Help your students master differentials and linear approximation with this clear, scaffolded, and engaging lesson designed for Year 11 Maths Methods / introductory calculus.

This resource builds understanding from first principles through to application, helping students confidently use dy=f′(x)dx to estimate changes and approximate values.

🔹 What’s Included:

✔ Step-by-step PowerPoint lesson (intro → worked examples → applications)
✔ Visual diagrams (tangent line, dxdxdx, dydydy, and curve comparison)
✔ Scaffolded practice questions (basic → advanced)
✔ Real exam-style problems
✔ Complete answer key
✔ Exit ticket for quick assessment

🔹 Topics Covered:

• Meaning of differentials (dxdxdx, dydydy)
• Deriving dy=f′(x)dx from the derivative
• Using differentials to estimate change
• Linear (tangent line) approximation
• Comparing approximate vs exact values
• Understanding sources of error

🔹 Why Teachers Love This Resource:

⭐ Strong scaffolding — perfect for mixed-ability classes
⭐ Visual, intuitive explanations (ideal for students who struggle with abstraction)
⭐ Minimal prep — ready-to-teach lesson
⭐ Designed to match Maths Methods / early calculus curriculum
⭐ Includes both conceptual and procedural fluency

🔹 Perfect For:

• Year 11 Maths Methods
• Introductory Calculus units
• Revision lessons on derivatives & applications
• Relief lessons (clear structure + independent tasks)

🔹 Learning Outcomes:

Students will be able to:

• Apply dy=f′(x)dx to estimate changes in functions
• Approximate values using differentials
• Interpret differentials graphically using tangent lines

🔹 File Type:

• PowerPoint (editable)