Concrete Operational Stage (7–11 years)
From about 7 to 11 years the child can perform logical mental operations — but only on concrete, real, tangible objects and situations, not yet on abstract or hypothetical ideas. Three big abilities arrive. Conservation is now mastered (the water is the same amount whatever the glass). Reversibility appears — the child can mentally reverse a sequence of steps (3 + 4 = 7, so 7 − 4 = 3). Decentration lets the child consider several features at once, so egocentrism declines. The child can also seriate (arrange in order, e.g. sticks shortest to longest) and classify objects by more than one property, and understands transitivity (if A>B and B>C then A>C) — as long as the materials are concrete. Hand this child a purely verbal, abstract 'if…then' puzzle, though, and they still struggle.
✅ Solved examples
✏️ Practice — try these, take hints as needed
📝 Topic test — 8 questions
Auto-graded with full solutions; saved to your dashboard. Use the calculator and formula sheet (top-right) any time.
Key Concepts — Quick Reference
The four stages (memorise the ages cold)
| Sensorimotor | 0–2 yrs · senses & action · object permanence |
|---|---|
| Preoperational | 2–7 yrs · symbols & language · egocentrism, no conservation |
| Concrete Operational | 7–11 yrs · logic on concrete things · conservation, reversibility |
| Formal Operational | 11+ yrs · abstract & hypothetical reasoning |
How thinking changes
| Schema | A mental framework for organising knowledge |
|---|---|
| Assimilation | Fit new information INTO an existing schema |
| Accommodation | CHANGE the schema to fit new information |
| Equilibration | The drive to balance assimilation & accommodation |