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Lesson PlanDR.V.S.RaveendraNath.

Subject: Arithmetic

Topic: Profit and Loss

Class: VIII

Apparatus: Ordinary class room apparatus

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Aim: To enable the students to know about profit and loss.i)To teach the method of finding gain or loss.ii)To teach the method of finding gain or loss percent.iii)To enable them to solve sums with the aid of the results speedily and accurately.

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Previous Knowledge (PK):The students have already read unitary method and percentage.

The following questions will be asked:1. If 9 books cost Rs.27/-, what will 4 books cost? Answer: Rs.12/-2. Find 10% of 600? Answer: 60.3. The number of students in a school has increased from 500 to 600. Find the increase percentage? Answer: 20%.

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Introduction:Everyone in this world has to earn his or her living.Some are in service, while others do independent business.How do shopkeepers earn their living?By selling articles.Do they sell articles at the same price at which they buy?No, at a higher price than which they buy.But sometimes they are compelled to sell at a lower price depending on circumstance.

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Announcement of the Aim:

Today we shall study profit and loss.

Presentation:First Stage:

To find gain or lossThe students will be made familiar with the term

‘Cost Price’ (CP) ‘Selling Price’(SP) ‘Gain’ and ‘Loss’, with examples.

Q. Suppose I buy a toy for Rs.220/- and sell it for Rs.240/-. Find the gain.

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The CP of the toy is Rs.220/- and the SP is Rs.240/-.

The gain will be 240 – 220 = Rs.20/-

But if it sell the same toy for Rs.210/-, I loss Rs.10/-

When do we have gain?

When we sell an article at a price higher than which it is bought.

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Or gain = SP – CP.

When we have loss?

When we sell an article at a price lower than which it is bought.

Or Loss = CP – SP.

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Second Stage: To find gain or loss percentage

Remya by a pen Rs.6/- sells it Rs.8/- .

Rakhesh buy a pen Rs.5/- and sells it Rs.6.

Who gain more? How can you compare their gains? The students will be told that for true

comparison in such transactions we compare gain or loss on 100.

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Matter Method

Q. I bought a shirt for Rs.250/-

and sold it for Rs.300/- . Find my

gain percentage?

CP of the shirt = Rs. 250/-

SP = Rs.300/-

Gain = 300 – 250 = 50/-

Gain on Re.1/- =50/250

Gain on Rs.100

= 50 x 100/250

Gain % = 20.

What have you to find in this sum?

How will you find?

What is the gain, etc.,

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Matter MethodQ. Rakhes bought a bicycle for Rs. 3000/- and sold after two years Rs.2500/-. Find gain or loss percentage?CP = 3000/-SP = 2500/-Loss = 3000 – 2500 = 500/-Loss on Re.1/- = 500 /3000Loss on Rs.100/- = 500 × 100/3000Loss% = 16.666….%

What we want to find?Loss %How will you find?What is given etc.,

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Give practice with three or four more sums and then arrive at generalisation.

Generalisation:The following generalisation will be arrived:1.The price, at which an article is purchased, is called its CP.2. The price, at which an article is sold, is called its SP.3. When the SP is greater than the CP, it is said to be sold at a gain.4. When CP is greater than SP, it is said to be sold at a loss.5. Gain = SP – CP ; Loss = CP – SP.6. Gain or loss percentage is always calculated on the CP.

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The teacher will write the results of the above problem on the black board and then arrive at

7. Gain or Loss Percentage = Gain or Loss × 100/CP.

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Q. A man buys a toy for Rs.60/- and sells it for Rs.65/-. Find his gain percentage?

Q. Akhil bought a house for Rs.520000/-and sold it for Rs.400000/- . Find his loss percentage? Q. What is the gain or loss percentage when

a watch which cost Rs.800/- is sold to Rs.700/-?

Application :

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Home task:The students will be asked to attempt the following problems at home.

See the test book page 90 Ex. 3.2

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Lesson PlanDr.V.S.RaveendraNath.Class: IXSubject: GeometryTopic: The sum of the angle of a triangle is equal to two right angles.Apparatus: Ordinary class room apparatus.Illustrative Aids: A triangle cut out of coloured cardboard.

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Aim:1. To exercise the reasoning power or the

pupils through a clear process of observation and inference.

2. To help the students to prove the above proposition and apply it in the solution of other riders.

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Previous Knowledge:

The students are already familiar with the following.1. A straight angle is equal to two right angles.2. If a st.line stands on another st.line, the sum of the two angles so formed is equal to two rt.angles.3. If a transversal cuts two parallel st.line, it makes (i) a pair of alternate angles equal (ii) a pair of corresponding angles equal and their converse.4 .The students are already familiar with experimental proof of the proposition.

To test their PK, the following equations will be asked:1. How many degrees are there in a st.angle?2. Draw a st.line.3. If a st.line stands on another st.line. What is the sum of the two angles so formed equal to?4. If a st.line cuts two // lines, name the interior alternates angles, corresponding angles and what is the relationship b/w them?

In order to create the need of the lesson, the teacher will put the following questions:1.Find the third angle of a triangle when its two angles are 00 and 600 .2. How will you make a triangular flower plot whose all the angles are equal?Statement of Aim:After creating the problematic situation, the teacher will announce the aim of the lesson that today we shall find that the sum of the angles of a triangle is equal to two rt.angles.

Presentation:o. The proposition will be written on the blackboard.o. The students will be asked to separate the “Given” and “To Prove”.o. The triangle will be drawn on the blackboard.o. First the experimental proof of the proposition will be given by means of a model.o. The demonstrational proof will be reduced by means of the true heuristic questions:

Matter Method

A B

C

D

E

1

2

34

5

Given: ∆ ABC To prove: A + B + C =2rts. Proof: 1 + 2 + 3 will be equal to 2rt.angles, if we reduce them to the sum of the angles on the same side of a st.line.

What is given in this proposition? What is to be proved? How will you prove that A + B + C =2rt.s?   What are you to prove now?

Matter MethodFor this purpose we produce AB to D. Now the proposition will be proved if we prove that 1 + 2 + 3 =3 + CBDOr to prove1 + 2 = CBDCut off 4 from CBDEqual to 2 and if the remaining 5 = 1Then 1 + 2 = CBDAngles 2 and 4 are alternate angles and also equal BE // AC 1 = 5Again BE//AC and AD cuts them

What is this reduced to? How can you prove that 1 + 2 = CBD?What type of angles are 2 and 4? What do you infer? What type of angles are 1 and 5?What is the relationship b/w them?

Matter Method

2 = 4 (alt.angles) 1 = 5 (Corrsp.angles)1 + 2 = 4 + 5Add 3 to both sides1 + 2 +3= 3 + 4+5 A + B + C =3rt.s

Then the teacher can give the proof in a formal synthetic form.

Generalisation: The sum of the three angles of a triangle is equal to two rt.angles.

Recapitulation: The following exercises will be done. 1. Prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles. 2. Find the third angle of a triangle whose two angles are 400 and 500 .3. Prove that the sum of the interior angles of a quadrilateral in equal to four rt.angles.

Home Task: 1. Prove the proposition by drawing through the vertex a st.line // to the base. 2. Write the analytic and synthetic proofs of the proposition in your note books. 3. Prove that the acute angles of a rt.angled triangle are complementary.

The Teaching of Mathematics in the New Education. – Aiyangar N.K. Teaching Essentials of Arithmetic. – Ballard P.B. The Principles and Methods of Teaching. – Bhatia and

Bhatia. Problems in Teaching Secondary School Mathematics. –

Bresalich. E. R. The Teaching of Secondary Mathematics. – Battler and

Wren. The Teaching of Mathematics. – Chandha B.N. Geometry through Practical Application. - Mira Julio. A. Introduction of Mathematical Philosophy. - Russell. B. Correlation in Basic Education. – Singh D.P.

Some Important Reference Book.

A History of Mathematics. – Smith. Guiding Children’s Learning of

Mathematics. – Leonard M. Kennedy. Curriculum and Evaluation Standards for

School Mathematics. – Reston.V.A. Teaching with the Brain in Mind. – Jenson.

E. Creative Problem Solving in School

Mathematics. – Lenchner G. The Maths Mate Activity Book. –David E. Williams.