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Chapter 7 · Period 1 of 17 · 45 min

Which Tiger Images Look Right? Spotting Proportional Change

Observing Similarity in Change · Inductive

Building from the concrete observation that some tiger images look 'right' and others look 'wrong' is the entry point for multiplicative reasoning. Watch for students who say 'the difference stays the same' — this additive error is exactly the misconception section 7.1 addresses, and surfacing it here is productive, not a detour. The worked examples in section 7.4 extend this multiplicative idea formally, so a clean articulation here pays forward throughout the chapter.

0–10Display or sketch five tiger image outlines labelled A–E on the board, with their width and height dimensions as given in section 7.1. Students observe which images look natural and which appear stretched or squashed, sharing initial impressions aloud.
10–25Students record the width and height of each image and compute the difference (height − width) and the ratio (width ÷ height) in their notebooks. They group images into 'looks correct' and 'looks wrong' columns, then compare groups with a partner to look for a pattern in which quantity — difference or ratio — stays the same across similar-looking images.
25–38Class discussion: students share findings. The teacher guides students to articulate that images A, C, and D share the same multiplicative relationship between dimensions while B and E do not, and that subtracting a constant from both dimensions does not preserve shape — the core idea of section 7.1.
38–45Students write a one-sentence summary in their own words: 'Two images are similar when their width and height change by ___.' A few volunteers read aloud; the class refines the sentence together.
Assessment

A rectangular image has a width of 80 cm and a height of 60 cm. Which of the following describes what happens when 20 cm is subtracted from both the width and the height?

  • A It is impossible to tell whether the ratio changes without knowing the colour of the image.
  • B The new image does not have the same width-to-height ratio as the original because the ratio changes when a constant is added to or subtracted from both terms.
  • C The new image has the same width-to-height ratio as the original because the same amount was removed from both sides.
  • D The new image is larger than the original because both sides were changed.

B. The new image does not have the same width-to-height ratio as the original because the ratio changes when a constant is added to or subtracted from both terms.

What each wrong option reveals

  • A The student does not recognise that ratio comparison requires only numerical values, not additional attributes.
  • C The student believes that equal changes to both terms preserve the ratio — the additive misconception that section 7.1 is designed to dislodge.
  • D The student has confused a change in dimensions with a change in overall size rather than reasoning about the ratio.
Chapter 7 · 17 periods of 45 min

Also saved as 10 periods or 14 periods.

  • 2Why Does Additive Change Distort? Building the Argument
    Observing Similarity in Change
  • 3Naming the Relationship: What Is a Ratio?
    Ratios
  • 4Simplest Form: The HCF Test for Proportionality
    Ratios in their Simplest Form
  • 5Ratios in Real Objects: Bricks, Bodies, and Rectangles
    Ratios in their Simplest Form
  • 6Checking Proportionality: From Lemonade to Cement Walls
    Problem Solving with Proportional Reasoning
  • 7Classroom Ratios and Missing Terms: Open-Ended Proportional Thinking
    Problem Solving with Proportional Reasoning
  • 8The Rule of Three: Aryabhata's Framework and Its Algebraic Proof
    Problem Solving with Proportional Reasoning
  • 9Cross Multiplication in Action: Distance, Time, and Tea Prices
    Problem Solving with Proportional Reasoning
  • 10Scaling a Recipe: Real-World Rule of Three
    Problem Solving with Proportional Reasoning
  • 11Is Price Proportional to Volume? A Market Investigation
    Problem Solving with Proportional Reasoning
  • 12Sharing 12 Counters: Building Intuition for Ratio Partitioning
    Sharing, but Not Equally!
  • 13Altering Mixtures and Partitioning Amounts: Multi-Step Ratio Problems
    Sharing, but Not Equally!
  • 14Idlis, Paint, and Ratios: Consolidating Partition Problems
    Sharing, but Not Equally!
  • 15Converting Units Before Proportions: Length, Area, and Volume
    Unit Conversions
  • 16Ancient Problems and Modern Contexts: Lilavati to Land Costs
    Unit Conversions
  • 17Four Problems, One Idea: Proportional Reasoning at Work
    Synthesis
Ganita Prakash · Class 8 · 14 chapters

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