AC9M7A02 · Year 7 · Algebra

Formulating algebraic expressions

ACARA v9 CONTENT DESCRIPTION “formulate algebraic expressions using constants, variables, operations and brackets”

Once you can read a formula, the next step is to write one. Turning a situation described in words into an algebraic expression is one of the most valuable skills in mathematics, because it lets you capture a general rule that works for any value. A phone plan, a taxi fare, the perimeter of a shape: each can be written as an expression built from numbers, letters and a few operations.

This year you learn to formulate expressions using constants, variables, operations and brackets. A constant is a fixed number, a variable is a letter standing for a value that can change, and brackets group parts of an expression so they are handled together. Putting these pieces together accurately is the foundation for solving equations later on.

Translating words into symbols

The cleanest way to build an expression is to translate a worded instruction one piece at a time. Take the instruction take a number, double it, then add 3. Let the number be n. Doubling it gives 2n, and adding 3 gives 2n plus 3. Each phrase becomes a small piece of algebra, and stitching them together in order produces the full expression without guesswork.

From words to an expression
Translate each phrase into symbols and build the expression step by step.
An algebraic expression is a worded instruction written in symbols. Start with a number as n, double it to get 2n, then add 3 to reach 2n plus 3. Building it one phrase at a time keeps the translation reliable.

Certain words map directly to operations. More than and increased by mean addition, less than means subtraction, times and product mean multiplication, and shared or per often signal division. A common trap is the phrase less than, which reverses the order: 5 less than a number n is n minus 5, not 5 minus n. Reading carefully and translating phrase by phrase guards against these slips.

Why brackets matter

Brackets are not decoration; they change what an operation applies to. The expression 2 times the bracket of n plus 3 means you first add 3 to n, then double the whole result. Without the brackets, 2n plus 3 means you double only the n and then add 3. These are genuinely different instructions and give different answers for the same value of n.

Brackets group first
Brackets show which parts are handled together before other operations.
Brackets change the meaning. 2 times the bracket of n plus 3 doubles the whole quantity, while 2n plus 3 doubles only the n and then adds 3. The brackets say which parts belong together and must be handled first.

This is why translating a worded problem demands care about grouping. If a recipe says double the combined weight of flour and sugar, the combined part must sit inside brackets, giving 2 times the bracket of f plus s. Putting the brackets in the wrong place, or leaving them out, quietly changes the meaning of the whole expression. Building expressions that say exactly what you intend, with constants, variables and brackets each in their proper place, is the heart of this topic and the groundwork for the equation solving that comes next.

Teaching tip: give the student a worded rule and ask them to build the expression aloud, phrase by phrase, before writing anything down. Speaking the translation, a number, then doubled, then plus 3, makes the structure clear and slows down the rush that causes most errors.

The less than reversal is worth drilling gently with a few quick examples. Ask for 4 less than 7, which is 3, then for 4 less than n, which is n minus 4. Anchoring the abstract case to a numerical one they can check makes the reversed order stick.

Builds on: Variables and substituting into formulas (AC9M7A01). That unit used variables in ready-made formulas; this unit builds expressions from words.
Quick self-check
1. Which expression means "a number multiplied by 5"?
2. Write an expression for "7 more than a number p".
3. What does the expression 3(x + 2) mean?
4. A taxi charges a $4 flagfall plus $2 per kilometre. Which expression gives the cost for k kilometres?
5. Which two expressions are different in meaning?