Mathematics classroom notes
Year 6 - Algebraic expressions and equations
Strand / topic: Number and Algebra / Algebraic expressions and equations
Based on Pi Leo Academy's Victorian Curriculum F-10 Mathematics year-level guide and aligned to NAPLAN-style mathematical reasoning. Official curriculum code: Not stated in the provided curriculum source.
By the end of this note, students should be able to explain algebraic expressions and equations, use a clear method, solve simple and test-style questions, and check their answers for Year 6 Number and Algebra work.
It helps students describe patterns, solve unknowns and prepare for secondary mathematics. This topic builds the reasoning, fluency and confidence students need for future NAPLAN-style questions and everyday mathematics.
1 What this means
Algebra uses letters, symbols and rules to describe number patterns and relationships.
Algebra is a way to write number relationships clearly when a value is unknown or changing. In Year 6, students should connect the words in the question to a model such as a diagram, table, number line, grid, formula or equation. They then work in small steps and check whether the answer matches the question, the units and the size of the numbers.
- Identify what the variable represents before calculating.
- Keep an equation balanced by doing the same operation to both sides.
- Substitute values carefully and follow order of operations.
- Check solutions by putting them back into the original statement.
Use this visual to organise algebraic expressions and equations before calculating.
Keep both sides balanced at every step.
2 Important rules / ideas
Define what the letter stands for.
Do the same operation to both sides of an equation.
Put the answer back into the original expression or equation.
Important vocabulary
A letter or symbol representing a number.
Numbers and symbols without an equals sign.
A mathematical statement with an equals sign.
Find the value that makes an equation true.
3 Step-by-step method
- Identify the variable.
- Simplify both sides if needed.
- Use inverse operations to isolate the variable.
- Substitute the answer back to check.
4 Worked examples
Evaluate 3n + 2 when n = 4.
- Substitute 4 for n.
- 3 x 4 + 2 = 12 + 2.
- Answer: 14.
Solve x + 7 = 19.
- Use the inverse operation.
- x = 19 - 7.
- x = 12.
Solve 3x - 5 = 16.
- Add 5 to both sides: 3x = 21.
- Divide by 3: x = 7.
Tickets cost $6 each plus a $4 booking fee. Write the cost for n tickets.
- n tickets cost 6n dollars.
- Add the booking fee.
- Cost = 6n + 4.
5 More examples
If n = 5, find 4n + 1.
4 x 5 + 1 = 21.
m - 8 = 14.
Add 8 to both sides, so m = 22.
NAPLAN-style thinking
In NAPLAN-style questions, algebraic expressions and equations may appear as a short calculation, a word problem, a diagram, a table or a multi-step reasoning question. Students should slow down and decide what the question is really asking before calculating.
Estimate first and eliminate answers that are too small, too large or use the wrong unit.
Write only the answer required, but use working on paper to avoid mental slips.
Circle the numbers, underline the action words and decide whether all numbers are needed.
Do one step at a time and label intermediate answers so the final step is clear.
6 Common mistakes
Whatever you do to one side of an equation, do to the other.
3x means 3 times x.
Substitute the answer back into the equation.
- Choosing the first operation seen in the wording.
- Forgetting units, labels or place value.
- Stopping after the first step when the question asks for a final comparison.
7 Tips to remember
Write what the variable means.
Equations are like balanced scales.
Substitution is the quickest way to test a solution.
Parent teaching tips
- Ask your child to explain the method aloud before writing the answer.
- Use a real-life context at home, such as shopping, cooking, sport scores, maps or timetables.
- Praise clear working and checking, not only speed.
- Encourage a quick diagram or table for word problems before calculating.
Remember
Keep equations balanced by doing the same thing to both sides.
8 Quick practice
- Evaluate 3n + 2 when n = 4.
- Solve x + 7 = 19.
- Solve 3x - 5 = 16.
- Tickets cost $6 each plus a $4 booking fee. Write the cost for n tickets.
9 Answers / explanation
Question 1
Answer: 14.
Substitute 4 for n. 3 x 4 + 2 = 12 + 2. Answer: 14.
Question 2
Answer: x = 12.
Use the inverse operation. x = 19 - 7. x = 12.
Question 3
Answer: Divide by 3: x = 7.
Add 5 to both sides: 3x = 21. Divide by 3: x = 7.
Question 4
Answer: Cost = 6n + 4.
n tickets cost 6n dollars. Add the booking fee. Cost = 6n + 4.
Extension challenge
Write an equation or rule for a real-life situation, solve it, then check by substitution.
Hint: Use tickets, taxi fares, savings, distances or growing patterns.
Answer guide
Answers will vary. A strong answer includes clear working, correct units and a final sentence.
Quick revision
- Know what algebraic expressions and equations is asking you to find.
- Choose a diagram, table, formula, number line or equation before calculating.
- Show enough working that you can find and fix mistakes.
- Check the final answer, units and reasonableness.