Percentage Decrease

Curriculum Area

The New Zealand Curriculum – Mathematics and Statistics

• Strand: Number and Algebra
• Achievement Objective (Level 5): Use appropriate methods to solve problems involving percentages and rates.

Lesson Overview

In this 50-minute lesson, Year 10 students will develop a deep understanding of percentage decrease through real-world scenarios and interactive activities. They will use mental strategies, calculators, and collaborative problem-solving to apply their learning.

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Lesson Plan Breakdown

1. Introduction & Warm-Up (10 minutes)

Objective: Activate prior knowledge and set the stage for learning.

• Quick Discussion (3 mins): Ask students: “When have you seen things decrease in percentage?” (e.g., sales in shops, discounts, weight loss, population decline).
• Warm-Up Exercise (7 mins):
  • Display three quick-fire percentage decrease problems where students use mental calculations.
  • Example: An item originally costing $120 is now discounted by 25%. What is the new price?
  • Think-Pair-Share: Students calculate individually, compare with a partner, then share strategies as a class.

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2. Concept Exploration (15 minutes)

Objective: Develop a clear understanding of percentage decrease with a structured method.

• Teacher explicitly teaches the step-by-step method for percentage decrease using the formula:
  [ \text{New Value} = \text{Original Value} \times (1 - \frac{\text{percentage decrease}}{100}) ]
• Example Problem (5 mins): A laptop was originally priced at $2,500 and is now reduced by 30%. What is the new price?
  • Break it down step by step.
  • Show multiple methods:
    • Using fractions: 30% = 3/10, so subtracting 3/10 of 2500.
    • Using decimal multipliers: ( 2500 \times 0.7 )
• Class Discussion (5 mins): Ask students which method they found easiest and why.
• Mini Quiz (5 mins): 3 quick questions on percentage decrease to check immediate understanding—students answer on mini whiteboards for instant feedback.

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3. Real-World Application: The Shopping Challenge (15 minutes)

Objective: Apply percentage decrease to real-life scenarios.

Activity: New Zealand Shopping Discounts!

• Students are placed into pairs and given a catalogue of mock store prices with discounts (e.g., Noel Leeming, The Warehouse, Pak’nSave).
• Each pair gets a budget of $500 and must choose three items, calculating the discounted price and seeing if they can afford them.
• Challenge Element: If students finish early, they're given a mystery “extra discount” card (e.g., an additional 15% off all items). They must recalculate their total.
• Share findings as a class: Did anyone have money left over? What discounts were the biggest? Was their budget strategy effective?

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4. Reflection & Wrap-Up (10 minutes)

Objective: Consolidate learning and address misconceptions.

• Exit Ticket Activity (5 mins):
  • Slide with a new problem: “A jacket’s price dropped from $180 to $135. What percentage decrease is this?”
  • Students must write the solution on a sticky note and place it on the board as they leave.
• Peer Explanation (3 mins): Select a few students to explain their methods to the class.
• Teacher Summary (2 mins): Recap key takeaways and preview tomorrow’s lesson (e.g., reverse percentage problems—finding the original price before a discount).

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Differentiation Strategies

• For struggling students: Use visual aids (bar diagrams) to illustrate percentage decrease step by step.
• For advanced students: Introduce reverse problems (e.g., “An item costs $72 after a 40% discount; what was the original price?”).

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Assessment & Homework

• Formative Assessment: Observation during activities, mini quiz, and exit ticket.
• Homework: Students find a real-life example of a percentage decrease in a store flyer or ad and calculate the new price of at least 2 items.

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Teacher Reflection After Lesson

• What worked well?
• Did all students grasp the concept?
• What would I adjust for next time?

This lesson aims to make percentage decrease meaningful, engaging, and relevant to students’ lives. The combination of structured explanations, collaborative work, and real-life application ensures deep understanding. 🚀