How to teach linear equations and expressions
Year 7 to Year 8 (ages 12 to 14)
Algebra starts by writing a worded rule as an expression using a variable, then substituting known values in to evaluate it, and finally solving an equation to find the unknown value that makes it true.
How to teach it
- Start with translating simple worded phrases into expressions, one operation at a time ('5 more than n' before '5 more than double n').
- Teach substitution as replacing the variable with a number, then following the order of operations to evaluate.
- Introduce solving as 'undo the operations in reverse order', always doing the same thing to both sides.
- Insist every solution is checked by substituting it back into the original equation.
- Use real formulas (perimeter, cost, distance) so substitution and solving feel purposeful, not abstract.
Worked example
Solve 5n - 8 = 27 Add 8 to both sides: 5n = 35 Divide both sides by 5: n = 7 Check: 5(7) - 8 = 35 - 8 = 27, correct
Common mistakes
- Reading '3 less than a number' as 3 - n instead of n - 3.
- Undoing operations in the same order they were applied, instead of reversing the order.
- Changing only one side of the equation instead of keeping both sides balanced.
- Skipping the order of operations when substituting (adding before multiplying).
Frequently asked questions
How do you turn a worded description into an algebraic expression?
Identify the variable (the unknown number), then translate each part of the sentence in order using the correct operation. '5 more than double a number' becomes 2n + 5: double the number first (2n), then add 5.
How do you solve a linear equation like 3n + 4 = 19?
Undo the operations in the reverse of the order they were applied. Since n was multiplied by 3 then had 4 added, first subtract 4 from both sides (3n = 15), then divide both sides by 3 (n = 5).
Why do you have to do the same thing to both sides of an equation?
An equation says two things are equal. If you only change one side, they are no longer equal. Doing the same operation to both sides keeps the balance, so the equation stays true at every step.
What year is solving linear equations taught?
In the Australian Curriculum, building expressions and substituting into formulas start at Year 7 (AC9M7A01-A02), with solving one-variable linear equations also at Year 7 (AC9M7A03), extending through Year 8 with graphing.
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.