Lines and Shapes serve as the basics to the mathematical domain known as geometry. Unlike other areas of mathematics, geometry has a visual and kinesthetic aspect to it. Geometry has always been a challenge for educators to get through to their students. The primary aim of this article is to offer various teaching strategies for teachers and educators to use while teaching geometry.
Contents
What is a Line?
It is pertinent to understand the types of lines and the applications of them. Understanding shapes is a cakewalk once lines are understood well.
A line is defined as a set of points that extend in opposite directions. It can be extended indefinitely and has no defining limit. It has no thickness. It is one dimensional. Listed below are the types of lines most used in geometry.
Line Segment
A line segment is a part of a line which has endpoints.
For example, if we consider a 15 cm scale as a line, a small portion of around 3 cm to 5 cm would be a line segment.
Ray
A ray is a line that has only one end/starting point. It extends in another direction endlessly.
For example, a ray of light coming from a torch.
Horizontal Line
A horizontal line is a ray that moves from left to right or vice versa in a
straight direction.
For example, the Horizontal Axis or X-Axis
Vertical Line
A vertical line is a ray that moves from top to bottom or vice versa in a straight direction.
For example, the Vertical Axis or Y-Axis
Parallel Lines
When two straight lines don’t meet at any point, even at infinity, they are known as parallel lines.
For example, lines of a notebook or railway tracks.
Perpendicular Lines
When two lines meet at a right angle (90o), the lines are considered
perpendicular to each other.
For example, The Red Cross symbol or the corners of two walls.
Tangent Lines
A tangent (line) is a line that touches the curve of a circle at any given point.
For example, the broadness and tallness of a building.
Secant Lines
A secant (line) is a line that meets the circumference of a circle exactly twice.
For example, used in illustrating electronic waves in different modes of communication.
Cuemath, an online education portal that is revolutionizing the study of mathematics and coding believes that even a simple concept like lines can have multiple interactive and smart approaches. Cuemath’s approach is highly personalized according to a student’s strengths and weaknesses.
To learn more about lines, click here. .
What are Shapes?
Shapes are made by using a combination of lines and points.
There are two categories of shapes.
1. Two Dimensional Shapes (2D Shapes)
2. Three Dimensional Shapes (3D Shapes)
While these two are the broad categories of shapes, listed below are two other types based on their symmetry.
1. Regular/Symmetrical Shapes
2. Irregular/Asymmetrical Shapes
Shapes that can be represented by a combination of lines and points on the X and Y planes are known as 2D shapes.
| Shape Name | Sides | Edges | Vertices | Angles | Examples |
| Triangle | 3 | 3 | 3 | Sum of Internal Angles = 180° | Pizza Slice, Pyramids of Giza, Road Signs |
| Square | 4 | 4 | 4 | Vertices, meet at 90° | Chessboard, Coasters, Keys on a keyboard |
| Rectangle | 4 | 4 | 4 | Vertices, meet at 90° | License Plates, Playing Cards, Indian Rupee Notes |
| Circle | 0 | 0 | 0 | ND | Coins, Pizza, Wheels |
| Semi-Circle | 2* | 2* | 2 | 2 angles at the ends of the straight edge forming a 90° angle. | Chinese Fans, Umbrella, Bowls |
| Parallelogram | 4 | 4 | 4 | Opposite angles are always equal (supplementary angles) and add up to 180°. | Neck of a Guitar, United States Postal Service Symbol |
| Rhombus | 4 | 4 | 4 | The opposite angles of a rhombus are equal. (Congruent Angles) | Kites, Baseball Field, Jewellery |
| Trapezium | 4 | 4 | 4 | Sum of all angles is equal to 360° | Handbags, Bridge Truss Supports, Popcorn Tins |
* Semi Circles have 1 straight side/edge and 1 curved side/edge.
Polygons are shapes with more than 5 sides. Some examples of polygons are,
1. Pentagon
2. Hexagon
3. Octagon
4. Nonagon
5. Decagon
Three Dimensional Shapes (3D Shapes)
3D shapes are represented on the x,y and z planes.
| Shape Name | Faces | Edges | Vertices | Angles | Examples |
| Cube | 6 | 12 | 8 | All vertices meet right angles. | Rubik’s Cube |
| Cuboid | 6 | 12 | 8 | All vertices meet right angles. | Matchbox |
| Cone | 2* | 2* | 1 | Angle at the Apex Θ = LR | Ice Cream Cone |
| Cylinder | 3** | 3** | 0 | In a right cylinder, the axis is perpendicular to both bases | Pringles Chips Can |
*Cone has 1 curved face/edge and 1 straight face/edge.
**Cylinder has 1 curved face/edge and 2 straight faces/edges.
This topic is vast and has a lot of scope in fields like design and architecture.
So it is important for the students to have a clear understanding. For this reason, at Cuemath, lessons are made as informative and interactive as possible. Enrol in Cuemath to shape your child’s math in the right way. Learn Math the right way with Cuemath.
Strategies for Teaching Lines and Shapes in 2020
While we are in the middle of a pandemic, teachers have had to take innovative approaches to teach online. Here have come with some strategies for teachers to follow which are internet friendly.
- Math Yoga
Exercise and Education together in one activity. In this activity, the teacher will ask students to form various shapes with their bodies. This way students are using their very own bodies as a medium of understanding. It is a fun activity and can be done over video calls.
- Stationary Games
In this activity, students just need standard stationery. They are expected to form various shapes using their stationary. Whether crayons or markers or pens, this activity can be done remotely.
- Geometry Scavenger Hunt
In this activity, students have to find various shapes around their house within a specific amount of time. It is a good way to start the day as it is a true adrenaline rush. Students have to run through the house and find all sorts of shapes.
- Extension
In a way, our bodies are extensions of various shapes. Ask students to draw their bodies in the form of shapes. The more elaborate the drawing and shapes, the higher the child’s marks.
- Geo Quiz
A very often asked question inexams and Olympiads is the number of the sides, edges and vertices in a shape. Despite it being such a popular question, students have problems recollecting the information. A terrific way to cement this information is a quiz based on geometry. A rapid-fire round about all information about shapes is a fun and powerful way to strengthen a student’s foundation.
- Sorting Shapes
On shopping sites like Amazon, many shape sorters are available which students can use to sort various shapes and put them into their respective slots. This helps students give a good practical approach to shapes and a more elaborate understanding.
- Drawing and Coloring
Often adopted by art teachers, these are activities that help students come in touch with their artistic side while also learning something new. Showing popular artists’ works that are made of shapes helps too, like Kandinsky’s.
- Make a Shape Collage
In a piece of paper, ask students to fit as many shapes as possible. This way students will learn how to manage shapes and learn concepts like congruence and symmetry.
- Sorting Household Objects
In this activity students will sort objects, they use on a day to day basis, according to shapes. This can help them in their understanding of the subject and might prove useful to their moms too!
- Play Dough
Every child owns a play dough set and needs to be put to better use than making shapeless blobs. Play Dough can be used to give children a better understanding of shapes and they can get as creative as possible by playing with them.
- Baking
While this is not an activity that a teacher can demonstrate in the class, parents can help to do this by using children’s help while baking. Baking is an art of precision and involves shapes of all sorts. This way children get to learn something and make their tummies happy as well.
- Animated Movies
Ask students to watch animated movies and spot all the different shapes in the movie. This is a fun activity that the parents and kids can do together.
Cuemath has been providing its game-changing services for students across the world. With a unique approach of making students understand a concept instead of rote memorization, Cuemath makes sure students learn math the right way.
Conclusion
Don’t let learning online become a boring activity. With these strategies, you can rest assured that your students are getting the best lessons sitting in the comforts of their homes.
