Chapter focus: Patterns help us notice regularity, describe rules, predict what comes next and connect numbers with shapes and diagrams. This page is an original study guide based on the chapter theme; it does not reproduce the NCERT textbook.

🎯 Learning Goals

• Recognise numerical and visual patterns.
• Describe how a pattern changes from one step to the next.
• Use a pattern rule to predict later terms.
• Represent patterns using tables, diagrams and expressions.
• Explain the reasoning behind an answer instead of only giving the answer.

📘 What Is a Pattern?

A pattern is a regular arrangement in which something changes according to a rule. The rule may involve adding, subtracting, multiplying, dividing, repeating shapes, changing positions or increasing the number of objects.

For example, in the sequence 4, 8, 12, 16, …, each term is obtained by adding 4 to the previous term.

🔢 1. Number Patterns

Increasing Patterns

An increasing pattern becomes larger according to a rule.

Sequence	Change	Next term
5, 10, 15, 20, …	+5	25
7, 14, 21, 28, …	+7	35
3, 6, 12, 24, …	×2	48

Decreasing Patterns

A decreasing pattern becomes smaller according to a rule.

60, 55, 50, 45, … follows the rule “subtract 5”. The next term is 40.

🔺 2. Visual and Shape Patterns

Patterns do not have to use numbers. A sequence of dots, matchsticks, tiles, colours or shapes can also follow a rule.

Suppose a design has 1 square in Step 1, 2 squares in Step 2 and 3 squares in Step 3. The number of squares increases by one at every step. The important task is not just to draw the next figure, but to explain the rule.

🧠 3. How to Find the Rule

1. Write the terms or draw the first few figures clearly.
2. Compare consecutive terms.
3. Look for a repeated change.
4. Test the suspected rule on more than one step.
5. Use the rule to predict the next term.
6. Explain the reasoning in a sentence.

📋 Worked Examples

Example 1 – Constant Addition

Question: Find the next two terms: 11, 15, 19, 23, …

Step 1: Compare consecutive terms: 15 − 11 = 4, 19 − 15 = 4, 23 − 19 = 4.

Step 2: The rule is add 4.

Answer: 27, 31.

Example 2 – Constant Multiplication

Question: Find the next two terms: 2, 6, 18, 54, …

Each term is multiplied by 3.

Answer: 162, 486.

Example 3 – Find a Missing Term

Question: 9, 13, __, 21, 25

The difference between consecutive terms is 4, so the missing term is 17.

🔍 Common Pattern Types to Know

Pattern type	Example	Rule
Addition	6, 10, 14, 18	+4
Subtraction	30, 25, 20, 15	−5
Multiplication	3, 9, 27, 81	×3
Division	64, 32, 16, 8	÷2
Alternating	2, 5, 4, 7, 6, 9	+3, −1 repeating

💡 Think Beyond the Next Number

A strong mathematics answer should be able to explain why a pattern continues. For a sequence such as 4, 8, 12, 16, …, saying “20” gives the result; saying “20 because 4 is added each time” gives the reasoning.

📝 Important Practice Questions

1. Find the next three terms: 12, 18, 24, 30, …
2. Find the next two terms: 5, 10, 20, 40, …
3. Find the missing number: 8, 12, __, 20, 24.
4. Describe the rule in the pattern 100, 90, 80, 70, …
5. Give one example of a pattern from daily life.
6. Can two different rules produce the same first three terms? Explain with an example.
7. Create a sequence in which each term increases by 7.
8. Create a visual pattern that grows by two shapes at every step.

🔥 Competency / HOTS Questions

1. A student says that 2, 4, 6, 8, … must always be a multiplication pattern. Do you agree? Explain.
2. Riya writes 3, 6, 12, 24 and says the rule is “add more each time.” Explain why a more precise rule is better.
3. Create two different sequences whose first three terms are 5, 10, 15. Explain how the later terms can differ.
4. A pattern increases by 4. Starting from 7, what will the 20th term be? Show your reasoning.

🧩 MCQ Practice

1. What is the next term in 7, 14, 21, 28, …?
   A. 32   B. 35   C. 36   D. 42
2. Which rule describes 50, 45, 40, 35, …?
   A. Add 5   B. Multiply by 5   C. Subtract 5   D. Divide by 5
3. What is the next term in 3, 9, 27, 81, …?
   A. 108   B. 162   C. 243   D. 324
4. Which action is most useful when identifying a number pattern?
   A. Guess immediately   B. Compare consecutive terms   C. Ignore earlier terms   D. Choose the largest number
5. A visual pattern can be represented using —
   A. only numbers   B. only words   C. shapes, diagrams or objects   D. only equations

Answer Key: 1-B, 2-C, 3-C, 4-B, 5-C

📄 Printable Worksheet

1. Complete: 15, 20, 25, __, __, __.
2. Complete: 81, 72, 63, __, __.
3. Complete: 4, 8, 16, 32, __, __.
4. Find the missing term: 6, 11, __, 21, 26.
5. Write the rule for 2, 5, 8, 11, 14.
6. Create a five-term pattern using subtraction.
7. Create a five-term pattern using multiplication.
8. Explain why checking more than one pair of terms is important.
9. Draw a simple growing shape pattern for four steps.
10. Write one real-life example of a repeating or growing pattern.

✅ Quick Revision Checklist

• ☐ I can explain what a pattern is.
• ☐ I can identify the rule between consecutive terms.
• ☐ I can complete missing terms.
• ☐ I can work with addition, subtraction, multiplication and division patterns.
• ☐ I can recognise visual patterns.
• ☐ I can explain the reasoning behind my answer.
• ☐ I can create my own pattern and describe its rule.

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