Free Grade 3 Introducing Reverse Differentiation Essentials Lesson Plans
Free Grade 3 lesson plans for Introducing Reverse Differentiation Essentials: 12 real questions with a full answer key and worked solutions. Differentiation finds the rate of change (the gradient) of a curve. For axⁿ, the derivative is naxⁿ⁻¹.
Free
Higher
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing reverse differentiation essentials
Identify introducing reverse differentiation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing reverse differentiation essentials
Explain introducing reverse differentiation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing reverse differentiation essentials
Calculate introducing reverse differentiation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing reverse differentiation essentials
Compare introducing reverse differentiation essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Introducing Reverse Differentiation Essentials works
Differentiation finds the rate of change (the gradient) of a curve. For axⁿ, the derivative is naxⁿ⁻¹.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Differentiate y = 4x^2 + 3x.[1]
- 2.Differentiate y = 6x^5 + 3x.[1]
- 3.Differentiate y = 6x^3 + 9x.[1]
- 4.Differentiate y = 3x^2 + 2x.[1]
- 5.Differentiate y = 1x^5 + 1x.[2]
- 6.Differentiate y = 4x^3 + 5x.[2]
- 7.Differentiate y = 2x^2 + 4x.[2]
- 8.Differentiate y = 4x^4 + 9x.[2]
- 9.Find the gradient of y = 6x^4 + 5x at x = 3.[3]
- 10.Find the gradient of y = 6x^3 + 2x at x = 1.[3]
- 11.Find the gradient of y = 3x^5 + 5x at x = 3.[3]
- 12.Find the gradient of y = 1x^2 + 6x at x = 2.[3]
Show answers and working
1. dy/dx = 8x^1 + 3
Multiply by the power, then reduce the power by 1. 4x^2 → 8x^1; 3x → 3.
2. dy/dx = 30x^4 + 3
Multiply by the power, then reduce the power by 1. 6x^5 → 30x^4; 3x → 3.
3. dy/dx = 18x^2 + 9
Multiply by the power, then reduce the power by 1. 6x^3 → 18x^2; 9x → 9.
4. dy/dx = 6x^1 + 2
Multiply by the power, then reduce the power by 1. 3x^2 → 6x^1; 2x → 2.
5. dy/dx = 5x^4 + 1
Multiply by the power, then reduce the power by 1. 1x^5 → 5x^4; 1x → 1.
6. dy/dx = 12x^2 + 5
Multiply by the power, then reduce the power by 1. 4x^3 → 12x^2; 5x → 5.
7. dy/dx = 4x^1 + 4
Multiply by the power, then reduce the power by 1. 2x^2 → 4x^1; 4x → 4.
8. dy/dx = 16x^3 + 9
Multiply by the power, then reduce the power by 1. 4x^4 → 16x^3; 9x → 9.
9. 653
dy/dx = 24x^3 + 5. At x = 3: 24 × 27 + 5 = 653.
10. 20
dy/dx = 18x^2 + 2. At x = 1: 18 × 1 + 2 = 20.
11. 1220
dy/dx = 15x^4 + 5. At x = 3: 15 × 81 + 5 = 1220.
12. 10
dy/dx = 2x^1 + 6. At x = 2: 2 × 2 + 6 = 10.
Worked examples
Differentiate y = 4x^4 + 6x.
- Multiply by the power, then reduce the power by 1.
- 4x^4 → 16x^3; 6x → 6.
- Answer: dy/dx = 16x^3 + 6
Differentiate y = 4x^2 + 6x.
- Multiply by the power, then reduce the power by 1.
- 4x^2 → 8x^1; 6x → 6.
- Answer: dy/dx = 8x^1 + 6
Find the gradient of y = 2x^5 + 4x at x = 3.
- dy/dx = 10x^4 + 4.
- At x = 3: 10 × 81 + 4 = 814.
- Answer: 814
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Forgets that a constant differentiates to 0.
Correction: Constants have zero gradient.
Reduces the power but forgets to multiply by it.
Correction: Multiply by the power, then reduce it by 1.
Teacher tips
- · Link to gradients of straight lines first.
Parent tips
- · Ask how speed relates to distance over time.
Real-life applications
- · Speed from distance, maximising profit.
Assessment objectives
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Frequently asked
- Is this Grade 3 Introducing Reverse Differentiation Essentials lesson plan really free?
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- What should a learner already know before this?
- Start with Differentiation. Each one has its own free lesson, worksheet and quiz.
- How is the lesson plan sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Introducing Reverse Differentiation Essentials?
- Move on to Introducing Reverse Differentiation Techniques, Introducing Reverse Differentiation Word Problems, Introducing Reverse Differentiation Common Errors, Working with Reverse Differentiation, which build directly on this idea.
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