Name
Golden ratio
Topic
Mathematics, Geography, History, Biology
Learning time
7 hours and 15 minutes
Designed time
7 hours and 5 minutes
Size of class
20
Description
The golden ratio is a concept pupils may have hear of but do not understand how it is applicable to the real world and mathematics in collaboration with other subjects.
Aims
Introduce the golden ratio to students, teach them to recognise it in their surroundings and apply it to mathematics.
Outcomes
Knowledge, Application, Analysis
Editor
anitasimac74
Edit
What is the golden ratio ?
100 minutes)
  • Discuss
    10
    20
    0
    Have you heard of the golden ratio ? Where have you heard of this topic ? The golden ratio is a special number. It is approximately equal to 1.618. To be more specific : the Golden Ratio is equal to: 1.61803398874989484820... The Golden Ratio is also sometimes called the golden section, golden mean, golden number,divine proportion, divine section and golden proportion.
  • Investigate
    45
    20
    0
    Let us investigate using the internet about the history of the golden ratio. In Greek history : Phidias (500 B.C. - 432 B.C.) was a Greek sculptor and mathematician who is thought to have applied the golden mean, phi to the design of sculptures for the Parthenon. Where is the Parthenon ? Find photos or draw the Parthenon. Plato (428 B.C. - 347 B.C.) considered the Golden ratio to be the most universally binding of mathematical relationships. Later, Euclid (365 B.C. - 300 B.C.) linked the Golden ratio to the construction of a pentagram. Have you heard of other ancient mathematicians ? In teams of four investigate other ancient mathematicians and prepare a short presentation for the following lesson. Investigate in your groups other ancient examples where the golden ratio was used. Mathematics in the middle ages. Around 1200, the mathematician Leonardo Fibonacci discovered the unique properties of the Fibonacci sequence. This sequence ties directly into the Golden ratio because if you take any two successive Fibonacci numbers, their ratio is very close to the Golden ratio. As the numbers get higher, the ratio becomes even closer to 1.618. For example, the ratio of 3 to 5 is 1.666. But the ratio of 13 to 21 is 1.625. Getting even higher, the ratio of 144 to 233 is 1.618. These numbers are all successive numbers in the Fibonacci sequence. It appears many times in geometry, art, architecture and other areas. Some artists and architects believe the Golden Ratio makes the most pleasing and beautiful shape. Discover artists who also applied the Golden ratio. Can you find pictures in the internet ? The Golden ratio also appears in da Vinci's Vitruvian Man and the Mona Lisa. Other artists who employed the Golden ratio include Michelangelo, Raphael, Rembrandt, Seurat, and Salvador Dali.
  • Collaborate
    45
    20
    0
    Devise a presentation following student investigation of ancient mathematics (Greek and Roman for example). How is this advancement of mathematics connected to the rich history and culture of ancient Greece and Rome ? Be creative and explore various internet sources. In your groups of four share responsibility. Do not work in parallel but towards the same goal. Give each other feedback and debate your thoughts, ideas and views. Perhaps present in the form of a video or poster. Be creative.
Notes:
At each stage of the lesson, the teacher is on hand to offer assistance, feedback and motivation. Following each presentation, suggestions are given on how to improve the quality of their work.
Resources linked: 0
The golden ratio and mathematics
70 minutes)
  • Read Watch Listen
    15
    20
    0
    Present the product of your teamwork. Display your posters and any other written work to the other groups and the teacher. The teacher will give you feedback and useful suggestions for work progression. What have you learned ? Answer any questions posed to you from the other pupils. Give each other constructive feeback and give peer assessment.
  • Produce
    25
    20
    0
    You can calculate the golden ratio yourself by starting with any number and following these steps: • A) divide 1 by your number (=1/number) • B) add 1 • C) that is your new number, start again at A You can draw a rectangle with the Golden Ratio: • Draw a square (of size "1") • Place a dot half way along one side • Draw a line from that point to an opposite corner (it will be √5/2 in length) • Turn that line so that it runs along the square's side Then you can extend the square to be a rectangle with the Golden Ratio. This is known as one of the most visually satisfying of all geometric forms – hence, the appearance of the Golden ratio in art. Spend ten minutes producing the perfect rectangle. Colour your rectangle, make the design creative and pleasing to the eye.
  • Investigate
    30
    20
    0
    With your rectangles, in different groups of four (as assigned by the teacher), produce a poster and conduct a survey in school. Which rectangles are the most pleasing to the eye ? Produce a graph detailing your results.
Notes:
At each stage of the lesson, the teacher is on hand to offer assistance, feedback and motivation. Following each presentation, suggestions are given on how to improve the quality of their work.
Resources linked: 0
The golden ratio around us
90 minutes)
  • Collaborate
    45
    20
    0
    Try and find examples of the golden ratio in the human face. The teacher takes a photograph of each pupil in the class. Help the pupils scan the photos, in Sketchpad. Ask them in pairs to measure the distance between the eyes, then measure the length of the nose of the photos scanned. Group the pupils into teams of four and ask them to find the ratio of these two measurements.
  • Produce
    45
    20
    0
    Each group proceeds to devise a plan to produce a Powerpoint presentation with all their findings. This is to be presented the following week. Divide your responsibility. Assign tasks and agree amongst yourselves as to your responsibilities.
Notes:
At each stage of the lesson, the teacher is on hand to offer assistance, feedback and motivation. Following each presentation, suggestions are given on how to improve the quality of their work.
Resources linked: 0
The golden ratio in our town
120 minutes)
  • Investigate
    45
    0
    Photograph your school, the local church, square and other monuments. Use your mobile phones. Print the photographs with the help of your IT teacher. Try and find the golden ration amongst the buildings. If you prefer, photograph plants and try and find the golden ratio amongst the petals, leaves etc. Talk to your biology teacher who will be able to assist you. Try and find examples on the internet of other famous buildings where the golden ratio is present.
  • Produce
    45
    0
    Produce a Powerpoint presentation with all your findings in pairs as assigned by the teacher.
  • Discuss
    30
    0
    Discuss your findings with your classmates. Did you photograph different buildings ? What were the most interesting buildings where you found examples of the golden ratio ? Peer feedback of the presentation is encouraged as is feedback from the teacher.
Notes:
At each stage of the lesson, the teacher is on hand to offer assistance, feedback and motivation. Following each presentation, suggestions are given on how to improve the quality of their work.
Resources linked: 0
Presentation and evaluation
45 minutes)
  • Read Watch Listen
    30
    0
    The presentations are presented by each team.
  • Discuss
    15
    0
    After each presentation, peer evaluation is encouraged and the teacher mediates until the end when he/she gives feedback and an assessment in the form of a formal evaluation.
Notes:
At each stage of the lesson, the teacher is on hand to offer assistance, feedback, mediation and motivation. Following each presentation, suggestions are given on how to improve the quality of their work.
Resources linked: 0

Learning Experience

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Social learning graph will not display correctly, because one or more learning types do not have group size set.