Understanding Percentages

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Overview

🎯 Lesson Duration: 60 minutes
🎯 Year Level: Year 6
🎯 Learning Area: Mathematics
🎯 Curriculum Reference:
ACMNA131 – Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies.

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Learning Intentions

By the end of this lesson, students will:

• Understand that a percentage is a number out of 100.
• Convert simple fractions and decimals to percentages.
• Calculate common percentages (10%, 25%, 50%, 75%) of whole numbers.
• Apply percentage concepts in real-life, relatable contexts.

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Success Criteria

Students will be successful when they can:

• Explain in their own words what a percentage is.
• Accurately convert between fractions, decimals, and percentages.
• Solve percentage problems involving sale items or population data.
• Participate and contribute positively in collaborative task work.

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Materials Required

🔸 Mini whiteboards and markers
🔸 Paper shopping catalogues/magazines with prices (or printed online versions)
🔸 Scissors and glue
🔸 Student maths books
🔸 Printed “Discount Detective” worksheet
🔸 Calculators (optional for checking)
🔸 Classroom smartboard
🔸 Timer or stopwatch

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Lesson Structure – 60 Minutes

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⏱ 1. Warm-Up (10 minutes) – Percent Hunt: What’s 100?

Activity:
Pose a quick-fire brainstorm:
🗣️ "Where have you seen percentages in real life?"

Write down responses on the board in a mind map format. Likely answers include:

• Discounts in stores (e.g., "50% off!")
• Battery life on a phone
• Test results ("You got 85%!")
• Weather chance of rain
• Sports statistics

Mini Discussion Prompt:
Ask: "If we say 25% of something, what do we mean? What number is always involved in a percentage?"

Collect ideas. Use fraction models or pie charts on the board to reinforce the concept that percent means ‘per hundred’.

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⏱ 2. Explicit Teaching (15 minutes) – What Are Percentages?

Using smartboard visuals or big printable diagrams:

1. Introduce the Definition: A percentage is a fraction out of 100.

2. Show visual representations of:

   • 25% as a quarter
   • 50% as a half
   • 10% as one tenth
   • 75% as three quarters

3. Link between fractions, decimals, and percentages:

   • ½ = 0.5 = 50%
   • ¼ = 0.25 = 25%
   • etc.

4. Model real-world problems:
   “What is 50% of $20?”
   “If a $60 jacket has a 25% discount, what’s the price?”

📌 Strategy Reminder: Model using both mental strategies (partitioning, doubling, halving) and written methods.

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⏱ 3. Guided Practice (15 minutes) – "Discount Detective" Game

Task:
Students in pairs receive shopping catalogues and are given a “Discount Detective” worksheet.

They choose 5–6 items and calculate discounts of:

• 10%
• 25%
• 50%

✂️ They cut out the items, write the original price, calculate the discount and discounted price, and stick onto their worksheet.

Example:
Sneakers - Original Price: $80 - 25% off = $20 discount - New Price: $60

Teacher roves to support and check strategies – look for misconceptions, especially with place value (e.g., 10% of $60 is not $6.00, not $0.60).

Encourage mental strategies first – calculators can be used to confirm answers.

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⏱ 4. Collaborative Activity (10 minutes) – Percentage Treasure Hunt

Outdoor / Around Classroom Movement Activity

Create mini cards with percentage problems and hide around the room.
Example cards:

• “You found a $100 bike. It's 50% off. What's the discounted price?”
• “A football used to be $40. It has a 25% discount. What’s the new price?”

Students move in pairs, with clipboard and record sheet, solving each problem they find.

This provides kinesthetic learning and helps engage energetic learners.

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⏱ 5. Reflection & Plenary (10 minutes)

Class Discussion Prompts:

• “What strategies helped you most when working out percentages today?”
• “Where might you use percentages in your life outside of maths class?”

Use the ‘Think-Pair-Share’ structure for quick peer discussion before whole-class share.

Finally, students complete a quick exit ticket:

✏️ "One thing I learned about percentages today is..."

Collect these to assess understanding and plan for next lesson.

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Differentiation

For support learners:

• Use visual aids such as pie models and base-10 blocks.
• Provide fraction-to-percentage conversion cards for reference.
• Work in mixed-ability pairs during guided task.

For extension students:

• Challenge to calculate 15%, 30%, or 70% of amounts.
• Include problems that require working backwards (e.g., “If the sale price is $75 after 25% off, what was the original price?”).
• Introduce problems involving GST (10%) and real-world budgeting.

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Assessment

• Formative observation during the guided task and treasure hunt.
• Exit tickets to check each student’s takeaway understanding.
• "Discount Detective" worksheets – review strategies and accuracy.
• Oral contributions during reflections.

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Cross-Curricular Links

• Economics & Business – Making smart spending decisions.
• Digital Technologies – Using online shops or apps to calculate savings.
• Health & PE – Using sports and fitness data expressed as percentages.

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Teacher Reflection (Post-Lesson)

• Which strategies did students grasp most easily?
• Were misconceptions identified and addressed?
• Who needs consolidation or extension in the following lesson?

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Extension Opportunities / Homework

Optional task:
Ask students to go home and find an example of a percentage discount (e.g., from a shop, label, ad). Bring it in to share for the "Maths in Real Life" wall.

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👩‍🏫 This lesson balances explicit instruction and real-world application to ensure deep understanding of percentages – a core numeracy skill for secondary success and daily life.