Lesson Notes By Weeks and Term v4 - JHS 1

Lesson Video

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Performance objectives

• Define a variable and identify it in word problems.
• Translate simple word problems into linear equations.
• Solve linear equations that come from word problems.

Lesson summary

This lesson introduces a very powerful tool in mathematics: algebra. We will learn how to change everyday problems, like those you might encounter at the market, when sharing items with friends, or when dealing with mobile phone credit, into a mathematical language called an equation. This skill is like being a translator. Instead of translating from Twi to English, we are translating from a "story problem" into a "math problem". This is the first and most important step in using mathematics to solve real-world challenges.

Lesson notes

This topic is about building a bridge between words and mathematical symbols. Let's break down the parts we need. a. What is a Variable? A variable is a letter or symbol that represents an unknown number or a quantity that can change. Think of it as an empty box you need to find the value of. We commonly use letters like `x`, `y`, `a`, or `n`. Example: If we say "a certain number of mangoes," we don't know the exact number. So, we can let the letter `m` represent this unknown number of mangoes. b. What is an Algebraic Expression? An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables, and operators (+, -, ×, ÷). It does not have an equals sign. Example: "5 more than a certain number." If we let the number be `n`, the expression is `n + 5`. Example: "Twice the age of Yaw." If we let Yaw's age be `y`, the expression is `2 × y` or simply `2y`.

To translate words into expressions, we need to know the keywords for our mathematical operations:

| Operation | Keywords / Phrases | Example | Expression | | :--- | :--- | :--- | :--- | | Addition (+) | sum, plus, more than, increased by, total, added to | The sum of a number and 10 | `x + 10` | | Subtraction (-) | difference, minus, less than, decreased by, take away | A number decreased by 7 | `n - 7` | | Multiplication (×) | product, times, of, twice (×2), thrice (×3) | The product of 4 and a number | `4p` | | Division (÷) | quotient, divided by, shared among, per | A number divided by 3 | `y / 3` or `y ÷ 3` | c. What is an Equation? An equation is a mathematical statement that two expressions are equal. It always has an equals sign (=). Think of it like a perfectly balanced scale. Expression: `x + 5` (This is just a phrase) Equation: `x + 5 = 12` (This is a complete sentence stating that `x + 5` has the same value as `12`) d. The Step-by-Step Process for Translation

To translate a word problem into an equation, follow these four simple steps: