Mathematics classroom notes
Year 6 - Algorithms with branching and iteration
Strand / topic: Number and Algebra / Algorithms with branching and iteration
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 algorithms with branching and iteration, use a clear method, solve simple and test-style questions, and check their answers for Year 6 Number and Algebra work.
It builds number sense, reasoning and confidence for classwork, quizzes and problem solving. This topic builds the reasoning, fluency and confidence students need for future NAPLAN-style questions and everyday mathematics.
How do the parts compare?
A ratio compares amounts in a fixed order.
A cordial mix of 1 part syrup to 4 parts water has 5 parts altogether.
For Year 6, focus on understanding the idea before rushing to the final answer.
Think about it: recipes, maps and sharing problems use ratios.
Use this visual to organise algorithms with branching and iteration before calculating.
Keep each part in the same order all the way through.
What you need to know for this topic
Use this as a study checklist before trying quizzes, worksheets or NAPLAN-style questions.
Comparisons
- part-to-part ratios
- part-to-whole thinking
- equivalent ratios
- simplifying ratios
Applications
- recipes
- scale drawings
- rates
- unit rates
- sharing in a ratio
1 What this means
A ratio compares two or more amounts.
Ratios and rates compare quantities in a fixed order. In Year 6, 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.
- Keep the quantities in the same order as the question.
- Use a bar model or table to see the parts clearly.
- Scale all parts by the same multiplier.
- Check units when working with rates.
2 Important rules / ideas
A ratio 2:3 is not the same as 3:2.
Equivalent ratios scale all parts by the same multiplier.
For sharing, add the ratio parts first.
Important vocabulary
A comparison between quantities.
A comparison using different units.
A relationship where quantities scale together.
The amount for one unit.
3 Step-by-step method
- Write the quantities in the same order as the question.
- Simplify the ratio if needed.
- Scale both parts by the same multiplier.
- Check the units and context.
4 Worked examples
Simplify the ratio 6:9.
- Divide both parts by 3.
- 6:9 = 2:3.
A cordial mix is 1 part syrup to 4 parts water. How many parts altogether?
- 1 + 4 = 5 parts altogether.
Share $45 in the ratio 2:3.
- Total parts = 5.
- $45 / 5 = $9 per part.
- Shares are $18 and $27.
A car travels 180 km in 3 hours. Find the average speed.
- Rate = distance / time.
- 180 / 3 = 60.
- Speed = 60 km/h.
5 More examples
10:15
Divide both parts by 5 to get 2:3.
A recipe uses 2 cups rice to 3 cups water. Double it.
Use 4 cups rice and 6 cups water.
NAPLAN-style thinking
In NAPLAN-style questions, algorithms with branching and iteration 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
Read the final sentence before calculating.
Name the topic and method before starting.
Estimate or use inverse operations to check.
- 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 the ratio in the same order as the words.
Bars help when sharing or scaling.
Rates compare quantities with different units.
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
For algorithms with branching and iteration, identify the question type, choose a clear method, show working and check the answer.
8 Quick practice
- Simplify the ratio 6:9.
- A cordial mix is 1 part syrup to 4 parts water. How many parts altogether?
- Share $45 in the ratio 2:3.
- A car travels 180 km in 3 hours. Find the average speed.
9 Answers / explanation
Question 1
Answer: 6:9 = 2:3.
Divide both parts by 3. 6:9 = 2:3.
Question 2
Answer: 1 + 4 = 5 parts altogether.
1 + 4 = 5 parts altogether.
Question 3
Answer: Shares are $18 and $27.
Total parts = 5. $45 / 5 = $9 per part. Shares are $18 and $27.
Question 4
Answer: Speed = 60 km/h.
Rate = distance / time. 180 / 3 = 60. Speed = 60 km/h.
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 algorithms with branching and iteration 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.