ChalkHour

Year 11 Maths: Vectors lesson pack

A complete, ready-to-teach GCSE lesson on vectors. Below is a real sample of what ChalkHour makes: the full pack adds three levels of worksheet, model answers, a teaching explainer and print-ready PDF and Word files.

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Real sample

Introduction to Vectors and Geometric Proof

This lesson covers the fundamentals of vectors for Year 11 students, progressing from basic column vector arithmetic to complex geometric proofs involving ratios and parallelism.

Learning objectives

  • Understand and use vector notation (column vectors and bold/underlined letters).
  • Perform addition, subtraction, and scalar multiplication of vectors.
  • Calculate the magnitude of a vector using Pythagoras' Theorem.
  • Solve geometric problems and proofs using vectors, including identifying parallel lines.

Lesson plan (60 minutes)

  1. Introduction · 10 min

    Starter: Column vector arithmetic and drawing vectors on a grid.

  2. Direct Instruction · 10 min

    Teacher-led explanation: Vector notation, addition, and scalar multiples.

  3. Guided Practice · 10 min

    Worked example: Finding a resultant vector in a geometric shape (e.g., a regular hexagon).

  4. Independent Practice · 20 min

    Differentiated worksheet practice (Support, Core, Stretch).

  5. Plenary · 10 min

    8-question MCQ quiz to check for understanding.

Key vocabulary

Vector
A quantity that has both magnitude (size) and direction.
Scalar
A quantity that only has magnitude (e.g., speed, time, mass).
Column Vector
A vector written vertically, showing the horizontal (top) and vertical (bottom) change.
Magnitude
The length or size of a vector.
Resultant
The vector resulting from adding two or more vectors together.

Core worksheet (first questions)

  1. If p = 2a + 3b and q = 3a + 2b, find p + q.
  2. In triangle OAB, OA = a and OB = b. Find vector AB in terms of a and b.
  3. Find the magnitude of the vector (5, -12).
  4. If vector v = (3, -2) and kv = (12, -8), find the value of k.

Quiz (sample)

  1. 1. What is the main difference between a vector and a scalar?

    • A. A vector has both magnitude and direction, a scalar only magnitude.
    • B. A vector is always positive, a scalar can be negative.
    • C. A vector is a coordinate, a scalar is a distance.
    • D. There is no difference between them.

  2. 2. If a = (2, 3) and b = (3, -4), what is a + b?

    • A. (5, 7)
    • B. (1, -1)
    • C. (5, -1)
    • D. (1, 7)

  3. 3. If v = (2, -4), what is 3v?

    • A. (5, -1)
    • B. (6, -4)
    • C. (2, -12)
    • D. (6, -12)

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