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Day 1 · Surd or rational root?Year 11 Methods · T1 W1–2 · Day 1 lesson

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Year 11 / Mathematical Methods / Term 1 / Weeks 01 02

Part of the full two-week lesson sequence. Check the pack guide and taught point before teaching.

Open for this lesson: Pack guide · Worked swaps · Fresh learner checks · Aids and text routes.

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.

Learner choices

Goal: classify roots and distinguish exact equality from approximation using Card A. Say: “The radical symbol alone does not make a value irrational.”

0–2: Recall 3^2=9, 4^2=16; ask where 10 sits.
2–7: Model sqrt(9)=3 and 3<sqrt(10)<4, since 9<10<16. Say that sqrt(10)≈3.162 is approximate.
7–13: Partners classify the three sides; ask what “principal square root” means for a side length.
13–20: Learners show exact/approximate notation and explain why sqrt(10) is a surd.
20–25: Exit: can sqrt(16) be called a surd here? Collect the reason.

Routes: write a three-row exact/approximate table; tell the comparison while a peer captures 9<10<16; arrange 9, 10, 16 square-number tiles and dictate the inequality. Other domains: Day 1 swaps. Optional/home: find two invented square areas, one perfect and one not, then classify side expressions on scrap paper. Move: if a learner says all radicals are irrational, replace 10 with 16; if they write =3.162, ask what symbol marks rounding.

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