Key takeaways
- Place value is the concept the whole number system rests on, secure it early.
- Teach new concepts concrete → pictorial → abstract (CPA), in that order.
- Many 'maths' difficulties are really vocabulary difficulties.
- Estimate before calculating to build number sense and self-checking.
- Understanding matters more than speed for concepts (unlike number facts).
Place value underpins everything
Place value, knowing the 3 in 30 means three tens, and the 3 in 300 means three hundreds, is the idea the whole number system depends on. Children shaky here struggle later with column methods, decimals and rounding. Base-ten blocks, place-value counters and reading numbers aloud ("two hundreds, five tens and four ones") build the model that abstract algorithms silently assume.
Concrete, then pictorial, then abstract
The most reliable way to teach a new concept is the CPA sequence. Start concrete (objects a child can move), move to pictorial (drawings, bar models), and only then to abstract symbols. It's why angles taught with a paper fan, or symmetry with a mirror, stick better than a definition read from a board, the physical experience becomes the meaning behind the notation.
Ask "about how much?" before every calculation. Estimation builds number sense and gives children a way to catch their own mistakes.
Language is half the battle
Words like difference, product, factor, perimeter and equivalent carry precise meanings that everyday language blurs. A child who hears "find the difference" but thinks of everyday 'difference' is lost before they begin. Name ideas clearly and consistently, and check children can use the words, not just hear them, it prevents a surprising amount of confusion in geometry, fractions and word problems.
Worked example, place value in action
Why does 46 + 27 need 'carrying'? Partition both: 40 + 6 and 20 + 7. Add the ones: 6 + 7 = 13, that's 1 ten and 3 ones. The extra ten moves into the tens column (40 + 20 + 10 = 70), giving 73. The 'carry' isn't a magic rule; it's place value doing exactly what it should.
If a child stumbles on a word problem, test the words first, 'sum', 'difference', 'product'. The maths is often fine; the language isn't.
When children learn this, a Year-by-Year guide
Roughly where each idea sits in the England primary maths curriculum. Every child is different, use it as a map, not a deadline.
| Stage | What children work on |
|---|---|
| Year 1–2 (ages 5–7) | Place value to 100; recognise 2D and 3D shapes; tell the time to five minutes. |
| Year 3–4 (ages 7–9) | Place value to 1,000+; perimeter; angles; introduce statistics with charts. |
| Year 5 (age 10) | Decimals and percentages; area; properties of shapes; line graphs. |
| Year 6 (age 11) | Ratio and proportion; volume; the first steps of algebra; the mean average. |
Concepts: understanding vs speed
| Concept type | Goal | How to practise |
|---|---|---|
| Number facts | Instant recall (speed) | Timed retrieval practice |
| Concepts (place value, fractions, shape) | Deep understanding | Concrete models, talk, estimation |
| Procedures (column methods) | Reliable accuracy | Understand first, then rehearse steps |
How to teach a new concept so it sticks
The CPA routine works for almost any primary concept.
- Start with real objects the child can hold and move.
- Have the child explain what they see in their own words.
- Move to a drawing or bar model of the same idea.
- Introduce the correct vocabulary and the symbols together.
- Ask the child to estimate before they calculate, then check.
Troubleshooting
| Problem | What to try |
|---|---|
| They muddle tens and ones | Return to base-ten blocks and read numbers aloud by place value before any written method. |
| Word problems throw them | Separate the reading from the maths: underline the vocabulary, draw the problem, then calculate. |
| They rush to an unreasonable answer | Insist on an estimate first, it turns a wild answer into an obvious error to catch. |
Free printable: Place Value Practice Sheet
A branded, print-ready worksheet to practise offline.
Frequently asked questions
What is place value and why does it matter?
Place value is the idea that a digit's position determines its worth, the 5 in 50 means five tens. It underpins the whole number system, so a secure grasp is essential before column methods, decimals and rounding.
What does concrete–pictorial–abstract mean?
It's a teaching sequence: introduce a concept with physical objects (concrete), move to drawings and models (pictorial), then to symbols (abstract). The concrete stage gives the symbols their meaning.
Why does maths vocabulary matter so much?
Terms like difference, product and equivalent have precise meanings. Many apparent maths difficulties are actually vocabulary gaps, so teaching the language explicitly prevents confusion later.