Lesson 1: Formulating and Evaluating Algebraic Expressions

👨🏽‍🏫 Introduction

Imagine you are at a fruit stand. Apples cost ₵2 each. If you buy x apples, how much will you spend? You could say “2 multiplied by x,” which we write in algebra as .

This is a simple example of an algebraic expression — a way of describing calculations using letters and numbers. Algebra helps us model real-world problems, from shopping and budgeting to calculating distances, areas, and time.

In this lesson, we’ll learn how to:

• Recognize the parts of an algebraic expression
• Write expressions from word problems
• Substitute values into expressions
• Evaluate expressions to find answers

🧠 Key Concepts

📌 1. What Is an Algebraic Expression?

An algebraic expression is a combination of:

• Variables (letters like x or y)
• Numbers (like 2, 5, 10)
• Operators (such as +, −, ×, ÷)

Unlike an equation, an expression does not have an equal sign (=). It’s like a “math phrase,” not a full “math sentence.”

Examples of expressions:

• → 3 times a number plus 5
• → a squared minus 4 times a plus 7
• → two-thirds of y plus 1

📐 2. Terms, Coefficients, and Variables

Let’s break down the parts of an expression:

• Variable: A symbol (usually a letter) that stands for an unknown number. Example: x
• Coefficient: A number multiplied by the variable. Example: In , 4 is the coefficient
• Term: A part of the expression. In , the terms are , , and
• Constant: A fixed number (no variable attached), like 5 or -3

📝 3. Formulating Expressions from Word Problems

This means turning words or real-world scenarios into algebra. Here are some useful patterns:

• “A number increased by 5” →
• “Twice a number minus 3” →
• “The cost of n oranges at ₵2 each” →
• “Half of a number, increased by 4” →

Tip: Choose a variable (usually x, y, or n) to represent the unknown.

🔢 4. Substituting and Evaluating Expressions

Substitution means replacing the variable with a specific number.

Evaluation means calculating the result after substitution.

Steps:

1. Identify the expression and the value to substitute
2. Replace the variable with the given number
3. Follow order of operations (BODMAS: Brackets, Orders, Division/Multiplication, Addition/Subtraction)

Example:
If , evaluate :
Substitute:

🧮 Sample Problem Walkthroughs

1. Formulate: “A number multiplied by 4, then 6 is added.”
   Let the number be x.
   Multiply by 4: .
   Add 6: .
   Final expression:
2. Evaluate: when
   Step 1: Replace x with 5 →
   Step 2: Multiply →
   Answer: 13
3. Formulate: “The total cost of t tickets at ₵12 each, plus a service fee of ₵5.”
   Cost of t tickets =
   Add service fee:
4. Evaluate: when
   Step 1: Replace y →
   Step 2: Add →
   Answer: 2
5. Evaluate: when
   Step 1: Replace a →
   Step 2: Simplify →
   Answer: 4

✍🏽 Practice Exercises

🅰️ A. Formulate Expressions

1. Four times a number added to 9
2. The cost of x pencils at ₵1.50 each
3. A number squared minus twice the number

🅱️ B. Substitute and Evaluate

1. Evaluate when
2. Evaluate when
3. Evaluate when

✅ Answers and Explanations

• A1:
• A2:
• A3:

• B1:
• B2:
• B3:

📌 Recap

• ✅ Algebraic expressions use numbers, variables, and operation signs
• ✅ You can translate real-life situations into expressions
• ✅ To evaluate expressions, substitute values for the variables and simplify using BODMAS

💭 Reflection Prompt

Can you think of a real situation where you calculate something repeatedly — like the cost of multiple items, or steps taken per day? Try writing it as an expression using a variable. For example: “If I take x steps daily, then in 7 days, I’ll take steps.”