- 1. The Balance Model
Understand that equations act like balanced scales. Apply the "Golden Rule of Algebra" by recognising that any operation applied to one side of an equation must be applied equally to the other side to maintain balance.
- 2. Solving Using Number Facts
Use known number facts to find the value of unknown numbers. Transition from using visual box notation (□) to algebraic letters (variables) to represent unknowns.
- 3. Solving with Addition and Subtraction
Systematically solve one-step equations involving addition and subtraction ($x + a = b$ and $x - a = b$) by using inverse operations and the balance method, including equations with negative numbers.
- 4. Solving with Multiplication and Division
Systematically solve one-step equations involving multiplication and division ($ax=b$ and $\frac{x}{a}=b$) using inverse operations. Normalise non-integer solutions (fractions/decimals) and safely handle negative coefficients.
- 5. Two-Step Equations (ax + b = c)
Solve two-step equations of the form ax + b = c by undoing operations in the correct reverse order, using inverse operations and the balance method.
- 6. Variables on Both Sides
Solve equations where the unknown variable appears on both sides of the equals sign by strategically collecting variable terms first.
- 7. Equations with Brackets
Solve equations containing brackets by choosing the most efficient method: either dividing first or expanding the brackets first.
- 8. Equations with Fractions and Decimals
Clear fractions from equations by multiplying every term by a common denominator, and apply the balance model to solve equations containing decimals.
- 9. Forming Equations from Contexts
Translate real-world situations, visual models, and geometric problems into algebraic equations, and solve them to find unknown values.
- 10. Mastery, Puzzles, and Problem Solving
Synthesize equation-solving skills to identify equivalent equations, solve consecutive number problems, and tackle logical algebraic puzzles.
