Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

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Performance objectives

• Identify patterns in financial sequences.
• Model real-life financial problems using algebra.
• Calculate savings and earnings using arithmetic and geometric sequences.
• Apply mathematical reasoning to solve financial problems.

Lesson summary

This lesson bridges the gap between abstract mathematical sequences and the real world of money that learners interact with daily. We will explore how to use the principles of Arithmetic and Geometric Progressions to understand, plan, and solve problems related to savings, investments, salaries, and depreciation. Understanding this helps in making wise financial decisions for the future, whether it's saving for university, starting a small business, or simply managing personal finances. A key value we will also touch on is the importance of honesty and discipline in handling money.

Lesson notes

Introduction (5 minutes) Teacher: "Good morning, class. Imagine you start a small `susu` saving plan. In the first month, you save GHC 20. You decide to increase your savings by a fixed GHC 5 every month. How much will you save in the 12th month? Now, imagine your friend gets a job where their salary increases by 10% every year. Are these two situations the same? Today, we will learn the mathematics to answer these questions and many more related to money." Recap of Key Formulas (10 minutes) Before we apply these to finance, let's quickly remember our tools.

| Progression Type | Key Idea | Formula for nth term (`U_n`) | Formula for Sum of n terms (`S_n`) | | :--- | :--- | :--- | :--- | | Arithmetic (AP) | A constant amount (d) is added to each term. | `U_n = a + (n - 1)d` | `S_n = n/2 * [2a + (n - 1)d]` | | Geometric (GP) | Each term is multiplied by a constant ratio (r). | `U_n = a * r^(n-1)` | `S_n = a * (r^n - 1) / (r - 1)` (for r > 1) |

Where: `a` = First term (initial amount) `d` = Common difference (fixed amount added/subtracted) `r` = Common ratio (multiplier) `n` = Number of terms (years, months, etc.) Identifying the Correct Progression in Financial Problems (15 minutes) This is the most important skill for this topic. When is it an Arithmetic Progression (AP)? When the value changes by a fixed amount per period. Keywords: "increases by GHC 50 each year," "fixed annual increment," "simple interest," "depreciates by a constant GHC 200." When is it a Geometric Progression (GP)? When the value changes by a fixed percentage (%) or factor per period. Keywords: "increases by 5% annually," "compounded interest," "grows by a factor of 1.1," "depreciates by 15% per year."

Crucial Calculation for GP: For a percentage *increase* of P%, the common ratio `r = 1 + (P/100)`. Example: A 5% increase means `r = 1 + (5/100) = 1 + 0.05 = 1.05`. For a percentage *decrease* (depreciation) of P%, the common ratio `r = 1 - (P/100)`. Example: A 10% depreciation means `r = 1 - (10/100) = 1 - 0.10 = 0.90`.

Evaluation guide

• Analyse, model, and solve real -life problems involving financial mathematics.
• Put learners in convenient groups and engage them to analyse and model real-life problems of a
• sequence involving finances. Initiate conversation on the need to be honest in handling money at home
• and in school.

Reference guide

• : Whiteboard, markers, calculator, charts showing AP/GP formulas, prepared word problems.
• Prerequisite Knowledge: Learners can identify and find the terms of Arithmetic and Geometric Progressions (AP & GP). They can also calculate the sum of the first 'n' terms of AP and GP.
• Core Competencies: Critical Thinking and Problem Solving, Personal Development and Leadership (Financial Literacy), Communication and Collaboration.
• Overview and Learning Objectives
• Overview:
• This lesson bridges the gap between abstract mathematical sequences and the real world of money that learners interact with daily. We will explore how to use the principles of Arithmetic and Geometric Progressions to understand, plan, and solve problems related to savings, investments, salaries, and depreciation. Understanding this helps in making wise financial decisions for the future, whether it's saving for university, starting a small business, or simply managing personal finances. A key value we will also touch on is the importance of honesty and discipline in handling money.