**Lesson Plan Title:**

Grade 10 Mathematics Lesson Plan: Introduction to Trigonometric Ratios

**Materials Needed:**

– Textbook: CAPS-aligned mathematics textbook

– Whiteboard and markers

– Scientific calculators

– Graph paper

– Protractors

– Rulers

– Worksheet on trigonometric ratios

– Laptop and projector for demonstrating online trigonometric tools (if available)

– Internet access (optional, for interactive resources)

**Learning Objectives:**

By the end of this lesson, students should be able to:

1. Understand the basic trigonometric ratios: sine, cosine, and tangent.

2. Identify the ratios in right-angled triangles.

3. Apply trigonometric ratios to solve problems involving right-angled triangles.

4. Use a scientific calculator to find trigonometric ratios.

**Vocabulary:**

1. **Trigonometric Ratios:** Ratios of the sides of a right-angled triangle.

2. **Sine (sin):** Ratio of the length of the side opposite to the hypotenuse.

3. **Cosine (cos):** Ratio of the length of the adjacent side to the hypotenuse.

4. **Tangent (tan):** Ratio of the length of the opposite side to the adjacent side.

5. **Hypotenuse:** The longest side of a right-angled triangle, opposite the right angle.

**Previous Learning:**

Students should have prior knowledge of:

– Basic properties of triangles, especially right-angled triangles.

– Pythagorean theorem.

– Basic algebraic manipulations.

**Anticipated Challenges and Solutions:**

1. **Confusion with defining the sides relative to the angle:** Use colour-coded triangular diagrams to label and consistently refer to the sides.

2. **Difficulty using a scientific calculator:** Provide a step-by-step guide and demonstrate the process.

**Beginning Activities (10% of time – 6 minutes):**

1. **Introduction (2 minutes):** Explain the lesson objectives and summarise prior learning on right-angled triangles.

2. **Warm-up Activity (4 minutes):** Show a right-angled triangle on the board. Ask students to identify and label the hypotenuse, opposite side, and adjacent side relative to a marked angle.

**Middle Activities (80% of time – 48 minutes):**

1. **Direct Instruction (10 minutes):**

– Introduce trigonometric ratios using the mnemonic “SOH-CAH-TOA”.

– Demonstrate each ratio (sine, cosine, and tangent) on the board with a diagram.

**Guided Practice (15 minutes):**- Hand out graph paper and protractors.
- Draw right-angled triangles and label the sides.
- Work through examples together, calculating trigonometric ratios using side lengths.
**Independent Practice (15 minutes):**- Distribute the worksheet.
- Allow students to solve several problems involving finding unknown side lengths or angles using trigonometric ratios.
- Circulate the room to provide assistance and check for understanding.
**Calculator Practice (8 minutes):**- Demonstrate how to input values into scientific calculators to find sine, cosine, and tangent.
- Have students practice calculating and verify their answers from independent practice.

**End Activities (10% of time – 6 minutes):**

1. **Exit Ticket Activity (4 minutes):**

– Provide a quick quiz with three problems: one sine, one cosine, and one tangent calculation.

2. **Review and Recap (2 minutes):**

– Recap the key points of the lesson.

– Answer any remaining questions.

**Assessment and Checks for Understanding:**

– Observation during guided and independent practice.

– Worksheet progress.

– Accuracy in the calculator practice.

– Responses on the exit ticket activity.

**Differentiation Strategies for Diverse Learners:**

– **Scaffolding:** Provide additional visual aids and step-by-step guides for students who struggle.

– **Extension Activities:** Challenge advanced students with real-world application problems or introduce them to the unit circle.

– **Peer Support:** Pair struggling students with peers who can provide assistance.

**Teaching Notes:**

– Ensure the lesson is interactive, engaging learners with both visual and hands-on activities.

– Make use of technology where available to demonstrate dynamic trigonometric tools.

– Maintain sensitivity to students’ confidence with mathematical concepts and provide positive reinforcement regularly.

– Adapt materials and instructions for students with disabilities, ensuring accessibility for all.

**Accessibility Considerations:**

– Provide larger print materials if needed.

– Ensure all digital content is accessible (captioned videos, screen reader-friendly documents).

– Use verbal instructions alongside written ones to cater to different learning styles and abilities.

This structured lesson plan provides clarity and direction for teaching Grade 10 students the foundational concepts of trigonometric ratios, aligning with the CAPS curriculum standards.