Mathematics classroom notes
Year 4 - Variables — identifying things that can change and things that stay the same
Strand / topic: Statistics and Probability / Variables — identifying things that can change and things that stay the same
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 variables — identifying things that can change and things that stay the same, use a clear method, solve simple and test-style questions, and check their answers for Year 4 Statistics and Probability work.
It helps with shopping, saving, budgeting and checking change in Australian dollars and cents. This topic builds the reasoning, fluency and confidence students need for future NAPLAN-style questions and everyday mathematics.
How do dollars and cents work together?
Australian money uses place value: 100 cents make 1 dollar.
$4.75 means 4 dollars and 75 cents.
For Year 4, focus on understanding the idea before rushing to the final answer.
Think about it: canteen orders and shopping change are money maths.
Use this visual to organise variables — identifying things that can change and things that stay the same before calculating.
Keep dollars and cents lined up like decimal place values.
What you need to know for this topic
Use this as a study checklist before trying quizzes, worksheets or NAPLAN-style questions.
Australian money
- dollars and cents
- coins and notes
- 100 cents equals $1
- write money with two decimal places
Money calculations
- add and subtract prices
- round to the nearest 5 cents when needed
- find the price, amount paid or change
- use price lists
Word problems
- choose the operation
- compare money amounts
- estimate the total before calculating
1 What this means
Money maths uses dollars and cents to work out costs, totals and change. Start by learning to write every amount in the same unit, then choose the operation the situation needs. A helpful visual is a labelled group of Australian coins and notes. For example, this idea can be used when checking a shopping total or change.
Money problems are really place-value problems with dollars and cents. In Year 4, students should first ask, 'What is the question really asking me to find?' Then they can draw a picture, make a table, use a number line, write a formula or build an equation. The final answer should match the story, the units and the size of the numbers.
- Use Australian dollars and cents, with 100 cents making $1.
- Write money with two decimal places when using dollar notation.
- For change, subtract the cost from the amount paid.
- Check that the change is less than the amount paid.
2 Important rules / ideas
Use $ for dollars and c for cents; $1 = 100c.
Write $4.50, not $4.5, in formal money answers.
Change = amount paid - cost.
Important vocabulary
Whole Australian money units.
100 cents make 1 dollar.
The amount altogether.
Money returned after paying more than the cost.
3 Step-by-step method
- List each cost in dollars and cents.
- Add costs or subtract from the amount paid.
- Write money with two decimal places.
- Check that change is less than the amount paid.
4 Worked examples
Add $3.40 and $2.25.
- Add dollars and cents carefully.
- $3.40 + $2.25 = $5.65.
You pay $10 for an item costing $6.75. Find the change.
- Change = $10.00 - $6.75.
- Subtract to get $3.25.
- The change is $3.25.
Three notebooks cost $4.50 each. Find the total.
- Multiply $4.50 by 3.
- $4 x 3 = $12 and 50c x 3 = $1.50.
- Total = $13.50.
A bus fare is $2.80 each way. How much for a return trip?
- A return trip has two fares.
- $2.80 x 2 = $5.60.
- The return trip costs $5.60.
5 More examples
Write 375c in dollars.
100c = $1, so 375c = $3.75.
Pay $20 for a $13.80 item.
$20.00 - $13.80 = $6.20 change.
NAPLAN-style thinking
In NAPLAN-style questions, variables — identifying things that can change and things that stay the same 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
Write money with two decimal places.
Remember 100 cents is $1.
Subtract the cost from the amount paid.
- 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
Use $7.90, not $7.9, for formal money writing.
Change can be checked by counting from the cost to the amount paid.
Use Australian coins and notes when making examples at home.
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
Use two decimal places for dollars and cents.
8 Quick practice
- Add $3.40 and $2.25.
- You pay $10 for an item costing $6.75. Find the change.
- Three notebooks cost $4.50 each. Find the total.
- A bus fare is $2.80 each way. How much for a return trip?
9 Answers / explanation
Question 1
Answer: $3.40 + $2.25 = $5.65.
Add dollars and cents carefully. $3.40 + $2.25 = $5.65.
Question 2
Answer: The change is $3.25.
Change = $10.00 - $6.75. Subtract to get $3.25. The change is $3.25.
Question 3
Answer: Total = $13.50.
Multiply $4.50 by 3. $4 x 3 = $12 and 50c x 3 = $1.50. Total = $13.50.
Question 4
Answer: The return trip costs $5.60.
A return trip has two fares. $2.80 x 2 = $5.60. The return trip costs $5.60.
Extension challenge
Create your own multi-step question for this topic using an Australian context, then solve it and explain each step.
Hint: Use shopping, sport, maps, timetables, weather, school events or measurement at home.
Answer guide
Answers will vary. A strong answer includes clear working, correct units and a final sentence.
Quick revision
- Know what variables — identifying things that can change and things that stay the same 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.