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Foundation Math

A grade that encompasses every branch of high school mathematics, from Geometry to Probability.

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 Saturday 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.

COURSE DELIVERY

SYLLABUS FOR 7TH-CBSE

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

CHAPTER 1: INTEGERS

An introduction to integers and operators like addition, subtraction, multiplication, and division on them.
Next for the first time, closure, commutative, and distributive properties are discussed with integers on the four major arithmetic operators considered above.
Finally, the concept of additive inverse.

CHAPTER 2: FRACTIONS

Fractions have been introduced since 5th grade and their understanding is key to comparing quantities.
Fractions are all the numbers that can be represented on the positive side of the real number line.
The others are negative fractions which together with fractions make Rational numbers.
Different types of fractions.
Addition and Subtraction of fractions along with word problems.
Finally arithmetic on decimals with multiplication and division limited to powers of 10.

CHAPTER 3: DATA HANDLING

The chapter introduces the purpose and stages of representation of data for analysis.
Here they also introduce the concepts of mean, median, and mode. These are important for arriving at a value that can represent the data set as the average in common terms.
This foundation will help you with statistics till 10th grade, only the dimension of data changes.
Here you are dealing only with discrete data which are only a set of data points without frequency.
Next, we have bar charts taken in detail.
Finally, the concept of probability is taken using theoretical analysis rather than statistical data.
This requires counting of outcomes favoring the event and the total number of outcomes. The ratio between these two quantities is the probability of the event.
Questions in this grade are simple and only in senior school, you would need counting tools like permutation and combination to arrive at the answer.

CHAPTER 4: SIMPLE EQUATIONS

Here the first chapter on Algebra is on simple equations before moving into the chapter on Algebraic expressions.
Solving simple equations which are linear in one variable, will help you connect with the subject, if you are trained to solve the equations using balancing, before transposing at the time when it is required.
Finally, you have word problems that test your comprehension to convert a problem in words to a simple algebraic equation and finally arrive at the solution.

CHAPTER 5: LINES & ANGLES

Here we start with the introduction of Euclid’s geometry.
Basic elements like points, lines, angles, and planes are defined as in Euclid’s version to start with, which he calls basic definitions.
Next, different types of relationships between angles like complimentary and supplementary angles.
From this we look at more relationships when two lines intersect.
And finally when two lines are intersected by a transversal and a special case when the lines are parallel.

CHAPTER 6: TRIANGLES AND PROPERTIES

All polygons can be divided into triangles and hence study of triangles is given a lot of importance in High school Geometry.
Even the study of parrelograms starts by dividing the triangle into two congruent triangles.
First, we need to understand all the types of triangles that can exist based on sides and angles.
Now here we study two important theorems on triangles based on the theorems that were taken in the previous chapter.
These are the Angle sum property and Exterior angle property which will be crucial in studying further theorems in triangles and quadrilaterals.

CHAPTER 7: CONGRUENCY OF TRIANGLES

Now every person with a mathematical bend would be aware of patterns around him and excited about congruent ones.
Now since every polygon can be divided into triangles, studying the congruency of triangles can singularly help us identify the congruency of the figure in total.
Now here 5 major rules that help to simplify arriving at the congruency of triangles, which otherwise would need a lot of information to connect the equality of all three sides and angles.

CHAPTER 9: RATIONAL NUMBERS

Finally, we complete numbers that can represent any point on the negative side of the number line.
Now, when either the numerator or denominator of a rational number is negative, then we have fractions that are negative, and hence along with standard fractions, they complete the set of rational numbers.
The real numbers also have irrational numbers taught only from 9th grade.
Starts with the representation of rational numbers on the number line and further finding rational numbers between two rational numbers.
Finally, all four operators on Rational numbers.

CHAPTER 10: PRACTICAL GEOMETRY

Here we study how to construct two important figures. One is a line parallel to it through a point outside the line. This is very important in Euclid’s geometry, where the 5th postulate says that parallel lines are always parallel, until the 18th century, when spherical geometry for map making showed that longitudes at the equator that were parallel met at the poles.
Finally, five types of inputs, the same as the rules for congruency, can be used to construct a triangle is discussed.

CHAPTER 11: PERIMETER & AREA

Starting with the areas of rectangles and squares which are just like multiplying units of a bar of chocolate.
Next calculate the area of different types of a triangle by dividing a square, rectangle, and parrelogram.
Next, circles.
Finally on units, conversions, and how application questions.

CHAPTER 12: ALGEBRAIC EXPRESSIONS

Now till 6th grade, a student had to deal with simple equations of linear equations in one variable.
Now here he is subjected to algebraic expressions, which have different variables, different degrees, different terms, etc.
The student would have to deal with the most abstract forms of mathematics for the first time in his life, which cannot be mapped into any practical problem.
It is easy to explain expressions that are linear and quadratic in one variable through examples in Physics.
Finally addition and subtraction of these algebraic expressions and application of formulas for calculating areas and perimeter.

CHAPTER 13: EXPONENTS & POWERS

Exponentiation is the next operator we deal with in high school.
When you multiply a number n by p times, the number n becomes the base and p becomes the power or exponent to which the number is raised.
In this grade, we deal only with non-zero exponents and hence avoid fractions which is a special case known as extraction.
For eg. When the exponent is 2, we are squaring the number or multiplying the number twice. And now, when the exponent is 1/2, we are dealing with square roots, taken in 8th grade.
The crux of the chapter is to understand and apply five important rules for exponents to simplify arithmetic problems.
This concept is introduced in a student's life for the first time.

CHAPTER 14: SYMMETRY

It deals with line symmetry and rotational symmetry.
This is an activity-based chapter supported by project works
This chapter is mostly deleted.

CHAPTER 15: VISUALISING SOLID SHAPES

Today we are talking about 4-dimensional Space-Time and most of us are not even able to visualise 3-D objects in space.
This chapter helps to visualize three-dimensional objects through oblique and isometric sketches to give a better understanding of 3-D shapes.

CHAPTER 8: COMPARING QUANTITIES

To compare two quantities of the same type we just need to express it as a fraction for solving algebraic problems.
Now, fractions are difficult to understand. Hence ratios which are the most simplified version of a fraction of two non-co-prime numbers are taken since man inherently is able to compare two small quantities.
Percentages help to even simplify these fractions for the common man who has been encountering percentages from an early age.
Finally application of these concepts in profit & loss, and simple and compound interest.

COURSE SUMMARY

50% of the course will be on the set of Rational numbers, the four major operators, and their properties on all sub-sets of Rational numbers. Ratio & Percentages in Applications, Ratios and Variations in Applications.
20% of the classes on Algebra and 20% on Geometry.
The rest of the classes are on Mensuration.
Will try to have a session on a case study of Statistics & Probability. And use dice and cards for a fun session on Theoretical Statistics.