Class Till IInd : Till class IInd the students face the problem in addition & Subtraction & the teachers in the schools follow the procedure of finger counting where the students do silly mistakes. A child gets into a habit of finger counting from the time he starts getting familiar with the numbers. He starts his journey of counting by representing numbers with lines & over a period of time from adding or removing lines on paper he starts using fingers.
|Course Duration||One Years
Once a Week
Outcome of the Course
Class IIIrd to VIth : These students work on Numbers & the Concepts of Unitary Method Students know numbers till 1 lakh or more but are not able to relate different Units & are not aware of what unitary method is?
For Eg :– There are three Questions
- A) 5 pen cost Rs.10, what is the Cost of 1 pen ?
- B) 5 men can complete a work in 10 days. In how many days 1 man can complete it?
- C) 5 clothes take 10 hours to dry off. In how much time 1 cloth will be dried off?
Question (A) has answer as 2 Rs
Question (B) has answer as 50 days
Questions (C) has answer 10 hrs
Look like the same but have different Answer. We work on the fundamentals. So that the student understand the same logically.
Outcome of the Course
Class VIIth to Xth : Once the students are clear about numbers & unitary Method then they face the problems in questions concerning T & W & percentage. There can be various thought processes through which student can solve the problem so the student should know all the methods & should be Capable of applying the right thought at the right question.
For Eg:- Different thoughts applicable to the questions of Time & Work
A can complete the work in 12 days while B can complete it in 15 days. They start the work together but A left after 4 days. In how many days the work will be completed.
The First Thought
A’s one day work = 1/12 and B’s one day work = 1/15
Combined one day work of A and B = 1/12 + 1/15 = 5+4/60
4 days work of A & B = 4× 9/60 = 3/5
remaining work = 2/5 which B alone can complete in 15 × 2/5 = 6 days
Hence, the total no. of days = 4 + 6 = 10 days
The Second Thought
A did the work for 4 days while B did the work for (4+x) days or
Fraction of the work completed by A + Fraction of the work completed by B = 1
4 + (x+4) = 1 or (x+4) = 1 – 4 or x = 6
12 15 15 12
so total number of days they take to complete the work = 4 + 6 = 10 days
The Third Thought
Let we say that the total work is putting 60 bricks from 1 place to another so A can put 5 bricks per day while B can put 4 bricks per day. In one day they can put
(5 + 4) = 9 bricks.
In 4 days they can put 4 x 9 = 36 bricks.
No. of Bricks left = 60 – 36 = 24 which B alone can put in 24/4 = 6 days.
Total No. of days = (4 + 6) = 10 days.
Class XIth to Xth : Once the students are aware of Conceptual Maths then calculations and analysis play a major role and the better the calculation, the better is the understanding and student can qualify any competition they want whether IIT/IIM’s or So.
lThe difference between the squares of two consecutive numbers is the sum of two numbers. Example
–As 40 & 41 are consecutive numbers so the difference in their squares is 40+41=81
l51² = 50²+(50+51) = 2601
l61² = 60²+(60+61) = 3721
l71² = 70²+(70+71) = 5041
l81² = 80²+(80+81) = 6561
l39² = 40²-(40+39) = 1521
l49² = 50²-(50+49) = 2401
l59² = 60²-(60+59) = 3481
l69² = 70²-(70+69) = 4761
l79² = 80²-(80+79) = 6241
lThe number having 5 as a unit digit always have 25 as the last 2 digits & the tens digit of the number has to be multiplied by the next consecutive number.
35² = 1225 3 is multiplied by 4 and 25 as
the last 2 digits
45² = 2025, 55² = 3025, 65² = 4225, 125² = 15625
and so on.