Understanding Translation, Symmetry, Geoboard, and Pythagorean Theorem

Problem solving approach to mathematics
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1 What is translation?
Translation is a transformation that occurs when a figure is moved without changing its size, form or emphasis from place to place.
Example: This transformation shifts the 5 units and 3 units of the parallelogram to the right. Written in (x, y) the value of (x+5, y+3).
Translation should be taught to students by presenting them with a form on a graph and sketching a translation, such as x+2, y+3 (Musser et al., 2018). Have pupils trace the distance from each location and ask if they have seen a trend. Students should realize that every point went up two places and up three spaces.
Translation may be used while moving an airplane across the sky. A tap sewing with a sewing machine has a lever action.
2 What is symmetry?
Symmetry says that whether moved, turned or flipped, one form is identical to the other. If a circle is used, any line in the middle of the circle is a symmetry line. The number of symmetry lines is unlimited. Basically, if a figure appears the same up-side down, it exhibits point symmetry. (A rotational symmetry of 180 degrees or order 2 may alternatively be represented as point symmetry).
Example of point symmetry: You would have created an example of point symmetry if you went to the mirror and touched the mirror with your finger (Musser et al., 2018). The spot is exactly where your finger contacts the mirror. It's like you have your image linked. This is the key idea of point symmetry.
Example of line symmetry:  Imagine that the two triangles produced after the intersection are the right-angled triangles, if we split an equilateral triangle into two equal halves. There are several more instances for line symmetry such as square, rectangle and circles.
Once you talk about how the wings fit, introduce the term "symmetrical." Once you get the concept (Musser et al., 2018). If it can be divided into 2 mirror-image parts, explain that there is symmetry. For instance, a butterfly is symmetrical, since you can fold an image halfway and observe that the two sides match.
In order to comprehend molecular vibrations, symmetry and group theory may be used. This is especially helpful for estimating the amount of peaks anticipated of a certain chemical in the infrarot (IR) and Raman spectrums.
3 What is a geoboard?
A geoboard is only one of several mathematical manipulations to promote a conception of mathematics. Geoboards allow users to manufacture various dimensions of the same form and to insert fractions of square units (Musser et al., 2018).  Geometric language starts to take form when pupils get involved in languages like scalene, isosceles and the right triangle and study various triangles.
The simplicity of this tightrope grid is the basis of its mathematical strength and flexibility. Students are invited to try out forms, to change the sides' lengths and the angles. It teaches you t...