Unit 5 – foundations of differentiation

An 8-lesson unit for Year 11 with resources.

This program of learning addresses content from the focus area of Introduction to differentiation. The lessons and sequences in this program of learning are designed to allow students to explore rates of change by looking at average speed vs instantaneous speed. The lessons introduce the concept of the derivative and use first principles to find the derivative of quadratic functions.

Lesson 1 – average speed

• Average speed (DOCX 6.4 MB)
• Average speed – slide deck (PPTX 3.5 MB)

Lesson 2 – instantaneous speed

• Instantaneous speed (DOCX 6.1 MB)
• Instantaneous speed – slide deck (PPTX 3.2 MB)

Lesson 3 – modelling change

• Modelling change (DOCX 5 MB)
• Modelling change – slide deck (PPTX 3.1 MB)

Lesson 4 – negative and fractional indices

• Negative and fractional indices (DOCX 8.3 MB)
• Negative and fractional indices – slide deck (PPTX 3.3 MB)

Lesson 5 – introducing the derivative

• Introducing the derivative (DOCX 5.8 MB)
• Introducing the derivative – slide deck (PPTX 10.2 MB)

Lesson 6 – algebraic fractions

• Algebriac fractions (DOCX 6.1 MB)
• Algebriac fractions – slide deck (PPTX 9.2 MB)

Lesson 7 – differentiating by first principles

• Differentiating by first principles (DOCX 7.2 MB)
• Differentiating by first principles – slide deck (PPTX 2.4 MB)

Lesson 8 – parallel and perpendicular lines

• Parallel and perpendicular lines (DOCX 5.8 MB)
• Parallel and perpendicular lines – slide deck (PPTX 2 MB)