Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

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Performance objectives

• Define simultaneous linear equations.
• Model real-life problems using simultaneous equations.
• Solve equations using substitution and elimination methods.
• Analyse and interpret solutions in context.

Lesson summary

This lesson focuses on translating real-life word problems into a pair of linear equations (simultaneous equations) and solving them to find a meaningful solution. Many situations in our daily lives, from buying items at the market to calculating ages or understanding business profits, involve more than one unknown quantity. This lesson equips learners with the algebraic skills to model these situations mathematically and find concrete answers. It moves beyond just solving equations to understanding where those equations come from and what the solutions mean in a real Ghanaian context.

Lesson notes

A. Introduction: From Words to Mathematics

A "word problem" is a real-life situation described in sentences. Our goal is to convert these sentences into the language of algebra. A system of simultaneous linear equations is a set of two or more linear equations that share the same variables. To solve a word problem with two unknown quantities, we need two pieces of information, which will give us two equations.

The Four-Step Process: Understand & Define: Read the problem carefully. Identify what you are being asked to find. These are your unknown quantities. Assign variables (like `x` and `y`, or more descriptive letters like `a` for age or `c` for cost) to represent them. Model (Translate): Read the problem again, sentence by sentence. Translate the relationships described into mathematical equations. Keywords are important: "Sum", "total", "altogether" often mean addition (+). "Difference", "more than", "less than" often mean subtraction (-). "Times", "product of" often mean multiplication (*). "Is", "are", "was", "will be" often mean equals (=). Solve: Use an appropriate algebraic method to solve the system of equations you have created. We will focus on two methods: Elimination and Substitution. Interpret & Check: State your answer clearly in a sentence. Does the answer make sense? For example, age cannot be negative. Substitute your values back into the original equations or the word problem to ensure they are correct. B. Method 1: The Elimination Method

This method works best when the coefficients of one variable in both equations are the same or are opposites (additive inverses, e.g., +3y and -3y). The goal is to "eliminate" one variable by adding or subtracting the two equations.

Evaluation guide

• Analyse, model, and solve word problems of simultaneous linear equations involving
• numbers , age, etc.
• Using Talk for Learning strategy , review with the whole class the concept of linear equations
• involving word problems.