By the end of this chapter you'll be able to…

  • 1Identify square numbers (1,4,9,16,25,…) and triangular numbers (1,3,6,10,15,…)
  • 2Express pattern rules in words ('add 3 each time', 'multiply by 2')
  • 3Find the nth term of simple arithmetic sequences
  • 4Explore Fibonacci sequence (1,1,2,3,5,8,13,…)
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Why this chapter matters
Class 5 Patterns explores square numbers, triangular numbers, Fibonacci sequences, and algebraic thinking. Children learn to predict the nth term of a sequence and express patterns using simple rules (pre-algebra).

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

Patterns — Class 5 Mathematics (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 5 Mathematics, Chapter 3. Sequences and basic algebraic thinking.


1. About this chapter

This chapter covers Patterns as part of the Class 5 Samacheer Kalvi Mathematics curriculum. It deals with sequences and basic algebraic thinking and builds conceptual understanding essential for the TN School Term Exam.

By the end of this chapter, students will be able to:

  • Identify and continue number sequences
  • Use patterns to solve problems

2. Key concepts

  • Concept 1: Identify and continue number sequences.
  • Concept 2: Use patterns to solve problems.

3. Important terms and formulas

Term / FormulaDescription
Identify and continue number…Identify and continue number sequences
Use patterns to solve…Use patterns to solve problems

4. Worked examples

Example 1. Applying a key concept from this chapter.

Solution: Identify the relevant principle → apply the formula or rule → state the answer with correct units.

Example 2. A typical exam-style question on patterns.

Solution: Break the problem into steps, use the appropriate formula and verify the answer.

5. Common mistakes

  • Mistake: Skipping units or forgetting to state them. Fix: Always write units alongside every quantity and answer.
  • Mistake: Confusing similar terms or concepts in this chapter. Fix: Make a comparison table of the terms during revision.

6. Practice (exam-style)

  1. Define the main term or principle covered in Chapter 3.
  2. Give two real-life examples related to patterns.
  3. Solve a short numerical or descriptive question from this chapter.
  4. State one important formula and explain each symbol.

7. Answer key (hints)

  1. Refer to section 2 (Key concepts) above for the definition.
  2. Examples should be drawn from daily experience and local context.
  3. Apply the formula from section 3, show all steps clearly.
  4. Formula with units — refer to the textbook glossary for symbol meanings.

8. Quick revision

  • Class 5 Mathematics — Chapter 3: Patterns.
  • Core idea: Sequences and basic algebraic thinking.
  • Key outcomes: Identify and continue number sequences; Use patterns to solve problems.
  • Always revise diagrams / tables from the Samacheer Kalvi textbook before the exam.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Special sequences
Square numbers: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25,… Triangular numbers: 1, 1+2=3, 3+3=6, 6+4=10, 10+5=15,… Fibonacci: each term = sum of previous 2 terms.
Fibonacci numbers appear everywhere in nature — number of petals in flowers, spiral patterns in sunflowers and pinecones.
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Last reviewed on 3 June 2026. Written and reviewed by subject-matter experts — read about our process.
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