We realised that although the students were introduced to ‘symmetry’ through various activities in the Class 3, 4 and 5 textbooks, they could not use it for these area related problems. The activities used for this purpose are illustrated in the rest of the article. This is consistent with the approach that mathematics is playing with numbers and shapes, their relations to each other, and the rules of the game. The concept of symmetry is utilised for different patterns in activities such as rangoli, brick tiling and weaving patterns, mirror halves, paper folding and in number patterns.Īt this stage, we also need children to explore the symmetry around them in nature. How and to what extent: An indirect approach is used in the primary textbooks. To develop imagination, creativity and a sense of aesthetics in children.To develop the reasoning power of children.To develop the ability of identifying geometrical patterns in objects around them.Now – why, how and to what extent should we introduce symmetry at the primary level? Some of the answers to the why are: These activities strengthen the idea of line symmetry as well as rotational symmetry (by rotating the objects using half, one-third, quarter or one-sixth turns).Ĭhapter 7 directly links rotational symmetry and patterns with ‘turns and pattern’ activities. Line of symmetry is discussed for more complex figures and complex mirror game activities in Grade 5, Chapter 5. Symmetry is used in Grade 4 – specifically in Chapter 9 with activities on completing the other half and implicitly in Chapter 10 with the activity on floor design and tiling patterns. Similarly, pattern activities given in Chapter 10 use ingrained concept of symmetry implicitly. In the Grade 3 NCERT textbook, the very first chapter discusses concepts of symmetry using a story ‘Tit for Tat’ and follows it up with activities like completing mirror halves with the introduction of line of symmetry (or dotted line) by using figures and alphabets. Though the patterns are nothing but the transformations or a movement of figures in a plane classified as translation (slide), a reflection (flip) and a rotation (turn), yet can we say that it is the introduction of symmetry in this textbook? In the Grade 2 NCERT textbook there are worksheets on visual recognition of patterns and symmetry (non- verbal reasoning). Primary level textbooks include only the first three types of symmetries in the form of various activities and worksheets. When zoomed, the red portion (or the blue, or the green, or the purple) is identical to the whole. Other symmetries include glide reflection symmetry (a reflection followed by a translation) and retroflection symmetry (combination of a rotation and a reflection – a special type can be helical symmetry) and scale symmetry (where enlarging or shrinking does not change an object, for example, in the case of fractals).Translational symmetry – when a 2D or 3D object can be translated (moving every point of the object by the same distance and in the same direction) resulting in no apparent change.Rotational symmetry – A 2D object has rotational symmetry if the object can be rotated about a fixed point by a certain angle resulting in no apparent change.Reflective symmetry – A 2D object has reflective symmetry if there is a line going through it which divides it into two pieces that are mirror images of each other.More specifically, it means that after you transform the object it looks exactly the same as its original version. Mathematically speaking we say an object is symmetric if it is invariant with respect to a transformation. What is symmetry? How does a young child perceive it? Here is a definition of symmetry from the Merriam Webster’s dictionary – Symmetry is the property of correspondence in size, shape and relative position of parts on opposite side of a dividing line or median plane or about a center or axis. Let us understand the basics of symmetry first. Have you noticed that they have intuitively replicated the symmetry distributed everywhere in nature? In the first drawings of a child, we often see flowers, butterflies, leaves and so on.
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