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Year 11 Maths: Direct and inverse proportion lesson pack

A complete, ready-to-teach GCSE lesson on direct and inverse proportion. 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

Direct and Inverse Proportion Teaching Pack

This lesson covers the algebraic and graphical representations of direct and inverse proportion. Students will learn to calculate the constant of proportionality (k) and use it to find missing values in linear, quadratic, and root relationships.

Learning objectives

  • Set up and solve equations for direct and inverse proportion using the constant of proportionality k.
  • Relate algebraic proportions to graphical representations (linear through origin vs reciprocal).
  • Solve complex proportion problems involving squares, cubes, and square roots.
  • Apply proportion knowledge to real-world contexts such as physics and finance.

Lesson plan (60 minutes)

  1. Introduction · 5 min

    Do Now: Quick fire mental maths on ratios and basic substitution into linear equations.

  2. Direct Explanation · 10 min

    Direct Proportion: Explain the constant 'k' and work through a direct proportion example (y ∝ x).

  3. Inverse Explanation · 10 min

    Inverse Proportion: Explain the reciprocal relationship (y ∝ 1/x) and graphical representations.

  4. Advanced Explanation · 10 min

    Powers and Roots: Demonstrate how to set up equations for x squared or square root of x.

  5. Independent Practice · 20 min

    Differentiated Worksheets: Students work through Support, Core, or Stretch tasks.

  6. Review · 5 min

    Plenary: Multiple-choice quiz to check for understanding and address misconceptions.

Key vocabulary

Proportionality (∝)
The symbol ∝ meaning two quantities maintain a constant ratio or product.
Constant of Proportionality (k)
The fixed value 'k' that relates the two variables in a proportion equation.
Direct Proportion
A relationship where the ratio of two variables is constant (y/x = k).
Inverse Proportion
A relationship where the product of two variables is constant (xy = k).
Reciprocal Graph
A graph with two curves that approach the axes but never touch them, representing y = k/x.

Core worksheet (first questions)

  1. y is directly proportional to the square of x. When x = 3, y = 18. Find y when x = 10.
  2. y ∝ x². When x = 4, y = 8. Find x when y = 18.
  3. y is directly proportional to the square root of x. When x = 16, y = 20. Find y when x = 25.
  4. y is inversely proportional to the square of x. When x = 2, y = 8. Find y when x = 4.

Quiz (sample)

  1. 1. Which equation represents direct proportion?

    • A. y = kx
    • B. y = k/x
    • C. y = x + k
    • D. y = kx + c

  2. 2. Which equation represents inverse proportion?

    • A. y = kx^2
    • B. y = k/x
    • C. y = x/k
    • D. y = k - x

  3. 3. If y is directly proportional to x, and y=12 when x=3, what is y when x=12?

    • A. 3
    • B. 12
    • C. 27
    • D. 48

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