Learning Objectives
You should be able to:
- Explain what a variable is.
- Explain what a constant is.
- Identify terms in an expression.
- Identify coefficients in simple algebraic expressions.
Introduction
This lesson develops Variables, Constants & Terms from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
🎬 See each part of an expression
Watch the coefficient, variable and constant take turns.
🤔 Let’s start with a simple idea
Imagine you are buying exercise books.
You do not know the price of one exercise book yet, so we call the price:
If you buy 3 exercise books, the cost is:
In this expression, the letter and the number each have a special name. Learning these names helps you understand Algebra more clearly.
🔤 What is a Variable?
A variable is a letter that represents a number we do not know yet, or a number that can change.
In Algebra, a letter is not there to confuse you. It simply stands for a value.
🔢 What is a Constant?
A constant is a number that does not change.
In the expression below:
x is the variable, because it can change. 5 is the constant, because it stays fixed.
📦 What is a Term?
A term is a single part of an algebraic expression. Terms are separated by plus or minus signs.
Look at this expression:
This expression has two terms:
- 3x
- 5
✖️ What is a Coefficient?
A coefficient is the number in front of a variable. It tells us how many of that variable we have.
In 4x, the coefficient is 4. It means we have 4 groups of x.
In 7y, the coefficient is 7.
🌍 Real-Life Example
Suppose one kombi trip costs x dollars.
If you take 5 trips, the total cost is:
- x is the variable.
- 5 is the coefficient.
- 5x is one term.
📝 Worked Examples
Example 1
Identify the variable and constant in:
Thinking...
The letter is the variable. The fixed number is the constant.
Constant: 8
Example 2
Identify the coefficient in:
Thinking...
The coefficient is the number in front of the variable.
Example 3
How many terms are in:
Thinking...
The plus sign separates the expression into parts.
Practice Questions
Answer the questions below.
- Identify the variable in n + 4.
- Identify the constant in x + 9.
- Identify the coefficient in 7a.
- How many terms are in 5x + 2?
- List the terms in 3y - 6.
✅ Show Answers
- n
- 9
- 7
- 2 terms
- 3y and -6
⭐ What You Can Do Now
- ✅ I know what a variable is.
- ✅ I know what a constant is.
- ✅ I can identify terms.
- ✅ I can identify coefficients.
🎉 Well Done!
You now understand the basic vocabulary of Algebra. These words will appear again and again, so this lesson is very important.
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
📈 Your Progress
Lesson 2 of 22
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Understand the meaning of each idea before selecting a method.
- Use definitions, properties and notation consistently.
- Show working and check that the final result is sensible.