Shape Pattern
Logic & Patterns: Shape Pattern
Shape Pattern
Shape Pattern
What you'll learn
- Spot repeating cycles of shapes (like Circle, Square, Triangle repeating).
- Find the next shape in a repeating pattern.
- Work out the shape at any position in a long repeating pattern using the cycle length.
Key concepts
Level 1 — Repeating cycle of 3
If a pattern repeats every 3 shapes (Circle, Square, Triangle, Circle, Square, Triangle...), find where you are in the cycle to know what comes next.
Level 2 — Repeating cycle of 2
Some patterns alternate between just two shapes, like Star, Moon, Star, Moon...
Level 3 — Finding the Nth shape
For a cycle of length 4, the shape at position N is the same as the shape at position ((N-1) remainder 4) + 1 in the cycle. This avoids having to draw out a huge pattern.
NCERT anchor: CBSE Class 4 logical reasoning; Math-Magic 4 Ch 12 — shapes and patterns
Worked example
The shapes repeat: Circle, Square, Triangle, Circle, ?
Step 1 — The cycle is Circle, Square, Triangle (length 3).
Step 2 — After the 4th shape (Circle), the cycle restarts.
Answer: **Square**
A pattern repeats every 4 shapes: Circle, Square, Triangle, Diamond. What is the 9th shape?
Step 1 — 9 divided by 4 leaves remainder 1 (since 4+4=8, and 9-8=1).
Step 2 — Position 1 in the cycle is Circle.
Answer: **Circle**
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| Forgetting the cycle restarts | Thinking the pattern keeps changing | Circle back to the first shape after the cycle length |
| Miscounting the cycle length | Not checking how many shapes before it repeats | List the shapes until you see the first one repeat |
| Wrong remainder for Nth position | Skipping the divide-and-remainder step | Use: remainder of (N-1) divided by cycle length, then +1 |
| Mixing up two different shape sets | Confusing a 2-shape and 3-shape cycle | Always re-check the shown shapes before answering |
Quick check
- Star, Moon, Star, Moon, ? — what is next?
- Circle, Square, Triangle, Circle, Square, ? — what is next?
- In a 4-shape cycle (Circle, Square, Triangle, Diamond), what is the 6th shape?
- Stretch: In the same 4-shape cycle, what is the 20th shape? (Hint: 20 divided by 4 has no remainder — that means the last shape in the cycle.)
Revision tip: Write shape positions as numbers (1, 2, 3, 4, 1, 2, 3, 4...) under the pattern to instantly see which shape repeats where.
Open the Practice tab for graded questions on Shape Pattern.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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