STEAM AGE IN EDUCATION

Lesson plan on Golden Ratio

                           Discovering the Golden Ratio 

Grade Level: Primary School (adaptable for high school)
Subject: Math, Art, Science 

Learning Objectives: 

  • Define the golden ratio and the Fibonacci sequence.
  • Calculate the golden ratio by measuring objects.
  • Identify examples in nature, art, and architecture.
  • Create a Golden Rectangle or Fibonacci spiral. 

Part 1: Introduction & Definition (15-20 mins) 

  1. Hook: Ask students to pick the most appealing rectangle from a set of options (some golden, some not).
  2. Define: Introduce the Golden Ratio (Phi, 𝜙≈1.618) and the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8...). Explain that the ratio of consecutive Fibonacci numbers approaches
  3. Video/Discussion: Show a short video on where the golden ratio appears (nature, pyramids) and discuss. 

Part 2: Hands-On Measurement & Calculation (20-25 mins) 

  1. Activity: Students work in groups to measure human body parts (finger lengths, arm span vs. height) or classroom objects (books, tables).
  2. Data Collection: Use a table to record measurements (e.g., longer segment / shorter segment) and calculate the ratio.
  3. Analysis: Average their ratios and compare to (1.618). 

Part 3: Exploring Nature & Art (15-20 mins) 

  1. Nature Walk/Images: Examine examples like nautilus shells, pinecones, or flower petals.
  2. Art/Architecture: Discuss the Great Pyramids, Parthenon, or famous paintings.
  3. Fibonacci Spiral: Demonstrate how to draw a Golden Rectangle and Fibonacci spiral using squares. 

Part 4: Consolidation & Creation (20-25 mins) 

  1. Project: Students create a poster or digital slide showcasing their findings, including measurements, examples, and a drawn spiral.
  2. Review: Share examples, discuss challenges, and answer any questions. 

Materials: Rulers, calculators, worksheets, paper, pencils, images/videos of golden ratio examples. 

This structure engages students with math, science, and art, providing concrete ways to understand a beautiful mathematical concept. 

Lesson Plan on Pendulum Momentum

                    Pendulum Momentum & Energy

Grade Level: Primary School (adaptable for high school)
Time: 45-60 minutes

Objectives:

  • Observe and quantify the relationship between pendulum length and period.
  • Understand the conversion between potential (height) and kinetic (motion) energy.
  • Apply the law of conservation of momentum in collisions. 

Part 1: Introduction & Simple Pendulum (20 min)

  1. Warm-Up (5 min): Gather students around a pendulum. Ask: "What makes it swing? What affects its swing time?".
  2. Activity (15 min):
  3. Build: Students build simple pendulums (string, bob/washer, support).
  4. Experiment: Measure period (time for 10 swings) for different string lengths (e.g., 20cm, 40cm, 60cm).
  5. Analyze: Discuss how length changes the period (shorter length = shorter period).
  6. Concept: Introduce potential energy (at peak) and kinetic energy (at bottom). 

Part 2: Conservation of Momentum (20 min) 

  1. Demo/Activity (10 min): Use a Newton's Cradle or a simple pendulum with clay.
    • Lift one ball, drop it: one ball swings out (elastic collision).
    • Lift two balls, drop them: two balls swing out.
    • Add clay to the bob: observe inelastic collision (less swing).
  2. Discussion (10 min):
    • Relate to    𝑝=𝑚𝑣 (momentum) and how momentum (and energy) is transferred.
    • Introduce elastic (energy conserved) vs. inelastic (energy lost to heat/sound, e.g., clay) collisions. 

Part 3: Application & Closure (10-15 min)

  1. Real-World Connection: Discuss seismometers (earthquake measurement) or pendulums in clocks/amusement rides.
  2. Assessment: Ask students to explain where potential/kinetic energy is at different points in a swing or roller coaster.
  3. Wrap-Up: Quick Q&A to check understanding of energy transformation and momentum transfer. 

Materials Needed: String, various weights (bobs), supports (desks, stands), stopwatches, rulers, clay (optional). 

This publication has been developed with the financial support from the European Commission in the framework of the Erasmus+ programme. The information and views set out in this publication are those of the authors and the EuropeanCommission may not be held responsible for the use, which may be made of the information contained herein. This work is licensed under Creative Commons Attribution 4.0 International. To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/