Grade 12 Mathematical Literacy: Finance – Hire Purchase & Loan Calculations (Exam Revision) – Week 4 Term 4

1. Hire Purchase

A payment system where goods (furniture, appliances, vehicles) are purchased using a long-term lease agreement. The buyer pays a deposit and then makes regular monthly instalments until the full price plus interest is paid.

2. Deposit

An upfront payment made to reduce the loan amount. For example, if a car costs R115,495 and you pay a R17,324 deposit, you only need to borrow R98,171. The deposit is subtracted from the purchase price.

3. Balloon Payment / Residual

A large lump sum payment due at the end of a balloon loan. This payment is higher than regular monthly instalments but can result in lower total interest. Often used in car financing.

4. Initiation Fee

A once-off fee charged by the lender to process a loan application. By law, this cannot exceed 15% of the principal debt for microloans. This fee is added to the total amount to be repaid.

5. Principal Debt / Loan Amount

The original amount borrowed, excluding interest and fees. This is the base amount on which interest is calculated. Formula: Principal = Purchase Price – Deposit

6. Interest Rate (p.a. compounded monthly)

“Per annum” means yearly. When compounded monthly, the annual rate is divided by 12 to get the monthly rate. Example: 6.41% p.a. = 6.41 ÷ 12 = 0.534% per month.

Hook Activity: “Finance in Real Life”

Present learners with a realistic scenario: “You’ve just finished matric and want to buy your first car for R150,000. You have R20,000 saved. Should you take a 3-year loan or a 5-year loan? Why?” Allow 2-3 learners to share their thinking – no right/wrong answers yet.

Exam Context Setting (3 minutes):

• Display on board: “Finance = 30-40 marks in Paper 1 + 20-30 marks in Paper 2 = Up to 70 marks total!”
• Emphasize that mastering finance calculations can secure nearly 25% of their final exam marks
• Show breakdown: “Today we focus on hire purchase and loans – worth approximately 15-25 marks per paper”

Prior Knowledge Check (4 minutes):

Quick oral questions (hands up):

• “If a TV costs R5,000 and you pay a 10% deposit, how much deposit do you pay?” [R500]
• “If you borrow R10,000 at 12% interest for 1 year, how much interest do you pay?” [R1,200]
• “What’s 8.5% divided by 12?” [0.708%] – emphasize converting annual to monthly rates

Lesson Objectives (1 minute):

Share objectives on board: “By the end of this lesson, you will confidently solve hire purchase problems and know exactly what examiners are looking for.”

PART 1: Direct Instruction – Key Concepts & Formulas (12 minutes)

Teacher Explanation with Worked Example (8 minutes):

PART 2: Guided Practice – Work Together (12 minutes)

PART 3: Independent Practice – Exam-Style Questions (16 minutes)

After 12 minutes: Review answers together (4 minutes). Select 2-3 learners to share their solutions on the board. Highlight correct methods and discuss any errors.

Consolidation Activity: Exam Strategy Session (5 minutes)

Exit Ticket: Quick Self-Assessment (3 minutes)

Learners complete individually on scrap paper (hand in before leaving):

1. A car costs R200,000. You pay a R30,000 deposit. What is your loan amount? [R170,000]
2. You borrow R10,000. After repaying everything, you paid R13,500 total. How much was the interest? [R3,500]
3. True or False: A longer loan term (more months) means you pay more interest overall. [TRUE]
4. On a scale of 1-5, how confident do you feel about solving hire purchase problems in the exam? [Self-reflection]

Closing & Preview (2 minutes)

“Excellent work today! You now have the tools to tackle finance questions confidently. Remember: practice makes permanent – complete your homework and review past papers. Next lesson: Data Handling revision – bring calculators and your minds ready for statistics!”

📝 Formative Assessment

• Oral questioning: Monitor responses during prior knowledge check – identify learners struggling with basic calculations
• Observation during guided practice: Circulate and observe learner methods, note common errors for immediate correction
• Exit ticket analysis: Quick review of exit tickets identifies who needs additional support
• Individual work monitoring: Check progress during independent practice, provide targeted intervention

📋 Summative Assessment

• Independent practice question [16 marks]: NSC-style question assesses application of all concepts taught
• Homework assignment [20 marks]: Past paper questions for consolidation
• Criteria for mastery: 70%+ on independent practice = exam-ready; 50-69% = needs more practice; <50% = requires intervention

🤝 For learners who need support:

• Formula reference cards: Provide printed cards with all formulas during independent work
• Worked example templates: Give partially completed solutions where learners fill in numbers
• Peer buddying: Pair with stronger learners for guided practice section
• Calculator support: Review calculator functions (percentage key, memory functions)
• Simplified questions: Start with 2-step problems before moving to complex multi-step questions
• Extra time: Allow additional 5 minutes for independent practice if needed
• Visual aids: Use color-coded steps (Step 1 in blue, Step 2 in green, etc.)

🚀 For advanced learners:

• Extension questions: Provide Paper 2 level unfamiliar context questions (Level 3-4 taxonomy)
• Comparative analysis: “Compare 3-year vs 5-year loan options – which is better and why?”
• Create own questions: Design a hire purchase question with memo for peers
• Financial advice task: “Write a 1-page advice document: Should young people avoid loans?”
• Balloon payment investigations: Research and explain when balloon payments are beneficial
• Peer teaching: Assist struggling learners during consolidation
• Challenge problem: Multi-part question involving loan comparison with inflation considerations

♿ For learners with barriers:

• Bilingual support: Key terms translated to home language (isiZulu/isiXhosa/Afrikaans)
• Assistive technology: Allow calculator with larger display, reading pen if available
• Modified assessment: Same concepts but with smaller numbers or fewer steps
• Step-by-step guides: Laminated cards showing exact procedure for each question type
• Oral explanation option: Allow learners to explain method verbally if writing is barrier
• Reduce cognitive load: Break complex questions into separate sub-questions
• Clear workspace: Remove distractions, provide quiet area for independent work

✅ What worked well:

[Teacher to complete after lesson]

Reflection prompts:

• Did learners engage with the real-world hook activity?
• Were the worked examples clear and effective?
• What percentage of learners could complete independent work successfully?
• Did the exam tips resonate with learners?

🔧 What could be improved:

[Teacher to complete after lesson]

Reflection prompts:

• Which concepts required more explanation than anticipated?
• Did timing work as planned or did sections run over?
• Which learners struggled and need follow-up support?
• Were differentiation strategies effective?

📝 Notes for next lesson:

[Teacher to complete after lesson]

Consider:

• Concepts that need re-teaching or reinforcement
• Learners requiring individual intervention
• Adjustments needed for Data Handling lesson (next topic)
• Exit ticket analysis – overall class performance