Lesson Notes By Weeks and Term v4 - SHS 1

Lesson Video

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Performance objectives

• Translate word problems into linear equations.
• Set up and solve systems of linear equations.
• Apply algebra to solve real-life problems.

Lesson summary

This lesson focuses on a powerful mathematical skill: mathematical modelling. We will learn how to translate everyday problems, described in words, into the language of algebra. Specifically, we will take word problems from our Ghanaian context—like buying items at the market, calculating farm yields, or managing a small business—and turn them into a system of two linear equations. By solving these equations simultaneously, we can find precise answers to real-world questions. This skill is not just for passing exams; it is a fundamental tool for critical thinking and problem-solving in business, science, engineering, and even personal finance.

Lesson notes

A. What is Mathematical Modelling?

Think of it as being a translator. You take a "story" written in English (a word problem) and translate it into the language of "mathematics" (equations). Real-World Problem: E.g., "Kofi bought two pens and one exercise book for GHS 5. Adwoa bought one pen and two exercise books for GHS 4. What is the cost of one pen and one exercise book?" Mathematical Model: This is the set of equations that represents the problem. Let `p` be the cost of a pen. Let `e` be the cost of an exercise book. Kofi's purchase: `2p + e = 5` Adwoa's purchase: `p + 2e = 4` Mathematical Solution: We solve these equations to find the values of `p` and `e`. Real-World Interpretation: We state the final answer in words: "The cost of one pen is GHS 2, and the cost of one exercise book is GHS 1." B. A 5-Step Framework for Solving Word Problems

To succeed, we will follow a structured approach. Always use these five steps: READ & UNDERSTAND: Read the problem carefully, more than once. Identify what you are given and what you need to find. DEFINE VARIABLES: Assign letters (like `x`, `y`, `p`, `c`) to represent the unknown quantities. Clearly state what each variable represents. E.g., "Let `x` be the number of goats." TRANSLATE & FORMULATE EQUATIONS: Convert the sentences in the problem into mathematical equations. Look for keywords: 'is', 'are', 'was', 'were' often mean `=` 'sum', 'altogether', 'more than' often mean `+` 'difference', 'less than' often mean `-` 'product', 'of' often mean `×` 'per', 'divided by' often mean `÷` SOLVE THE SYSTEM: Use an algebraic method (Elimination or Substitution) to find the values of your variables. CHECK & INTERPRET: Substitute your answers back into the original word problem (not just your equations) to see if they make sense. Write your final answer as a clear sentence. C. Methods for Solving Systems of Linear Equations

Let's review the two main algebraic methods.

Evaluation guide

• Recognise and model statements into linear mathematical equations and solve them
• simultaneously.
• reasoning