Lesson Notes By Weeks and Term v4 - JHS 1

Lesson Video

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Performance objectives

• Define and identify components of an algebraic expression.
• Create simple expressions from words.
• Simplify expressions by combining like terms.
• Evaluate expressions for given values.

Lesson summary

This lesson introduces the foundational concept of algebraic expressions. We will learn how to translate everyday language and situations into the language of mathematics using letters and symbols. This skill is very important because it helps us solve problems in real life, from calculating costs at the market to understanding business profits and planning our finances. Think of it as learning a new, powerful language to describe the world around us. For example, if you know the price of one egg, how can you write down the cost for *any* number of eggs you decide to buy? Algebra helps us do that!

Lesson notes

This topic is like learning a new code. We use letters to represent numbers we don't know yet, and then we combine them with numbers we *do* know using familiar math signs. a) What is a Variable? A variable is a letter or symbol that represents an unknown or changing quantity. We often use letters like `x`, `y`, `a`, or `n`. Example: If we say "Kofi has *some* mangoes," we don't know the exact number. We can use the variable `m` to represent the number of mangoes Kofi has. If he gets more mangoes, the value of `m` changes. b) What is a Constant? A constant is a fixed number that does not change. Example: In the phrase "5 more than a number," the number `5` is a constant because it will always be 5. c) What is an Algebraic Expression? An algebraic expression is a mathematical phrase that combines variables, constants, and mathematical operations (+, −, ×, ÷). Key Feature: An algebraic expression does not have an equals sign (=). It is a phrase, not a full sentence. Examples: `x + 5` (An unknown number plus five) `2y - 3` (Two times an unknown number, then subtract three) `8p` (Eight multiplied by an unknown number, p. Note: When a number and a variable are next to each other, it means multiplication). `c / 4` (An unknown number divided by four) d) Translating Words into Operations To create expressions, we need to know the "code words" for each mathematical operation.

| Operation | Keywords / Phrases | Example Phrase | Algebraic Expression | | :--- | :--- | :--- | :--- | | Addition (+) | sum, plus, more than, increased by, total, added to | The sum of a number `n` and 7 | `n + 7` | | Subtraction (−) | difference, minus, less than, decreased by, take away, reduced by | 10 less than a number `y` | `y - 10` (Be careful! "Less than" reverses the order) | | Multiplication (×) | product, times, of, multiplied by | The product of 4 and a number `k` | `4k` | | Division (÷) | quotient, divided by, shared among, per | An amount `a` shared among 5 people | `a / 5` or `a/5` |

Worked Examples (Step-by-Step)

Example 1: A Simple Situation Ama has a basket with some oranges. Let's use the variable `o` to represent the number of oranges. Her mother gives her 3 more oranges. Write an expression for the new number of oranges Ama has. Step 1: Identify the unknown. The starting number of oranges is unknown. We represent it with the variable `o`. Step 2: Identify the operation. The keyword is "more," which means we need to add. Step 3: Identify the constant. The constant is `3`. Step 4: Combine them. The expression is `o + 3`.