10 regularly make place value errors. Why? Because we teach children to count — 1, 2, 3 — before we teach them that numbers have internal structure. When they start working with 2-digit and 3-digit numbers, many children treat them as sequences of single digits rather than as structured wholes.
💡 Why it matters beyond primary school
Column addition and subtraction, long multiplication, long division, fractions, decimals, algebra — all of these rely on a secure understanding of place value. A child who doesn't fully understand why 47 = 40 + 7 will struggle with carrying in addition, borrowing in subtraction, and multiplying by 10 or 100.
The CPA approach: the best way to teach place value
The most effective framework for teaching place value is the Concrete–Pictorial–Abstract (CPA) approach, developed by psychologist Jerome Bruner and widely used in Singapore Maths, which consistently ranks first in international maths tests.
Concrete — physical objects
Start with real, touchable objects. Base-10 blocks are ideal. The child physically holds a rod (worth 10) and 7 unit cubes to make 17. They feel that the rod is bigger. This builds genuine understanding, not just memory.
Pictorial — drawings and diagrams
Move to pictures: draw the blocks, use a place value chart, show number lines. The child can see the structure without needing physical objects. This bridges the gap between touching and thinking.
Abstract — digits and symbols
Only now introduce the standard written form: 47, 4 tens and 7 ones, 40 + 7. The child now has a mental image to anchor the abstract symbols. The digit "4" means something real — it's the rod they held in Step 1.
🎯 The most common teaching mistake
Jumping straight to abstract (writing numbers and doing sums) before the concrete and pictorial stages are secure. Children who struggle with place value have almost always missed the concrete phase. Go back to blocks — even with older children. It works.
Grade-by-grade teaching guide
Grade 1 (Ages 6–7): Ones and Tens
The goal at this stage is for children to understand that 10 ones make 1 ten, and that every 2-digit number is built from tens and ones.
- Use base-10 blocks or bundles of 10 sticks — physical objects children can group and regroup
- Count collections of objects and sort them into groups of 10 and leftovers
- Practice writing the expanded form: 34 = 30 + 4
- Use a two-column place value chart (Tens | Ones) with digit cards
Grade 2 (Ages 7–8): Hundreds
Extend the chart to three columns. The key new idea is that 10 tens make 1 hundred — and 0 is a placeholder.
- Build 3-digit numbers with flats (hundreds), rods (tens) and units (ones)
- Practise reading numbers with zero in the middle: 305, 420, 607
- Compare 3-digit numbers using > and < — always start from the hundreds digit
Grade 3 (Ages 8–9): Thousands and Rounding
Add the thousands column and introduce rounding as a practical skill.
- Use the comma rule: 4,729 — the comma sits between thousands and hundreds
- Teach the rounding rule: look right, decide left. 4,729 rounded to the nearest 100 = 4,700
- Write numbers in all three forms: standard (4,729), expanded (4,000 + 700 + 20 + 9), word form (four thousand, seven hundred and twenty-nine)
Grade 4–5 (Ages 9–11): Millions, Billions and Decimals
The place value chart extends in both directions. Millions and billions follow the same period pattern. Decimals extend the chart to the right of the decimal point.
- Teach periods: ones period, thousands period, millions period. Each period has three columns and a comma separating it from the next
- For decimals: tenths = ÷10, hundredths = ÷100, thousandths = ÷1000. The decimal point is the anchor
- Compare decimals by lining up decimal points and comparing column by column — more digits does NOT mean bigger
Best manipulatives for teaching place value
Base-10 Blocks
The gold standard. Units, rods, flats and cubes. Proportional — each piece is physically 10× larger than the one below it.
Place Value Digit Cards
Cards showing 1, 10, 100, 1000 that fan out to show expanded form. Great for a visual "aha" moment.
Coins and Notes
Real or plastic money connects place value to everyday life. 10p coins and £1 coins show the 10× relationship concretely.
Place Value Charts
A laminated chart on every desk. Students write with dry-erase markers. Our free interactive chart tool works on tablets too.
What to do when a child is struggling
If a child consistently makes place value errors — reversing digits, ignoring zeros, misreading large numbers — the issue is almost always that the concrete stage was rushed. Here is a targeted intervention:
- Go back to base-10 blocks. Build the number physically before writing it. No shortcuts.
- Say the value out loud. Don't let children say "four seven" — insist on "forty-seven" every time. Language reinforces structure.
- Cover one digit. In 47, cover the 7 and ask "what does the 4 mean?" Cover the 4 and ask the same about the 7. Repeat daily for a week.
- Use the Number Expander tool. Our free Number Expander shows each digit's value in colour. Let struggling students type in numbers and discuss what they see.
⚠️ What not to do
Don't give a child more abstract practice (more sums) if they haven't mastered the concept concretely. Speed drills and worksheets will not fix a conceptual gap — they only reinforce confusion faster.
Free digital tools that help
Digital tools are especially valuable for practice and for visual learners. These are all free on PlaceValue:
- Place Value Chart — type any number and see each digit highlighted in its column, from billions to thousandths
- Base-10 Blocks — virtual blocks that update instantly as students type a number
- Number Expander — breaks any number into colour-coded expanded form
- Digit Detective game — students identify digits in specific place value positions under time pressure
🎮 Ready to practise?
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