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Draft activity8–10 minutes

When the radius grows, what grows with it?

See and explain why doubling radius makes the area four times as large.

Targets7 learners3 connected reasoning needs
Activity sequence

Make the relationship visible

prediction before explanation
  1. 1

    Predict

    Before moving the radius, predict how the area will change when 3 cm becomes 6 cm.

  2. 2

    Explore

    Move the radius and compare the area scale factor in real time.

  3. 3

    Explain

    Use the diagram and the expression πr² to explain the scale factor.

  4. 4

    Reflect

    What idea would you revise in your original response?

Interactive model

Change the radius. Watch the area.

Move from the original 3 cm radius and compare both the picture and the numbers.

r = 3.0
Area28.3 cm²π × 3.0²
Compared with r = 31.00×area scale factor
Transfer check

A circle’s radius changes from 5 cm to 15 cm. By what factor does its area change? Explain.

A new scale factor reveals whether the learner can transfer the square relationship, not just repeat the example.