GRADE 6 · MATHEMATICS

Introduction to Algebraic Expressions

Algebra uses letters to represent numbers. These letters help us describe patterns and write general rules. Learn what variables, constants, coefficients and terms mean, then write and evaluate simple expressions.

Learning time: approximately 30 minutes · Beginner level

What You Will Learn

Understand variables, constants, coefficients and terms.
Translate simple words into algebraic expressions.
Evaluate an expression by substituting a value.
Identify and combine like terms.
Use algebra to describe simple patterns.

1. What Is Algebra?

Algebra is a part of mathematics that uses letters and symbols to represent numbers and relationships. A letter such as x can stand for a number that is not yet known or for a number that can change.

x + 5

This expression means “a number plus five”. If x is 3, the value is 3 + 5 = 8.

2. Variables, Constants and Coefficients

Variable: a letter that represents a number, such as x or n.
Constant: a fixed number, such as 7 in x + 7.
Coefficient: the number multiplying a variable. In 4x, the coefficient is 4.

Example: In 6a + 9, the variable is a, the coefficient is 6 and the constant is 9.

If a variable appears without a written coefficient, its coefficient is 1. For example, x means 1x.

3. Understand Terms

Terms are parts of an expression separated by addition or subtraction signs.

In 3x + 5, the terms are 3x and 5.
In 7a − 2b + 4, the terms are 7a, −2b and 4.

Sign matters: In 7a − 2b + 4, the second term is −2b, not just 2b.

4. Write Expressions from Words

Words	Expression
A number plus 6	x + 6
Five times a number	5n
A number decreased by 4	y − 4
Twice a number plus 3	2a + 3
A number divided by 7	m ÷ 7 or m/7

Be careful with order: “4 less than a number” means x − 4, not 4 − x.

5. Evaluate an Expression

To evaluate an expression, replace the variable with the given number and calculate using the correct order of operations.

Worked example: Find 3x + 2 when x = 4

Replace x with 4: 3 × 4 + 2.
Multiply first: 12 + 2.
Add: 14.

Another example: Find 2a − 5 when a = 6

2 × 6 − 5 = 12 − 5 = 7.

6. Combine Like Terms

Like terms have the same variable raised to the same power. At this level, focus on terms with the same letter. You can add or subtract their coefficients.

Example: 3x + 2x = 5x because there are 3 x's plus 2 more x's.

4a + 3a = 7a.
8y − 5y = 3y.
2x + 4 + 3x = 5x + 4.

Unlike terms cannot be combined: 3x + 2y cannot be simplified to 5xy or 5x. The variables are different.

7. Describe a Pattern with Algebra

Suppose a pattern starts with 4 tiles and adds 3 tiles each time. If n is the step number, the number of tiles is described by 3n + 1.

Step (n)	Calculation	Tiles
1	3 × 1 + 1	4
2	3 × 2 + 1	7
3	3 × 3 + 1	10
4	3 × 4 + 1	13

8. Common Mistakes to Avoid

Confusing multiplication and addition: 4x means 4 multiplied by x, not 4 + x.

Ignoring the order in a phrase: “5 less than x” is x − 5.

Combining unlike terms: 2x + 3y cannot be combined into 5xy.

Forgetting substitution brackets: When substituting a negative number, use brackets to keep the calculation clear.

9. Practice Exercises

Try these before revealing the answers.

In 5x + 8, identify the variable, coefficient and constant.
Write “7 more than a number n” as an expression.
Write “three times a number y, decreased by 2” as an expression.
Evaluate 4x + 1 when x = 3.
Evaluate 2a − 5 when a = 8.
Simplify 3x + 4x.
Simplify 6y − 2y + 5.
Can 2a + 3b be combined? Explain.

Show practice answers and explanations

Variable x; coefficient 5; constant 8.
n + 7.
3y − 2.
4 × 3 + 1 = 13.
2 × 8 − 5 = 11.
7x.
4y + 5.
No. The terms have different variables, so they are unlike terms.

11. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

Learnora — Grade 6 Mathematics

Algebraic Expressions Worksheet

Name: __________________________ Date: _______________

Instructions: Write expressions clearly and show your working.

In 9m + 6, identify the variable, coefficient and constant.
Write “a number t increased by 8” as an expression.
Write “four times p, then add 5” as an expression.
Evaluate 5x − 2 when x = 4.
Evaluate 3a + 1 when a = 7.
Simplify 6y + 2y − 3.
Explain why 2a + 5b cannot be combined into one term.

Keep practising — you are making progress!

Learnora — Learn Better. Practice Smarter.

Teacher / Parent Answer Key

Variable m; coefficient 9; constant 6.
t + 8.
4p + 5.
5 × 4 − 2 = 18.
3 × 7 + 1 = 22.
8y − 3.
They have different variables and are unlike terms.

12. Lesson Summary

Variables are letters that represent numbers.
Constants are fixed numbers; coefficients multiply variables.
Terms are separated by addition or subtraction signs.
Evaluate expressions by substituting values and following operation rules.
Combine like terms by adding or subtracting their coefficients.

Next learning goal: Use algebraic expressions to understand simple equations and solve for an unknown number.

Educational note: This is a curriculum-neutral Grade 6 lesson. Teachers and parents can adapt examples and practice to their local curriculum.