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Angle cannot be “Seen”
We have seen above that the angle between 2 lines is related to the rotation of the lines. The rotation cannot be “seen”. It is implied and has to be imagined. What the children initially see is a static figure with 2 lines. This is the major difficulty that children have with the idea of the angle. This is why they confuse the angle with the figure in which the angle is situated.
Hence the teacher has to mirror the idea of angles using activities with concrete materials. Let us see some examples.
Activities to understand Angles
Movement of the hands of a clock
Physical Exercises & Dance – The arms, legs and the body make various angles.
Broom or plastic sticks – to form various angles, representing a sharp or dull knife point or a steep or gentle hill slope
Paper folding - Angles can also be folded using paper. However, in the early stages of doing activities, students are likely to get confused between an angle and a closed figure in which the angle exists. One way to avoid this confusion would be to use circle shaped papers (like the filter paper in the chemistry lab) to fold angles. This would always show the arms as straight lines and the third side as a curve.
Initially these activities are better than drawing on paper. An angle drawn on paper is a static figure. In contrast the above activities can present angles in a dynamic changing manner. An angle can be seen to change when we move the sticks or our hands. Drawing on paper with a pencil and a ruler takes a longer time, reducing the time available for absorbing the idea.
Angles in Our Life
The study of angles & the lengths of sides which contain them developed into the science of Trigonometry. It was trigonometry which enabled understanding of the vastness of space & the celestial bodies in it and the drawing of accurate maps of physical features of Earth without flying over them. Mount Everest was declared as the tallest mountain on Earth before anyone ever reached its peak.
Life on Earth also owes a debt to an angle! – the inclination of the Earth’s axis to the plane of its revolution around the Sun. This inclination is the cause of the 4 seasons and the evolution of life on Earth.
Chapter 22.12 gives a list of real-life problems & events which demanded an understanding of angles. These can be explored with students.
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