Lesson Plan

• Describe the difference between scalars and vectors.
• Decompose a vector into perpendicular x‑ and y‑components using trigonometric relations.
• Calculate component magnitudes from a given vector magnitude and angle.
• Reconstruct a vector’s magnitude and direction from its components.
• Apply the component method to solve simple force problems.

• Whiteboard and markers
• Projector with slides showing vector diagrams
• Ruler and protractor
• Worksheet with practice vectors
• Scientific calculator (or app)
• Graph paper

Begin with a quick real‑world example, such as a force acting on a sled on an inclined surface, to capture interest. Review that scalars have only magnitude while vectors have magnitude and direction, linking to prior work on displacement. Explain that today’s success criteria are to break any vector into horizontal and vertical parts and to use those parts to find magnitude and direction.

1. Do‑now (5'): Students sketch a vector on graph paper, label its magnitude, and identify it as a vector; teacher checks understanding of scalar vs vector.
2. Mini‑lecture (10'): Present component notation, unit vectors, and the formulas Ax = A cosθ, Ay = A sinθ with projector examples.
3. Guided practice (12'): Work through the 50 N, 30° force example together; students calculate components and verify with calculators.
4. Independent activity (15'): Worksheet where learners decompose several vectors and then recombine components to find magnitude and angle; teacher circulates for formative feedback.
5. Quick check (5'): Exit ticket – give a vector’s components and ask students to state its magnitude and direction to a partner.

Summarise that representing a vector by perpendicular components simplifies analysis of motion and forces. Ask students to write one key takeaway on a sticky note as an exit ticket. Assign homework to complete the remaining worksheet problems and to bring a real‑world example of a vector for the next class.