grade V

In this section we all are going to discuss about geometry help and lines of symmetry which are usually studied in grade V. Here I am going to tell you the best way of understanding these topics.Now let us start with basics about geometry:
Geometry is on the whole about the points, lines, angles, areas, volumes etc. And to learn it we should keep some points in our mind. A point is represented as a dot in a plane, a line is described as the collection of points, a line does not have any end point, a line segment is a part of line that has two end points, a ray is defined as a line which starts from a point and extends in a direction forever, when two rays start from same point then they form an angle between them, plane can be defined as a flat surface that extends forever. Triangle, circle, quadrilateral, polygons etc. are the examples of geometrical shapes.
Now let us talk in detail about Lines of symmetry. When an image or a figure is folded from the middle and if the half part is completely symmetric to the other half part or in other words one half part is mirror image of the other part then that figure or image is said to be symmetric. And when you unfold that figure or image you will see a line of crease, that line is known as line of symmetry. Let’s see lines of symmetry of some shapes.
Lines of symmetry of triangles:
In a triangle we can have 3, 1 or 0 number of lines of symmetry.
                          
Equilateral triangle ( having all sides and angles equal )
It has 3 lines of symmetry.
                     
Isosceles triangle ( having two sides and angles equal )
It has 1 line of symmetry
                
Scalene triangle ( having no sides and angles equal )
It has no lines of symmetry

Lines of symmetry of quadrilaterals:
There are many types of quadrilaterals

                 
Square ( having all sides and angles equal and also all angles are 90 degrees )
It has 4 lines of symmetry.
         
             
Rectangle ( having opposite sides equal and all angles are 90 degrees )
It has 2 lines of symmetry.

            
Irregular Quadrilateral
It has no lines of symmetry

                  
Kite
It has 1 line of symmetry.

                     
Rhombus ( having all sides equal in length )
It has 2 lines of symmetry.

Lines of symmetry of regular polygons:
In a regular polygon we have all sides and angles equal to each other.

                                       
Regular Pentagon ( having 5 sides )
It has 5 lines of symmetry

                 
Regular Hexagon ( having 6 sides )
It has 6 lines of symmetry

               
Regular Heptagon ( having 7 sides )
It has 7 lines of symmetry

                  
Regular Octagon ( having 8 sides )
It has 8 lines of symmetry

Lines of symmetry of circles:
A circle has infinite number of lines of symmetry and the lines of symmetry must be go through the radius of circle.

              

In upcoming posts we will discuss about Probability and Statistics. Visit our website for information on syllabus of economics for ICSE class 12

How to Sketch Transformations?

Hello friends,Previously we have discussed about properties of rational numbers and now Sketching transformations which sometimes become a tough task and we need a continuous practice and hard work to understand this intersting and a bit complex topic. Here I am going to tell you the best way of understanding Sketching Transformations with geometry help. And this is for grade V of gujarat secondary education board. In basic transformation geometry there is two basic types that are rigid transformations and non-rigid transformations. And also there are three types of rigid transformations known as translations, reflections and rotations. In other words, a transformation is a copy of a geometric figure and copy holds certain properties. Let’s take a simple example when we copy/paste a picture on our computer. Then the original figure is called the pre-image and the new copied picture is called the image of the transformation. The rigid transformation is one in which the pre-image and the image both have same size and shape. In simple word transforms means to change. In geometry, a transformation changes the position of a shape on a coordinate plane. That means shape is moving from one place to another
 Translations: - The definition of a translation is every point of the pre-image is moved the same distance in the same direction to form the image. Let’s take an example of triangle each point of triangle is translated or moved 6 inches to the right and 4 inches up.In this case, the rule is 6 to the right and 4 up.  You can also translate a pre-image to the any combination of two of the four directions.
The transformation for this example would be T(x, y) = (x+6, y+4).
Reflections: - is a flip of an object over a line. The example of Reflection is given below. This will helps you to understand Reflection.(want to Learn more about Transformations,click here),
Reflection in the coordinate plane over x-axis: -    T(x, y) = (x, -y).
Reflection in the coordinate plane over y-axis: -    T(x, y) = (-x, y).
Reflection in the coordinate plane over line y = x: - T(x, y) = (y, x).
Rotation: - In rotation (turn) a letter can turn on a point away from its original position. When we watch the T move it turns in place so that it now looks like it is lying on its side and almost look like a clock hand turning around the face of a clock.
Scaling: - Scaling is a linear transformation and the scale factor is the same in all directions. It is also called dilation and the result of uniform scaling is similar to the original.
When one shape can become another using Turns, Flips and/or Slides called Congruent.
Resizing: - The other important Transformation is resizing. In resizing the shape becomes bigger or smaller.
Similar or Congruent: - In Similar or Congruent if one shape become another using transformation, the two shapes might be just similar.

Translation of points: -
A point (p,q) can be moved to another position by applying a column matrix vector.
 The column matrix vector is just two numbers, one above the other surrounded by long brackets. The top number adds to the p-coordinate while the bottom number adds to the q-coordinate.
From the above I hope it would help you to understand Sketching transformations, geometry and if anyone want to know about Problem solving strategies and also on Estimating probability then they can refer to internet and text books for understanding it more precisely.

Math Blog on Grade V

Hello Friends,Previously we have discussed about list of rational numbers and today we are going to learn about the mathematics of the grade V of indian certificate of secondary education board. We will learn about some few discussion of syllabus of fifth standard mathematics. Grade V is the level of learning, after that the schooling ends, so these are the end years of the school for any child.
In grade fifth, we learns about the numbers as read the number having multiple digits like 100000 and locate, represent, identify and compare such numbers by the use of expanded or regular form of them. We should have the proper understanding of the place values for 0-4 places in number to the right and left places. We should be able to perform addition, subtraction, division and division the decimals. We should have the proper understanding of converting fractions to decimals related values. We can make the selections for the strategies for problem solving and we should also have mathematical thinking in problems solving. In term of measurements we should have understanding of length unit like inches, feet, yards, miles, millimeters, centimeters, meters, and kilometers and we also the proper use of these terms in problem solving. We should have ability to make rounds accurately in measurements. In term of geometry we learn about the plane figures, solid geometry, area, surface area, volume, perimeter, and circumferences etc. so for this we have the proper understanding of coordinate system on either map or grid.(To understnd geometry in more precise manner ,click here)
The grade V also includes the learning and modeling 2d and 3d objects. We learn about different types of polygons, symmetry of planes, and sides of them. It includes the use of venn-digrams to short the shapes having curved faces and their vertices. We can identify, sort, construct, measure, and also can apply a variety of shapes and figures in the geometrical and other problems. We should have the understanding of geometric properties and their relationship. As per shapes, we can classify them, their property and type like angle and type of the triangle (isosceles, obtuse etc.) also we have to know that the same thing can also be done with the help of protractor.
The learning and modeling 2d and 3d objects includes the description of characteristics of 2D shapes and 3D objects and relation between them. We should learn about the description of sides, vertices, faces, and edges of any of the shape in the 2D or 3D geometry. Several two- and three-dimensional games can also be used to understand the concepts regarding the dimension for the purpose of extend knowledge of students' about shapes and to give them hands-on experience working with shapes. Use of such game will help us to become familiar with the names and properties of two- and three-dimensional shapes and their views.
We have to learn about the money exchange problems, date models to read and write (model like Feb. 08, 1988, 06/01/2012 etc.).We should determine the value of equations when there is some missing terms in the operations, also ability to find the missing term in the equation having more than one operation.
In grade V we should also learn about some basic problems like Tools to solve problems, probability to design surveys, collection of data. We should discuss the real world need for some type of data and collection of that data. We should go through the logical reasoning and experiment regarding that collection of data.

Math Blog on Grade V

Geometry is full of different figures and designs. If you understand geometry then it is one of the interesting math answers for the problems. In geometry we have basic geometric shapes like circle, triangle, square, rectangle, rhombus, parallelogram, etc. geometry doesn’t end. Here we also have many other advanced level of construction, since analytical geometry problems deals with shapes, its constructions and properties. Each and every geometric shape has its own well defined set of properties. Every construction of geometry problems involve some steps that has to be followed. In this article, we will focus on the very first geometrical topic of Grade V in which you will learn the basic geometrical shapes constructions like line, circle, etc.

Let's first see the construction of line: Line is a basic construction of all figures in geometry. To construct many figures in geometry we join two or more lines. In order to construct line use a ruler. Ruler is a rectangular object helps to measure the length of line in centimeter. Keep the ruler on the paper and move the pencil adjacent to the ruler on the longer side, our line is ready. Here is a diagram of line:

                      A---------------------B
Now, let’s see the construction of the triangle. Before moving to its construction let’s answer a question that what do you understand by triangle. A triangle is a closed three sided plane figure. You can easily construct a triangle with the help of ruler, compass and protractor. Since a triangle has three sides, so it also has three angles. to understand the geometry problems related to construction let's see few examples.
Example: Construct a triangle ABC in which AB = c units, BC = a units, CA = b units.
You can also take any mathematical units in place of variable a, b and c.
Steps for basic geometric construction of triangle are:
    


We are going to draw a triangle with sides a, b and c
1) Draw the line AB = c units with the help of a ruler.
2) Take a compass and measure b units using ruler.
3) With A as center, cut an arc above the line segment AB using compass.
4) Take a compass and measure ‘a’ units.
5) With B as center cut an arc above the line segment AB.
6) Both the arcs cut at a point, say C.
7) Join AC and BC. Now, ABC is the required triangle.
Example: construct atriangle with sides 5,5 and 5.
Construction:



There are several different types of triangles and you can easily construct them without facing any difficulty. If you know construction of one triangle then other can also be constructed.
My dear friends if you love dealing with shapes then no one can beat you in this game of shapes. With a bit concentration and efforts you can become master of the geometry.
In next post we will talk on Parallelism in Grade V. For more information on syllabus of economics for ICSE class 12, you can visit our website