Algebra and Equations — NSW Year 7 Maths
Using letters for unknown numbers and then finding them, from the laws of arithmetic to two-step equations. Eleven subtopics and 220 practice questions, each with a fully worked solution, aligned to NESA outcomes MA4-ALG-C-01 and MA4-EQU-C-01.
Algebra and Equations in NSW Year 7
Algebra uses letters, called pronumerals, to stand for numbers, so one expression can describe many cases at once. In Year 7, students first see why the laws of arithmetic let them reorder and regroup a calculation, then learn to write, simplify and evaluate expressions, and finally solve equations, first by guess and check and then by using inverse operations on both sides.
The eleven subtopics below start with the commutative, associative and distributive laws, move on to variables, turning words into algebra and substitution, then build equation solving from guess and check through one-step and two-step equations to worded problems. Algebra and Equations is one of the 13 topics in NSW Year 7 Maths and sits in the Number and Algebra strand (NESA outcomes MA4‑ALG‑C‑01 and MA4‑EQU‑C‑01). These skills support later work on linear relationships, index laws, formulas and harder equations.
Subtopics
Algebra and Equations: common questions
What is algebra in Year 7 maths?
Algebra uses pronumerals, letters such as \(x\) or \(n\), to stand for numbers. In Year 7 students write and simplify expressions like \(4n\) or \(3x + 2\), substitute values into them and solve simple equations.
How do you solve a two-step equation?
Undo the operations in reverse order, doing the same thing to both sides. For \(3x + 4 = 22\), subtract \(4\) to get \(3x = 18\), then divide by \(3\) to get \(x = 6\).
What is a common mistake with substitution?
Ignoring the order of operations or leaving out the brackets around a negative number. For \(m - n^2\) with \(m = 4\) and \(n = -2\), square first: \(4 - (-2)^2 = 4 - 4 = 0\).
Which NESA outcomes cover algebra and equations?
They sit in Stage 4 of the NSW Mathematics K–10 Syllabus (2022) under outcomes MA4‑ALG‑C‑01 (algebraic techniques) and MA4‑EQU‑C‑01 (equations), usually started in Year 7.
What comes after algebra and equations in Year 7?
Later in Stage 4, students expand and factorise expressions, use index laws and graph linear relationships on the number plane. Equation work also extends to simple quadratic equations such as \(x^2 = 49\).