| Lesson Plan |
| Grade: |
Date: 25/02/2026 |
| Subject: Additional Mathematics |
| Lesson Topic: Transform given relationships to and from straight-line form and determine unknown constants by calculating gradient or intercept of the transformed graph |
Learning Objective/s:
- Recognise when a given relationship can be transformed into the straight‑line form y = mx + c.
- Apply the appropriate algebraic manipulation (e.g., square‑root, reciprocal, logarithm) to obtain a linear equation.
- Plot the transformed variables, read the gradient and intercept accurately, and relate them to the original constants.
- Solve for unknown constants in the original relationship using the derived gradient and intercept.
- Complete practice problems that require selecting and executing the correct transformation.
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Materials Needed:
- Projector and screen
- Whiteboard and markers
- Graph paper or digital graphing tool (e.g., GeoGebra)
- Worksheet with data tables and transformation tasks
- Scientific calculators
- Rulers
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Introduction:
Begin with a short video clip showing how engineers linearise complex data to extract useful constants, linking to students’ prior knowledge of y = mx + c. Review how gradient and intercept are interpreted on a straight‑line graph. State that by the end of the lesson students will be able to transform non‑linear relationships, plot them, and determine the hidden constants.
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Lesson Structure:
- Do‑now (5 '): Quick quiz on identifying linear vs. non‑linear equations and stating the gradient‑intercept form.
- Mini‑lecture (10 '): Explain why and how to transform equations; introduce common transformations (square‑root, reciprocal, log, ln).
- Guided Example 1 – Quadratic relationship (10 '): Demonstrate transforming y = kx² to √y = √k x, plot, calculate gradient, solve for k.
- Guided Example 2 – Inverse relationship (10 '): Transform y = b/x to 1/y = (1/b)x, plot, find gradient, determine b.
- Independent Practice (15 '): Students work on the three practice questions, selecting appropriate transformations and completing calculations.
- Review & Exit Ticket (5 '): Whole‑class recap of steps; students write one concise summary of the transformation process on a sticky note.
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Conclusion:
Summarise the five‑step routine: identify, transform, plot, read gradient/intercept, back‑substitute. Collect exit tickets to check understanding. For homework, assign a set of additional data tables requiring students to choose and apply the correct transformation and solve for the unknown constants.
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