Properties of Two-Dimensional Figures

Properties of Two-Dimensional Figures

 

Introduction

Mathematical concepts and knowledge should be imparted using relevant and realistic contexts instead of trying to impart fixed body of knowledge to students for better comprehension. Construction of individual mathematical meaning through rising levels of abstraction, exploration of personal experiences, comprehension and knowledge should be used to enable learners acquire and understand mathematical concepts (Annenberg Learner, 2013). Usually, in most cases students’ construct meanings based on their past experiences and interactions with objects and ideas. Therefore, it is necessary for teachers to include active learning processes like interaction with manipulative, conversation engagement with others, concrete models usage, and technological tools in learning to enhance mathematics comprehension (Beckmann, 2013).

Regular two-dimensional shapes include equilateral triangle, isosceles triangle, right-angled triangle, scalene triangle, quadrilateral, rectangle, square, oblong, parallelogram, rhombus, trapezium, kite, pentagon, hexagon, octagon, decagon, and circle among others (Van et al., 2013). These figures have properties in terms of number of sides, length of sides, lines of symmetry, rotational symmetry, angles, congruency, and perpendicular or parallel lines.

Concrete model

Angle marker concrete model is a simple way of teaching students the different types of angles that diverse two-dimensional figures form (Stefan et al., 2012). Two-dimensional figures have different angles at their vertices. To enable students easily understand the different angles found in different shapes, they require cardstock strips and brass fasteners. These materials will be used to replicate angles found on real objects like hands of analog clocks, corners of rooms, corners of playgrounds, or even open pair of scissors.

Normally, an equilateral triangle has three equal sides with three equal angles (Beckmann, 2013). Therefore, joining three equal cardstock strips together using three brass fasteners forms an equilateral triangle. If those jointed cardstock strips are to be cut into equal halves without changing the angels they had formed then joint at a point, you realize they form a complete circle of 360degrees comprising equal angles. Otherwise, students can also measure the three angles formed by joining cardstock strips of equal length using their mathematical set tools. Looking at the angles formed, it is clear they are less than 90 degrees therefore the equilateral triangle has equal acute angles. If the three angles formed total to 360 degrees then each of the acute angles clearly has 60 degrees (Learner, 2013).

Isosceles triangle has two equal sides with two equal angles, one line of symmetry, and no rotational symmetry (Van et al., 2013). From the equilateral triangle formed above, remove any one of the three sides and replace it with a shorter or longer cardstock strip. Using mathematical set apparatus, students can measure all the three angles now formed. Students can also cut each of the strips into half and the three angle-like pieces formed on-top of each other. They will realize that two of those pieces form equal angles while the other piece has a different angle. Depending on the triangle formed, a right-angled triangle can be an isosceles triangle whereby the different angle has 90 degrees therefore forming a right angle (Stefan et al., 2012). In an otherwise scenario, the different angle is greater than 90 degrees hence forming an obtuse angle. However, all three angles formed total to 360 degrees which can be shown through joining the three different pieces at a point (Laureate Education (Producer, 2013).

Scalene triangle has three sides with different lengths, three different angles, no lines of symmetry, and no rotational symmetry (Beckmann, 2013). From the isosceles triangle formed above, remove one of the two cardstock strips with equal length and replace it with another strip of different length from the other two strips. If the strips are cut into equal halves without changing the angles formed then all three angular pieces placed on top of each other, you discovery that they have different angles (Stefan et al., 2012). This kind of triangle, in most cases, comprises acute and obtuse angles of different degrees. Taking one of the cut pieces that form an acute angle, right-angle or obtuse angle and looking at the exterior part of the vertices, students will see that the angle formed is greater than 180 degrees (Learner, 2013). This is the reflex angle.

 

 

Technology tool

Microsoft office PowerPoint Slide Show is a relevant technological advancement tool that can be used by teachers to enhance study of properties of two-dimensional figures. This tool together with projectors in class rooms can be used as a pictorial model of study (Van et al., 2013). Usually PowerPoint Slide Shows use concise, brief, and precise language together with well elaborated diagrams and pictures to outline different properties of two-dimensional shapes. Each slide will comprise a particular shape whether equilateral triangle with double lines on each line to show they are equal and curves on all three angles to also show they are equal (Learner, 2013). Beside or below the diagram depending on a slides format, characteristics of that shapes will be clearly outlined.

Conclusion

Concrete models and technological tools play a major role in enhancing excellent comprehension of mathematical facts (Beckmann, 2013). Mathematical details are diverse and to some extent difficult to understand and remember. Therefore, teachers need to incorporate these models and tools during learning to increase students love for mathematics, ease learning, and promote high level of understanding.

 

 

References

Annenberg Learner. (2013). Teacher’s lab: Shape and space in geometry. Retrieved from www.learner.org/teacherslab/math/geometry/

Beckmann, S. (2013). Mathematics for elementary teachers with activities (4th ed.). Boston, MA: Pearson.

Laureate Education (Producer). (2013e). Two-dimensional figures [Video file]. Retrieved from https://class.waldenu.edu

Stefan, M. L., McManus, G. E., Dickey, A. L., & Arb, M. S. (2012). Defining supports geometry. Mathematics Teaching in the Middle School, 18(2), 92–98.
Defining supports geometry by Stefan, M. McManus, G., Dickey, A. & Maxwell, S.A., in Mathematics Teaching in the Middle School, Vol.18, Issue 2. Copyright 2012 by National Council of Teachers of Mathematics. Reprinted by permission of National Council of Teachers of Mathematics via the Copyright Clearance Center.

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson.

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