Introduction to Ratios

Curriculum Details:

Year Level: Year 8
Australian Curriculum Strand: Number and Algebra
Sub-Strand: Real Numbers
Content Descriptor: Solve a range of problems involving rates and ratios, with and without digital technologies (ACMNA188).

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Lesson Objectives

By the end of the lesson, students will be able to:

1. Understand the concept of ratios as a way to compare two quantities.
2. Represent ratios in different forms (e.g., 2:3, 2 to 3, 2/3).
3. Solve real-life problems using ratios.
4. Work collaboratively and think critically to apply ratios in practical scenarios.

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Lesson Structure – 60 Minutes

1. Introduction (10 Minutes)

A. Hook – “Ratio in Real Life” (5 Mins):

• Begin by holding up two jars of lollies: one with 10 red lollies and 5 green lollies.
• Ask: “Which jar has more red compared to green? How can we describe this mathematically?”
• Students might naturally start describing the quantities. Introduce the term “ratio” as a mathematical way to compare quantities.

B. Building the Concept (5 Mins):

• Write examples on the board:
  • 10 red lollies to 5 green lollies = 10:5
  • Simplify to show 2:1 (two red lollies for every one green lolly).
• Use everyday examples: how recipes use ratios to scale ingredients, or how teams in sport are often compared (e.g., number of wins to losses).

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2. Teacher-Directed Learning (15 Minutes)

A. Representing Ratios (10 Mins):

• Explicitly teach that ratios can:
  • Be written in three ways: e.g., "2:3", "2 to 3", or as a fraction, "2/3".
  • Describe part-to-part (red lollies to green lollies) or part-to-whole relationships (red lollies to total lollies).
• Model these concepts on the whiteboard:
  • Example 1: If there are 3 apples and 5 oranges, what is the ratio of apples to oranges? (3:5).
  • Example 2: If 3 apples and 5 oranges make 8 pieces of fruit, what is the ratio of apples to total fruit? (3:8).

B. Guided Practice (5 Mins):
Pose these to the class:

• If a basketball team won 12 games and lost 4, what’s the ratio of wins to losses?
• If a farm has 15 cows and 10 sheep, what’s the ratio of cows to total animals on the farm?
  Students work with a partner and share answers. Discuss as a class.

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3. Interactive Group Activity (20 Minutes)

A. “Ratio Scavenger Hunt” (10 Mins):

• Prepare 6 stations around the classroom, each with easy-to-find objects (e.g., pencils, rulers, coloured paperclips). Each station will contain a card with a task like:
  • “Count the blue and yellow paperclips in the jar. Write the ratio of blue to yellow.”
  • “Pick 8 pencils from the pile. Make up a part-to-whole ratio for the red pencils compared to all pencils.”
• In pairs, students rotate through each station and record their answers on a worksheet.

B. Real-Life Ratio Scenario – “Design a Smoothie” (10 Mins):

1. Present students with a smoothie recipe:
   2 parts strawberries, 1 part banana, and 3 parts milk.
2. Tell students to work in small groups to "scale up" the recipe to serve 10 people instead of 2.
3. Prompt questions:
   • What will be the new ratio?
   • How many parts will each ingredient have?
   • How can ratios help us double or triple recipes accurately?
4. Groups share their scaled-up recipes with the class.

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4. Consolidation and Reflection (15 Minutes)

A. Quick Quiz – “Ratio Riddles” (5 Mins):

• Pose three rapid-fire ratio problems on the board:
  1. A recipe uses 4 teaspoons of sugar for every 6 teaspoons of flour. What’s the simplified ratio?
  2. A student reads 12 chapters of a book and has 4 left to go. What’s the ratio of chapters read to the total chapters?
  3. A car travels 150 km using 10 litres of petrol. What’s the ratio of distance to petrol used?
• Students work independently to solve and share answers.

B. Exit Ticket – “What Stuck with Me?” (10 Mins):

• Hand out sticky notes and ask students to write:
  1. One thing they learned about ratios.
  2. A question they still have.
  3. Where they see ratios in everyday life.
• Collect and discuss the most common responses.

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Materials

1. Two jars of lollies (red and green).
2. Classroom objects (pencils, paper clips, rulers, etc.) for scavenger hunt stations.
3. Station activity cards.
4. Whiteboard and markers.

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Differentiation

1. Support for Struggling Students: Provide visual aids such as ratio blocks or number lines. Pair weaker students with supportive peers during group work.
2. Challenge for Advanced Learners: Extend tasks by introducing more complex ratios or multi-step ratio problems (e.g., combining two or more part-to-part ratios to form a total).

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Assessment

• Formative assessment through class discussions and observations during the scavenger hunt and smoothie activity.
• Quick quiz answers checked for retention of core ratio concepts.
• Exit tickets reviewed to identify gaps in understanding for future lessons.

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Homework (Optional)

• Find an example of ratios at home (e.g., ingredients, sports statistics, or objects in a room) and bring it to share with the class tomorrow.

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Teacher’s Reflection After Lesson

• What aspects of the lesson worked well in engaging students?
• Which parts need adjusting (e.g., pacing, scaffolding)?
• Did students show understanding of both the concept and its applications?