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FOUNDATION MATH

A foundational course for upcoming higher grades, where you'll engage with abstract branches like Algebra and Trigonometry.

SYLLABUS FOR 8TH GRADE CBSE

For those serious about this course, we recommend viewing on a laptop for the best experience.

COURSE DELIVERY

  • A 12-day course over 12 weeks starting at the earliest from June for a batch of a maximum of 8 students.

  • The course will be on Friday from 4 pm to 7 pm.

  • Importance will be given to conceptual understanding, projecting videos, and problem-solving from different perspectives.

  • Tests for building competitiveness and home assignments to hone a student's mathematical ability and confidence will be given for the week.

CHAPTER 1: RATIONAL NUMBERS

  • Rational numbers are the superset of all numbers we have dealt with so far, the only type of numbers outside this being irrational numbers, introduced in 9th grade.

  • Most of the chapter is based on properties of Rational numbers on the four major arithmetic operators. Properties are closure, commutative, associative, and distributive.

  • Finally represents rational numbers on the number line and also finding any number of rational numbers between two rational numbers.

CHAPTER 2: LINEAR EQUATIONS IN ONE VARIABLE

  • This chapter is introduced before two chapters based on Algebra in this grade which are more difficult and relevant.

  • It is easier to introduce the basic purpose of Algebra through these simple equations and the art of balancing before being forced to transpose.

  • We have three exercises on solving linear equations in one variable, with the complexity increasing through the chapters.

  • After each of these chapters, we have word problems 

CHAPTER 3: UNDERSTANDING QUADRILATERALS

  • It is interesting to note that the first three chapters are each based on Arithmetic, Algebra, and Geometry respectively.

  • Here we explore some properties of polygons and then move to triangles and quadrilaterals.

  • Lastly, we consider special cases of quadrilaterals: Parrelogram and special cases of parallelogram: Rhombus, Rectangle, and Square.

CHAPTER 4: PRACTICAL GEOMETRY

  • Here we learn to construct quadrilaterals depending on the information given.

  • And also special cases of quadrilaterals : parrelograms and squares.

CHAPTER 5: DATA HANDLING

  • Introduction to data handling or statistics has been dealt with from 5th grade, the complexity changing with grade.

  • Here a detailed explanation of the purpose of data, collection of data, and representation of data is given.

  • The representation of data is covered extensively through bar charts and pie charts and also problems based on it.

  • It is interesting to note that not even calculation of the mean is dealt here.

  • The last part is based on probability which is also based on Statisical data.

CHAPTER 6 : SQUARES & SQUARE ROOTS

  • This is the first time a student encounters both exponentiation and extraction of numbers, though it is limited to a factor of 2.

  • The first part of the chapter deals with square numbers and its basic properties.

  • The second part of the chapter is on square roots.

  • In between, you learn patterns of numbers which help you arrive at squares and square roots. This helps to make the chapter interesting, without which the chapter would have been very straightforward.

  • Finally the square roots of decimals and also estimating square roots.


 

CHAPTER 7: CUBES & CUBE ROOTS

  • Here we take exponentiation and extraction of a number to the next level, by a factor of 3.

  • This chapter is very straightforward explaining cubes and cube roots through mainly prime factorisation.

  • There are some application questions in the last exercise.

CHAPTER 8: COMPARING QUANTITIES

  • This is a continuation of the chapter in 7th grade.

  • It deals with ratios, percentages, percentages more, and percentages less.

  • These concepts are further used to solve problems based on profit, loss, simple interest, compound interest and finally taxation.

CHAPTER 9 : ALGEBRAIC EXPRESSION

  • Starting from a general algebraic expression and its specific properties like degree and number of variables.

  • Next addition and subtraction of algebraic expressions based on like terms.

  • Concept of multiplying a monomial with a monomial and extending that to multiplying a polynomial with a polynomial.

  • Now, in some cases, when two polynomials are multiplied we arrive at certain patterns called identities which help multiplication easier.

  • In the chapter on factorization, these identities also help to factorize a polynomial for the basic purpose of division.

CHAPTER 10: VISUALISING SOLID SHAPES

  • This chapter is often omitted.

  • Though this chapter can help a student develop spacial and directional mapping if approached through very good activities.

CHAPTER 11: MENSURATION

  • Now starting with simple shapes like triangles, squares, rectangles, and circles in the first chapter, we move to more complicated shapes like trapezium.

  • Also, questions based on polygons.

  • Finally, for the first time in a student's life, he is introduced to solid shapes: cubes, cuboids, and cylinders.

CHAPTER 12: EXPONENTS & POWERS

  • The chapter follows the same flow of concepts as in 7th grade.

  • Here for the first time, negative exponents are introduced.

  • Laws of exponents and problems based on it, at a higher difficulty level compared to 7th grade.

  • Finally, the application of exponents to standardize very small and very large numbers helps to compare between them easily.


CHAPTER 13: DIRECT & INVERSE PROPORTION

  • This chapter is based on one of the purposes of Algebra to connect the variation between two variable which is a linear variation.

  • Here we consider two cases of natural phenomena or man-made systems. Then we look at the ratio of both variables in these two cases.

  • If the ratios are equal, we say the variation is direct.

  • If we need to take the reciprocal of one of the ratios of a variable to find both ratios to be equal, we say that the variables vary indirectly.

CHAPTER 14: FACTORISATION

  • The purpose of this chapter is to divide polynomials after factorization of the numerator and denominator to have common factors.

  • Starting with simple methods like regrouping, we use identities to factorize algebraic expressions.

  • Finally, we are based on the division of polynomials.

CHAPTER 15: INTRODUCTION TO GRAPHS

  • Introduces all major graphs dealt with in high school: Bar chart, Pie chart, Histogram 

  • Introduces coordinate geometry, where we understand how to represent a linear variation on a graph paper.

  • Some practical problems are to be interpreted using graphs to help understand how algebra helps to have a better understanding of practical problems around us.

CHAPTER 16: PLAYING WITH NUMBERS

  • Some puzzles to end the text with numbers and letters representing numbers.

  • Also different symbols for operators.

  • Finally divisibility test upto 9, which you will learn that, this will help to identify whether a number below 100 is prime.

COURSE SUMMARY

  • 40% of the course will be based on the set of Rational numbers, all six operators, and their properties on all sub-sets of these Rational numbers.And tools like Ratios and Percentages for variation and other applications.

  • 25% of the course will be on Algebra, which is taken at an unprecedented level.

  • 25% of the course will be on Geometry & Mensuration, giving more importance to Geometry.

  • For rest of the days, there will be case studies for Statistics & Probability.

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