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Day 3 — Zero and undefined gradients are differentYear 9 Maths · T1 W1–2 · Day 3 lesson

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Year 9 / Mathematics / Term 1 / Weeks 01 02

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

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Goal/materials: distinguish horizontal zero gradient from vertical undefined gradient; grid, Cards 3–4.

  1. Notice, 3: Ask what happens to y on Card 4 as x changes. Key: y remains -2.
  2. Model, 5: “Card 4 has Δy=0, Δx=8, so m=0/8=0. Card 3 has Δx=0, so a rise/run fraction would divide by zero; its gradient is undefined, not zero.” Use perpendicular paper strips.
  3. Together, 8: Sort (0,2)→(5,2), (3,-1)→(3,4), (-2,-2)→(2,2). Keys: zero, undefined, +1. Explain before applying a label.
  4. Try, 6: Learner creates one new horizontal and one new vertical pair inside grid limits, gives reasons and marks them. Accept: any distinct points sharing y or sharing x respectively.
  5. Check, 3: “Gradient from (-4,3) to (-4,-2)?” Key: undefined, because Δx=0. If called 0, contrast one horizontal and one vertical pair with explicit denominators.

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