## Content description

Introduce the concept of variables as a way of representing numbers using letters. (ACMNA175)

### Elaboration

• Understanding that arithmetic laws are powerful ways of describing and simplifying calculations and that using these laws leads to the generality of algebra

Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

#### Using pronumerals

In algebra we are doing arithmetic with just one new feature − we use letters to represent numbers. Because the letters are simply stand-ins for numbers, arithmetic is carried out exactly as it is with numbers.
Pronumerals are used in many different ways, as shown below.
Substitution: 'Find the value of 2x + 3 if x = 4.' In this case the pronumeral is given the value 4.
Solving an equation: 'Find x if 2x + 3 = 8.' Here we are seeking the value of the pronumeral that makes the sentence true.
Identity: 'The statement of the commutative law: $$a + b = b + a$$.' Here a and b can be any real numbers.
Formula: 'The area of a rectangle is $$A = lw$$.' Here the values of the pronumerals are connected by the formula.
Equation of a line or curve: 'The general equation of the straight line is $$y = mx + c$$.'  Here $$m$$ and $$c$$ are parameters. That is, for a particular straight line, $$m$$ and $$c$$ are fixed.