Real-World Ratios

Year Level: Year 9

Curriculum Area: Mathematics
Content Descriptor:

• ACMNA188 (Australian Curriculum): Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems.
• NAPLAN Context: Use mathematical reasoning to solve real-world numerical problems, with a strong focus on ratios and their applications.

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Lesson Objectives:

By the end of this 20-minute session, the student will be able to:

1. Understand and apply ratios in real-life scenarios.
2. Translate a problem into a ratio form and solve it.
3. Strengthen reasoning skills under NAPLAN conditions by practising with time constraints.

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Materials Required:

• Worksheet prepped with NAPLAN-style questions on ratios.
• Calculator (optional, based on student requirement).
• Pen and scrap paper for workings.
• Whiteboard and marker, if helpful for visual illustrations.

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Lesson Breakdown (20 minutes):

1. Introduction and Warm-Up (3 minutes):

Goal: Ease the student into the theme of ratios by connecting it to their daily life.

Teacher Prompts:

• Ask: "Have you ever followed a recipe at home? Do you remember how ingredients are measured in proportions like 1:3 or 2:5?"
• Use a quick, relatable example: "Imagine making cordial by mixing 1 part of concentrate with 4 parts of water. What happens if you need to make 10 cups in total?"
  (Answer: 2 cups concentrate, 8 cups water).
• Write the question and solve it together while explaining the steps.

Outcome: The student should understand that ratios are everywhere and prepare to engage.

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2. Core Activity — NAPLAN-Style Ratios (12 minutes):

Goal: Solve real-world ratio problems in a structured, time-conscious manner.

Step 1: Present Two NAPLAN-Style Questions (6 minutes)

Hand the student the following questions written out on the prepared worksheet:

1. Question 1 (3 marks — Medium Difficulty):
   A cafe serves three types of coffee: 5 regular coffees for every 2 lattes for every 3 cappuccinos. Over one busy day, the cafe sold 150 coffees in total.
   Question: How many lattes did the cafe sell?

   (Answer: Ratio of regular:lattes:cappuccinos is 5:2:3. Total parts = 5+2+3 = 10. One part = 150 ÷ 10 = 15. Lattes = 15 × 2 = 30.)

2. Question 2 (4 marks — Higher Cognitive Demand):
   In a school canteen, sandwiches are sold in the ratio of 2 chicken to 5 vegetarian. If the canteen earns $578 from selling 102 sandwiches, how much does one vegetarian sandwich cost if a chicken sandwich costs $6 each?
   (Answer: Chicken sandwiches = 34 sold, Vegetarian = 68 sold. Chicken revenue = 34 × $6 = $204. Vegetarian revenue = $578 - $204 = $374. Cost per vegetarian sandwich = $374 ÷ 68 = $5.50)

Encourage the student to underline keywords like "ratio" and isolate solution steps for clarity.

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Step 2: Quick Feedback Session (3 minutes)

• Review the answers together, step-by-step.
• Emphasise the importance of careful reading and checking calculations — both essential for NAPLAN.

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Step 3: Live Demonstration (3 minutes)

• Provide an additional challenging question orally. Example:
  "The ratio of boys to girls in a Year 9 class is 3:4. If 28 girls are in the class, how many boys are there?"
  (Answer: 3:4 → Boys = 3 × 7 = 21.)
• Solve it aloud as the student explains each step, building their verbal reasoning confidence.

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3. Closing and Reflect (5 minutes):

Quick Recap Exercise

• Write a creative, unexpected real-life question on the whiteboard (or verbally):
  "You are making a playlist with a ratio of 2 upbeat songs to 1 chill song. If you have time for 9 songs, how many chill songs do you need?" (Answer: 3 chill songs).

Teacher Exit Questions:

• "How do ratios help us in everyday life?"
• "If you’re given a tricky ratio question in NAPLAN, what’s the first thing you will do to tackle it?"

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Assessment and Homework (Optional):

• For further independent practice, assign 2-3 additional NAPLAN-style ratio questions to be completed for homework, using analogous real-world scenarios (e.g., sports statistics, travel distances, or recipe conversions).
• Discuss the completed work during the next session for feedback.

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Teacher Notes:

• Keep the pacing tight to cover all components of the lesson. Adapt and condense instructions if the student struggles to stay focused.
• Reinforce that thorough reading of questions and logical reasoning are just as important as rapid solving, especially under NAPLAN conditions.
• Balance instructional support with student independence to build confidence.