🎯 What You Will Learn

• Ratio and equivalent ratios
• Unit rate
• Proportional relationships
• Scaling up and down
• Tables and graphs of proportional situations
• Real-life rate problems

📖 Chapter Explanation

This chapter develops proportional reasoning through situations in which two quantities change together. Students learn to distinguish a proportional relationship from a relationship that merely looks similar. Ratios, equivalent ratios, unit rates, scaling and direct variation are treated as connected ways of thinking about the same multiplicative relationship. Work through the chapter by first identifying the quantities or geometric objects involved, then finding the relationship between them. The aim is not merely to obtain an answer but to explain why the method is valid.

🧮 Worked Examples

🧠 Concept Check

🧩 Concept-Based MCQs

1. If 5 pens cost ₹50, the unit price is: A) ₹5 B) ₹10 C) ₹15 D) ₹20
2. Equivalent ratios are formed by multiplying both terms by: A) different numbers B) the same non-zero number C) zero only D) subtracting 1
3. If y is directly proportional to x, y/x is: A) constant B) always zero C) always 1 D) changing randomly
4. A recipe for 4 people uses 300 g rice. For 8 people, keeping the ratio unchanged, use: A) 450 g B) 500 g C) 600 g D) 900 g

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

📌 Competency-Based Case

A student solves routine questions correctly but gets confused when the same mathematical relationship is presented through a table, diagram or real-life situation. The task is to identify the underlying structure before choosing a method.

1. What quantities should be identified first?
2. What relationship connects them?
3. Which representation would make the relationship easiest to see?
4. Explain how you would check whether your answer is reasonable.

🔥 HOTS & Competition Corner

1. Find a statement from this chapter that is true only under a particular condition. State the condition.
2. Create a counterexample to a plausible but incorrect claim.
3. Design a real-life problem that requires the chapter’s main idea but does not state the method directly.
4. Explain a common mistake and show how to detect it before submitting an answer.

✍️ Exam-Ready Practice

1. Define the main concept in your own words.
2. Solve a direct application question with all steps.
3. Solve a word problem and explain the choice of method.
4. Justify one property or relationship.
5. Write a complete 5-mark solution with reasoning and conclusion.

🏆 Five-Level Mastery

🔁 One-Minute Revision

Concept → Representation → Rule/Relationship → Example → Reasoning → Application → Error Check.

✅ Mastery Checklist

• ☐ I can explain the concept without copying the textbook.
• ☐ I can solve routine and unfamiliar questions.
• ☐ I can represent the idea in more than one way.
• ☐ I can justify my method.
• ☐ I can identify and correct a common error.

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