A one-dimensional figure which has length and no width is known as a line. It is constructed using a set of points which extend infinitely in opposite directions. It has no ends.
Some of the basic types of lines are listed here:
●Horizontal lines: Extend from left to right.
●Vertical lines: Extends from top to bottom.
●Parallel lines: Straight lines that never meet or intersect when extended infinitely in both directions
●Perpendicular lines: Straight lines intersecting at a right angle (90 o).
A portion of the line with two definite endpoints is called a line segment. It always has clearly defined starting and ending points.
A portion of the line which has one starting point with no endpoint is called a ray. It extends infinitely in the other direction.
WHAT ARE SHAPES?
A shape is a form of an object or its boundary. There are several types of shapes. Few examples of two-dimensional shapes are circles, triangles, polygons, etc. In solid geometry, examples of three-dimensional shapes are cube, cuboid, cylinder, etc.
Lines, points and angles are used for drawing a shape in geometry. For example, a square is a shape which is composed of four points that make up the vertices of the square. The four sides are constructed using four lines, and these lines intersect each other at a 90 o angle.
Shapes and Lines form the basics of Geometry, and hence, learning about them is imperative. There are several sister subjects which are based on these concepts such as surface areas and volumes, integration, differentiation, etc. Thus, teaching and studying become complicated for a vast subject like this. Moreover, visualising shapes and solving problems is a pain point. In this article, we will go over five methods which could potentially help the learning process.
METHOD 1: GET THEM INTERESTED
The topics that have so many tributaries make it difficult to focus on. Hence, with such wide-ranging topics, students need to be motivated before starting the subject. The best way to introduce a topic is to present it in the form of a story, as that garners attention. A lot of these topics are introduced to students at a very young age, hence associating it with some interesting facts or history can leave a long-lasting impression throughout their lives.
Let’s talk about some History!
A line with negligible width and depth, in ancient times, was introduced as a way to represent and study straight objects. One of the most distinguished mathematicians, Euclid, who is often referred to as the founder of Geometry, describes a line as “breadthless length" which "lies equally with respect to the points on itself”.
He introduced several postulates around which he constructed Geometry, which is also sometimes referred to as Euclidean Geometry. Around the 19th century, other types of Geometry were also introduced, such as Non-Euclidean geometry, Projective and Affine Geometry. Lines may have multiple meanings across various branches of Geometry. However, in this article, we will only talk about a line in terms of Euclidean Geometry.
Speaking of shapes, Archimedes has been credited with introducing the formal concept of volumes as he was the first one to introduce the formula for the volume of a sphere.
Geometry is one of the oldest branches of mathematics, and its origins can be traced back to the 2nd Millenium BC in Mesopotamia and Egypt.
Tracing the colourful history of Geometry can be a fun session for both the teacher and the student. It helps in sharing knowledge and invoking interest in the subject.
METHOD 2: GIVE THEM VISUALS
Learning about lines, shapes and Geometry goes hand in hand with visuals. Hence, building up a student’s visual power is a key step in teaching them any of these topics. You can make use of a variety of videos for this purpose. Using interactive apps is also an excellent way to teach students. By using such apps, a student may find it easy and exciting to perform investigations on a particular shape and reach logical conclusions.
This method is usually beneficial while solving problems on volumes and surface areas of different shapes. For simple shapes such as cuboids or cylinders, it’s easy to find solutions to simple problems. However, when complicated questions are framed on simple shapes, or the shape in question is itself complicated, finding solutions becomes a problem. In such a situation, the best tool that you can arm your students with is the power of visualisation.
By teaching students to approach a problem by way of visualisation, you pave way for them to solve questions of any level of difficulty in a better manner. Thus, helping students visualise is an essential and highly recommended step in the learning process.
METHOD 3: PLAY A GAME
Geometry and other topics associated with it have several postulates, axioms and formulas. All students must know the theorems and the derivations associated with each of them. However, during an assessment, students do not have the time to derive a formula or a postulate. Hence, they are required to retain these formulae and theorems in their memory. After explaining the origins of the theorems, you can play a game to help them remember all the relevant formulae.
A simple template can be used as a guideline to come up with a game as follows:
●Assign a topic such as lines, triangles, cuboids etc.
●Give them a few days to prepare well.
●Have a rapid-fire game with students. One student can ask all the teams/individuals a question. The student answering the question fastest gets a chance to pose the next question. The questions can be based on theorems, applications of theorems, small computations based on formulae or general trivia or facts.
●You can act as the referee to check who answers the fastest and has the most accurate answers.
This helps students to learn a topic while having a good, enjoyable experience. It helps in endorsing healthy competition among the students and in team building. It enhances their thinking abilities and precision while answering questions.
METHOD 4: USE REAL OBJECTS
While studying 2D and 3D Geometry, it’s best if the problems are related to real-life objects. Inter-associations also helps.
For example, show students how to construct a simple 2D figure such as a rectangle or a polygon using lines, angles and points. Furthermore, you can trace out the rectangle on a piece of paper, cut it and roll it into a 3D cylinder. This is an excellent method to ensure that the students have good clarity in the concepts.
This method of association and usage of real objects is very useful while teaching topics such as surface areas and volumes. After introducing the basics of a concept, you can ask students to perform computations on real-life objects like a water bottle or a laptop. Usually, regular objects, that we use in our day-to-day lives, are made of different shapes. So, by approaching complex questions with the help of visualisation techniques, students will be equipped to tackle any challenging question.
Another approach is to use computer programming languages such as R, MatLab, Python, etc., to perform simulations. It aids students in learning about coding as well as the topic at hand. Using these languages has the added advantage of displaying solutions with graphics. Inclusion of graphs and drawing conclusions develops a student’s analytical abilities.
METHOD 5: EXTERNAL HELP
Teaching what is required for the school curriculum, adding history, facts, as well as coding to supplement the learning process, while adhering to the academic schedule can become a little stressful. Hence, to aid this process, taking help from an external source is a good idea. It helps to organise yourself better while conveying information in a comprehensive way and meeting deadlines. You can turn to an online learning platform such as Cuemath Program to help you out.
Cuemath provides a plethora of coding and mathematical resources for students belonging to grades 1 to 10. Math boxes and internal apps help with the visualising process. Worksheets and workbooks help in practising all that the student was taught. You can also check a student’s progress on their app. This helps in giving a better understanding of a student’s problem areas to focus on them. This way, no student is left behind, and everyone has a clear understanding of the basics.
Focussing on all areas of development of a student is very important, and by following these methods, you can provide the best quality of education to a student. These methods aren’t just restricted to an educator. Anyone who is looking to learn about lines and shapes can tailor these methods to suit them.
Learning is the main aim, no matter the age. All one needs is motivation and interest to accomplish any feat. Open your minds to this wonderful topic, and hopefully, you get inspired to learn more about Geometry.
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