Patterns in Mathematics Class 6 Worksheet — Free PDF Download with Answers

Mathematics is often described as the science of patterns. From the spiral of a sunflower to the rhythm of a heartbeat, patterns are everywhere — and recognising them is the first step toward mathematical reasoning.

In Class 6, students explore number patterns (sequences where each term follows a rule), visual or geometric patterns (shapes that repeat or grow according to a rule), and special number families like triangular numbers ($1, 3, 6, 10, \ldots$), square numbers ($1, 4, 9, 16, \ldots$), and cube numbers ($1, 8, 27, 64, \ldots$).

Studying patterns develops a critical skill: the ability to observe, hypothesise, and generalise. When a student spots that the differences between consecutive triangular numbers are $2, 3, 4, 5, \ldots$, they are essentially discovering a rule — and that is the heart of algebra, which they will study formally in later classes.

Review these before starting the worksheet:

* Arithmetic sequence — Each term is obtained by adding a fixed number (common difference $d$) to the previous term. E.g., $5, 8, 11, 14, \ldots$ ($d = 3$).
* Geometric pattern — Each term is obtained by multiplying the previous term by a fixed number. E.g., $2, 6, 18, 54, \ldots$ (multiply by $3$).
* Triangular numbers — $T_n = \dfrac{n(n+1)}{2}$. First few: $1, 3, 6, 10, 15, 21, \ldots$
* Square numbers — $S_n = n^2$. First few: $1, 4, 9, 16, 25, 36, \ldots$
* Cube numbers — $C_n = n^3$. First few: $1, 8, 27, 64, 125, \ldots$
* Fibonacci-type patterns — Each term is the sum of the two preceding terms. E.g., $1, 1, 2, 3, 5, 8, 13, \ldots$
* Visual/dot patterns — Shapes made with dots where the count follows a number rule. E.g., a triangle with rows of $1, 2, 3, \ldots$ dots gives triangular numbers.
* Growing patterns — Each stage adds more tiles/blocks in a predictable way (e.g., add one column each time).

1. Print the PDF — Download from the links below. Working on paper helps you sketch patterns and annotate freely.

2. Start with Level 1 (Easy) — These 20 questions ask you to continue simple sequences, identify the rule, and count dots in visual patterns.

3. Time yourself — 15 minutes for Level 1, 20 for Level 2, 25 for Level 3.

4. Check answers — Use the answer key at the end of the PDF.

5. Revise mistakes — For wrong answers, write the rule you missed and redo the question.

6. Move to the next level — Progress when you score 16/20 or higher.

Level 1 — Easy

1. Find the next two terms: $4, 7, 10, 13, \ldots$
Solution: Common difference $= 3$. Next terms: $16, 19$.

2. Which triangular number comes after $10$?
Solution: $T_4 = 10$, so $T_5 = 10 + 5 = 15$.

3. How many dots are in a $4 \times 4$ square array?
Solution: $4^2 = 16$ dots.

Level 2 — Medium

1. The pattern is $2, 6, 18, 54, \ldots$ What is the $6$th term?
Solution: Each term is multiplied by $3$. $T_5 = 162$, $T_6 = 486$.

2. Find the $10$th triangular number.
Solution: $T_{10} = \dfrac{10 \times 11}{2} = 55$.

3. A pattern of matchsticks forms squares: $4, 7, 10, 13, \ldots$ matchsticks for $1, 2, 3, 4$ squares. How many matchsticks for $10$ squares?
Solution: Rule: $3n + 1$ matchsticks for $n$ squares. For $n = 10$: $3(10) + 1 = 31$.

Level 3 — Hard

1. Show that the sum of the first $n$ odd numbers equals $n^2$. Verify for $n = 6$.
Solution: $1 + 3 + 5 + 7 + 9 + 11 = 36 = 6^2$.

2. A sequence is defined by $a_1 = 1$, $a_{n+1} = 2a_n + 3$. Find $a_5$.
Solution: $a_2 = 5$, $a_3 = 13$, $a_4 = 29$, $a_5 = 61$.

3. The $n$th term of a pattern is $n^2 + n$. Find the first 5 terms and the sum of these 5 terms.
Solution: Terms: $2, 6, 12, 20, 30$. Sum $= 70$.

CBSE (NCERT — Ganita Prakash)
The new NCERT Ganita Prakash textbook has a dedicated chapter on "Patterns in Mathematics" that encourages exploration through dot diagrams, matchstick patterns, and number walls. CBSE exam questions focus on finding the next term, stating the rule, and verifying properties of special numbers.

ICSE (Selina / ML Aggarwal)
ICSE integrates patterns into chapters on Number System and Algebra Introduction. Students are expected to express the $n$th term algebraically (e.g., $2n + 1$) even at the Class 6 level. ICSE papers include more formula-based pattern questions.

IB MYP (Mathematics Framework)
The MYP approach emphasises investigation: students are given a pattern and asked to make a conjecture, test it, and justify it in words. The focus is on reasoning and communication rather than just finding the answer.

Key Differences:
* CBSE: Visual and exploratory; Ganita Prakash uses hands-on activities.
* ICSE: Algebraic generalisation expected earlier.
* IB: Inquiry-based with emphasis on written justification.

Download your free Patterns in Mathematics worksheet:

* Patterns in Mathematics CBSE Worksheet — 60 questions aligned to NCERT Ganita Prakash

Practise interactively online:

* Practice Online — CBSE

Each worksheet contains 20 questions per level with a detailed answer key.

* AI Maths Solver — Stuck on a pattern question? Upload it and get a step-by-step solution.
* Spark Coach — AI tutor that gives hints, not answers, to help you think through patterns.
* Free Worksheets for All Classes — Worksheets from Class 1 to 10 across all boards.
* Play Mode for Class 1-4 — Game-based maths for younger siblings.

Continue your Class 6 maths journey:

* Numbers & Place Value Class 6 Worksheet
* Whole Numbers Class 6 Worksheet
* Number Play Class 6 Worksheet
* Prime Numbers & Factors Class 6 Worksheet
* Algebra & Simple Equations Class 6 Worksheet