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Day 19 · Square products and their positive rootsYear 7 Maths · T1 W3–4 · Day 19 lesson

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Year 7 / Mathematics / Term 1 / Weeks 03 04

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

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

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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 prompts

Codes: AC9M7N01, AC9M7N02. Goal: connect 144=12², √144=12 and prime powers. Prepare: square-root link mat or tactile grid.

  1. Launch · 2 min. A fictional 12-by-12 pixel panel has how many cells? 144.
  2. Model · 5 min. 12²=12×12=144, so √144=12. Factor 12=2²×3; squaring gives 144=2⁴×3². Check 16×9=144. The root asks for the nonnegative side length, not ±12 in this setting.
  3. Guide · 6 min. 100=10²; 10=2×5, so 100=2²×5², and √100=10. Compare 81=9², 9=3², so 81=3⁴ and root9.
  4. Choice · 6 min. D19-A/B/C: square grid, exponent pairs or square-root error repair. Require both multiplication and root explanation.
  5. Exit · 4 min. “What is √81, and why?” 9 because 9×9=81; 3⁴=81 does not mean the root is 3.
  6. Note · 2 min. Check side/area units and distinguish evaluating a power from taking a square root; recheck 64 after instruction if needed.

Optional home/extension: Sketch 10×10 and 12×12 arrays. Extension: explain why 2⁴×3² can be grouped into two equal 2²×3 products.

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