Stage 4, Algebra & Equations

Module 2: Algebra & Equations

This module introduces students to the language of algebra and equips them with the skills to represent, manipulate, and solve problems using equations. It bridges arithmetic with abstract reasoning, helping learners see how algebra models real‑world situations.

1. Introduction to Variables & Algebraic Expressions

• Variables: Letters used to represent unknowns or quantities that can change.

• Expressions: Combinations of numbers, variables, and operations (e.g., 3x+2).

• Students learn to interpret and construct expressions from word problems.

• Outcome: Build fluency in recognising algebra as a generalised form of arithmetic.

2. Expanding & Simplifying Brackets

• Expansion: Applying distributive law, e.g., 2(x+3)=2x+6.

• Simplification: Combining like terms, e.g., 3x+5x=8x.

• Practice with single and double brackets.

• Outcome: Students develop skills to manipulate expressions into simpler or more useful forms.

3. Substitution & Evaluation

• Substituting values into expressions, e.g., if x=4, evaluate 2x+5.

• Applying substitution in formulas (geometry, physics, finance).

• Outcome: Students connect algebra to practical contexts by calculating with given values.

4. Solving Simple Linear Equations

• Step‑by‑step solving: balancing both sides, inverse operations.

• Equations with brackets and fractions.

• Checking solutions by substitution.

• Outcome: Students gain confidence in solving for unknowns, a skill essential for higher algebra.

5. Word Problems Using Algebra

• Translating everyday scenarios into algebraic equations.

• Examples:

  • “A number increased by 5 equals 12” → x+5=12.

  • “Twice a number minus 3 equals 7” → 2x−3=7.

• Applications: budgeting, distance‑speed‑time, age problems.

• Outcome: Students see algebra as a tool for modelling and solving real‑life problems.

Learning Outcomes

By the end of this module, students will:

• Understand variables and construct algebraic expressions.

• Expand and simplify expressions with accuracy.

• Substitute values into formulas and evaluate results.

• Solve simple linear equations systematically.

• Apply algebra to everyday word problems, strengthening problem‑solving skills.