CONTENT MEASURE. UNIT PROPORTION VOLUME SKELETON MUSCLES
COGNITION UNDERSTANDING MAKING HYPOTHESIS REMEMBERING 3D-FIGURES SKELETON PARTS MUSCLES PROPORTION FIBONACCI NUMBERS MEASURE ANALYSING CREATING APPLYING EVALUATING DISCUSSING IF A METHOD IS GOOD WRITE YOUR THEORY ABOUT VOLUME MEASUREMENT CALCULUS OF MEASURES AND RATIOS ESTIMATING MEASURES
COMMUNICATION GEOMETRIC VOCABULARY LANGUAGE OF LEARNING SKELETON VOCABULARY MUSCLES VOCABULARY LANGUAGE FOR LEARNING MAKING HYPOTHESIS AND SUGGESTIONS EXPRESSING OPINIONS PRESENT AND DEFEND AN ARGUMENT DISCUSSING IDEAS LANGUAGE THROUGH LEARNING ANALYSING SPEAKING SPONTANEOUSLY QUESTIONING BASIC ENGLISH STRUCTURES ABOUT GEOMETRY AND ANATOMY READING LANGUAGE FOR DESCRIBING PARTS OF THE BODY AND 3D FIGURES READING SKILLS ASKING AND ANSWERING QUESTIONS
CULTURE ANCIENT BODY MEASURE UNIT DISEASES AND ILLNESSES TRIDIMENSIONAL OBJECTS IN DAILY LIFE MEASURE USUAL SYSTEM
<ul><li>Use your HAND , ELBOW , FEET length to calculate your classroom length </li></ul>EXERCISE 1: From Ancient times , men used parts of their bodies to measure . So,
Match these body measures with their meaning Digit: 28th part of a cubit. Width of a finger. Approx Inch: Width of man's thumb Palm: Width of man's palm Hand: Width of man's hand Span: Width of man's spread fingers 11.6 inches (approx). Roman Roman foot: EXERCISE 2a:
Match these measures with the numbers Palm: 3 inches Hand: 4 inches Span: 9 inches 11.6 inches (approx) Roman foot: 30,5cm foot: EXERCISE 2b:
Use the following words in order to build a sentence that explains what the volume is. You have to use some extra words EXERCISE 3: VOLUME OBJECTS COMPARE IS NOT VOLUME VOLUME TIMES FITS
This is a cube which sides measure 1 metre: 1 cubic metre How many people could you put inside ? Check your answer using the cubic metre and your classmates EXERCISE 4:
Do you know this picture? Make a list of some mathematical content you can find in it EXERCISE 5: This is the Vitruvian man by Leonardo da Vinci
The golden ratio , also known as the divine proportion or golden section , is a number often encountered when taking the ratios of distances in simple geometric figures such as the pentagon , pentagram , decagon and dodecahedron . Do you know the golden ratio?
THE GOLDEN RECTANGLE SIDES RATIO 1:x the a into unique in rectangle the sides results original in as has rectangle the defined also new partitioning is which and that PHI rectangle square such ratio new a number WRITE THIS SENTENCE IN ORDER: ANSWER: PHI is defined as the unique number such that partitioning the original rectangle into a square and new rectangle results in a new rectangle which also has sides in the ratio PHI: 1 = 1: PHI-1 EXERCISE 6:
<ul><li>Phi is one of the two great treasures of geometry </li></ul><ul><li>Phi or , which is 1.618 0339 887 ..., was described by Johannes Kepler as one of the "two great treasures of geometry." (The other is the Theorem of Pythagoras .) </li></ul>LOOK FOR THE GOLDEN NUMBER IN YOUR BODY PARTS
Let’s have a look at your index finger : Consider that your fingernail is 1 unit in length and complete the following table: EXERCISE 7: Fingernail Pink Line Green Line Yellow Line Blue Line 1
We divide each by the number before it, we will find the following series of numbers: 1 / 1 = 1, 2 / 1 = 2, 3 / 2 = 1·5, 5 / 3 = 1·666..., 8 / 5 = 1·6, 13 / 8 = 1·625, 21 / 13 = 1·61538... Each section of your index finger, from the tip to the base of the wrist , is larger than the preceding one by about the Fibonacci ratio of 1.618, also fitting the Fibonacci numbers 2, 3, 5 and 8. The ratio seems to be settling down to a particular value, which we call the golden ratio or the golden number
. Calculate the ratio of your forearm to hand : Let’s see some other ratios Your hand creates a golden section in relation to your arm, as the ratio of your forearm to your hand is also 1.618, the Divine Proportion . COULD YOU FIND THE GOLDEN NUMBER IN OTHER PARTS OF YOUR BODY? EXERCISE 8:
BODY The human body is based on Phi and 5 The human body illustrates the Golden Section or Divine Proportion. We'll use the same building blocks again: Check if the relation between a man’s height and his navel height is the golden relation The Divine Proportion in the Body Check if the relation between hip height and knee height is the golden relation EXERCISE 9:
he human face is based entirely on Phi The human face is based entirely on Phi The human face abounds with examples of the Golden Section or Divine Proportion. We'll use our building blocks again to understand design in the face: The head forms a golden rectangle with the eyes at its midpoint . The mouth and nose are each placed at golden sections of the distance between the eyes and the bottom of the chin . The beauty unfolds as you look further.
The Human Lungs Number the following lines in the correct order: EXERCISE 10: ( ) It was determined that in all these divisions ( ) This asymmetrical division continues into the subsequent subdivisions of the bronchi. ( ) one long (the left) and the other short (the right). ( ) The windpipe divides into two main bronchi, ( ) the proportion of the short bronchus to the long was always 1/1.618.
LOOK AT THESE EXAMPLES: The DNA spiral is a Golden Section
HEALTH AND PROPORTION <ul><li>Fill in the gaps with one of the following words: </li></ul><ul><li>breathing / shorter / length / cheek/ health /race </li></ul><ul><li> </li></ul><ul><li>Ideal facial proportions are universal regardless of .........., sex and age, and are based on the phi ratio of 1.618. For example, if the width of the face from .......... to .......... is 10 inches, then the .......... of the face from the top of the head to the bottom of the chin should be 16.18 inches to be in ideal proportion. </li></ul><ul><li>Deviations from this ideal can result in .......... problems. Corrective procedures that return the face to this ideal can improve ........... For example: People with longer than ideal faces tend to have ..........problems, people with .......... than ideal faces tend to have jaw problems or headaches. </li></ul>EXERCISE 11:
What volume do you think you occupy? EXERCISE 12:
Think about different ways to measure or calculate your volume. Discuss with your classmates if all the methods are possible or not. EXERCISE 13:
Write your conclusions about how you would measure the volume of any irregular object EXERCISE 14: