Lesson 10: Calculus Differentiation Capstone Portfolio Synthesis
Applying differentiation methods, rules, optimisation, and related rates for NCEA Level 3 Calculus.
🎯 Ngā Whāinga Akoranga | Learning Intentions
Comprehensive synthesis of differentiation methods: power rule, trig/exp/log derivatives, product/quotient/chain rules, curve sketching, optimisation, and related rates.
Synthesise your complete Level 3 Calculus differentiation logbook, present a real-world optimisation engineering solution, and complete final mastery revision check.
🎥 Media Anchor & Pedagogical Scaffold
The Paradox of the Derivative — 3Blue1Brown
Video (16 min 50 sec, 3Blue1Brown, ⏱ 17 min): The celebrated visual essay on what a derivative is — instantaneous rate of change as a paradox resolved by limits. The right capstone: after nine lessons of rules and technique, this reconnects every method in your logbook to the single idea underneath.
🧠 1. Before Viewing (Activate & Predict)
How does calculus serve as the foundation for modern physics, engineering, economics, and computer science modelling?
👁️ 2. During Viewing (Watch With a Job)
Watch the full 3¾-minute clip as a final capstone review. In your logbook synthesis notes, record:
- Rule mastery checklist: For each of the 8 lessons completed, write one line summarising the key formula or concept (power rule, trig derivatives, chain rule, tangents, stationary points, optimisation, related rates, exam technique). Rate your confidence 1–5 for each.
- Synthesis task: Design ONE original problem that combines at least 3 different differentiation techniques (e.g., product rule + chain rule + optimisation). Solve it completely and write it into your logbook.
- Reflection: What was the biggest insight you gained about derivatives? How would you explain the derivative concept to a Year 10 student?
🗣️ 3. After Viewing & Kaiako Move (Process & Apply)
Kaiako Move: Facilitate logbook review and celebrate student mastery of Level 3 Calculus Differentiation.
Immediate Task: Final review of your Level 3 Calculus differentiation logbook, and an exam-readiness check against the standard.
⚡ Whakaoho | Do Now: Choosing the Rule (10 mins)
For each of x²eˣ, sin(3x), (x + 1)/(x − 1) and x⁵: name the rule you would use and why. Naming only. Rule selection under pressure is what the external actually tests.
📖 Activity 1: Mixed Set With No Rule Given (25 mins)
Work through a set where nothing tells you which rule applies, including at least one that needs two rules combined and one that is faster to simplify first. For each, write the rule name before you start. Then compare with a partner: where you chose different routes to the same answer, work out which was cheaper and why.
📝 Activity 2: Full Exam-Style Section, Self-Assessed (20 mins)
Complete an exam-style section covering differentiation, a curve-sketching justification and one applied rate. Then self-assess against Achieved, Merit and Excellence, and write one line naming the single thing that would most improve your grade. Bring that line to your next study session.
🏫 Kaiako Planning & Pedagogy Notes
NCEA Level 3 Alignment: Direct preparation for Level 3 Calculus (Apply differentiation methods in solving problems). Emphasise complete algebraic working and clear context conclusions for Merit/Excellence grades.