Teacher copy: This page may include teaching prompts or answer keys. Answer keys in this public library can be viewed by anyone. Give learners a clean prompt, use checks as formative evidence, and change a case locally when prior access matters.
Goal: preserve value while writing Card G with a rational denominator. Say: “Multiply by one, not by a new value.”
0–2: Recall sqrt(5)sqrt(5)=5.
2–7: Model multiplying 7/sqrt(5) by sqrt(5)/sqrt(5).
7–13: Students explain why the denominator becomes 5 and why the numerator changes too.
13–20: Independently rationalise 4/sqrt(2) and compare equivalent decimal approximations.
20–25: Ask what went wrong if someone writes only 7sqrt(5).
Routes: fraction steps; spoken “multiply top and bottom” with recorded exact equality; paired numerator/denominator strips labelled with the same factor. Other domains:Day 7 swaps. Optional/home: write a ratio of your own with a single square-root denominator and verify both forms numerically. Move: if a student cancels sqrt(5) without multiplying numerator, have them test both values at three decimal places.