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Day 3 · Compare exact expressionsYear 11 Methods · T1 W1–2 · Day 3 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: simplify and compare Card C. Say: “A common radical factor lets us compare without rounding.”

0–2: Review sqrt(72)=6sqrt(2) from Day 2.
2–7: Model sqrt(50)=5sqrt(2); ask students to find the square in 98.
7–13: Pairs get sqrt(98)=7sqrt(2) and explain why 7sqrt(2)>5sqrt(2).
13–20: Independent exact difference; attach units to a length, not to a pure coefficient.
20–25: Quick decimal check of order; discuss why rounding cannot prove exact equality.

Routes: symbolic steps and inequality; verbal comparison with a recorded common-factor statement; draw two bar lengths of 5 and 7 identical sqrt(2) tiles with labels. Other domains: Day 3 swaps. Optional/home: compare sqrt(27) and sqrt(75) exactly. Move: if learners compare 50 and 98 correctly but cannot state the exact difference, bring out the matching sqrt(2) tiles.

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