Eighth Grade syllabus

Hello friends, here I am going to discuss about the overall syllabus of eighth grade mathematics which we supposed to do. Students often think that the only purpose of figuring things out is to get the answer with the minimum amount of ado and effort. But there are certain things which student needs to follow to get the desired answer in the most optimum way. If student opt to choose shortest path or longest path to arrive an answer then there is a possibility of getting a wrong answer so students need to follow the optimum path to arrive an answer. A daily practice and hard work is necessary to arrive at an answer. The most important thing to remember is that there is no alternative of hard work.

Following are the topics which we all are going to study in eight standard.

1. Algebra : Analyzing and representing linear functions and solving linear equations and systems of linear equations.
2. Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle.
3. Data Analysis and Number and Operations and Algebra: Analyzing and summarizing data sets.

In more generalize manner, the topics to cover are

1. Integers
2. Perimeter
3. Area
4. Algebraic Expression
5. Equations
6. Perimeter
7. Fractions
8. Decimals

In Grade 8, student must focus on the following main categories:

(1) Understanding linear relationship along with proportional relationship and numerical relationship. Concentrating more on arithmetic sequences, variables sequences etc.....formulating and reasoning about expressions and equations, including molding a combination in bivariate data with a linear equation, and solving linear equations and systems of linear equations. Clinching the concept of a function and using functions to describe quantitative relationships.

(2) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem. Few of the other concepts are : Geometric concepts, triangle inequality theorem, tessellations along with graphing equations (Linear equations or non-linear equations).

(3) Analyzing and measuring 3 dimensional figures and applying Pythagorean theorem and calculating measurements of figures using formulas for measurements. In addition to these, we are also going to learn scale drawing and proportions to convert to equivalent measurements.
(4) In the number and operation category of eight syllabus, I am going to discuss about problem involving percents along with rationalization techniques used with rational numbers and scientific notations and unit rate. Understanding and formulating the properties of real numbers, estimation of solutions, numbers, sequences etc...
(5) Finally we all are going to see the most interesting topic of eighth standard that is Probability and statistics where we formulate the dependency of events and calculating conditional probability. Some of the statistics analysis like mean, mode, median along with sampling techniques.

Now I am going to discuss about the most important topics of mathematics that are Algebra, Geometry and measurements, and Data analysis, and number and operations and algebra. So start with the first section that is Algebra.
Algebra :

In the algebra section what students going to use is linear functions, and systems of linear equations to represent and analyze the information provided and to solve a variety of problems. Students just recognize a proportion (Y/X = K, or Y = KX) as a special case of a linear equation having a form of

y = mx + b, understanding the properties that the constant of proportionality (K) is the slope and the resulting graph is a line through the origin. Students need to understand that Slope of a line is a concept which tells us how a straight line angles away from the horizontal or, we can say that it describes the steepness, incline or grade of the straight line. What students need to understand is that the slope (m) of a line is a constant rate of change.  Student recognize that tabular and graphical representations are usually only partial representation (translate among verbal, tabular, graphical, and algebraic representations of functions), and they describe how such conditions of a function as slope and Y intercept appear in distinct representations. Proceeding further students need to solve systems of two linear equations in two variables and relate the systems to pairs of lines that are parallel, or are the same lines in the plane. The overall result of the above discussion is that students need to use linear equations, systems of linear equations, linear functions, and their understanding of the slope of a line to analyze situations and solve problems.

Geometry and measurements:

In this section students deal with facts and figures. Geometry is an important area of mathematics which deals with the shape, size, relative position of figures, and the properties of space. It is all about shapes and their properties. Geometry is of two types : Plane geometry and solid geometry. Plane geometry deals with the shapes on a flat surface like lines, circles and triangles ... shapes that can be drawn on a piece of paper whereas Solid geometry is all about three dimensional objects like cubes, prisms and pyramids. Students need to use fundamental facts about distance and angles to describe and analyze figures and situations in two and three dimensional space and to solve problems, including those with multiple steps. What we are going to understand or prove is that particular configurations of lines give rise to similar triangles as the congruent angles created when a traversal cuts parallel lines. Students apply this statements for the similar triangles which helps them to solve a variety of problems. Some of the problems related to above statements are to find heights and distances. They must use the facts about the angles that are formed or formulated when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students also use Pythagorean theorem and explain why it is valid by using different methods. The Pythagorean Theorem states that in a right triangle the squares of the two short sides add to the square of the long side. If we call the lengths of the two short sides “a” and “b”, and the length of the long side “c” this leads to the familiar statement

c² = a² + b²

Students apply the Pythagorean theorem to calculate distances between points in the Cartesian coordinate plane to measure lengths and analyze polynomials and polyhedra.

Data analysis and number and operations and algebra :

Here we are going to discuss about probability, conditional probability, statistical analysis etc. Probability is a way of telling or expressing a knowledge that an event will occur or has occurred. The probability of an event occurring given that another event has already occurred is called a conditional probability. Statistics, on the other hand is the practice or science of collecting and analyzing numerical data in large quantities. It is basically a study of the collection, organization, analysis and interpretation of the data. So, the two things probability and statistics together play an important role in finding out measures of central value, measures of spread of different data and this helps in comparing of two data. Both probability and statistics are interrelated with each other and play an important role in analyzing the data. Students have to use descriptive statistics which comes loaded with concepts like mean, median, and range, to summarize and compare data sets. They also need to organize and display data to act and answer questions. Comparing the information comes out from the mean and the median and investigating the different effects that changes in data values have on these measures of center. Students need to understand the most important concept that a measure of center alone does not completely describe a data set because very different data set can share the same measure of center. Students have an option to select any of the two (mean or the median) as the appropriate measure of center for a given purpose.

Angles and triangles:

Here students need to use different ideas about distance and angles, and how they vary or behave under the following situations or conditions translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. If we talk about concepts behind triangle then they need to show that the sum total of the angles in a triangle is the angle formed by a straight line. The various configurations of the lines play an important role to find out a similar triangles because of the angles created when a transversal cuts parallel lines. The another topic which students needs to work out is Volume by solving problems involving cones, cylinders and spheres. Now in next class we all going to practice each and every section of eighth grade mathematics syllabus. Starting from the Algebra section to the Probability section.