PRESENTATIONSubject: MathematicsTopic: AlgebraClass: VPresented by: Shaheena Raja DA SKBZ College SKB - 229

INTRODUCTIONAlgebra is known as a gatekeeper subject. It is used

by professionals ranging from electricians to architects to computer scientists. It is the gateway to success in the 21st century.

Students make transition from concrete arithmetic to the symbolic language of algebra. They develop abstract reasoning skills necessary to excel in math and science

History of Algebra

The history of Algebra began in ancient Egypt and Babylon where people learned to solve linear equations (ax = b).

The ancient knowledge of solution of equations in turn found a home early in the Islamic world where it was known as the science of restoration and balancing.

(The Arabic words for restoration, al – jabru is the root of the word algebra.) In the 9th century, the Arab Mathematician Al - Khowarizmi wrote one of the first Arabic algebras, a systematic expose of the basic theory of equations with both examples and proofs.

Origin of the word Algebra

The word algebra is a Latin variant of the Arabic word al – jabr. This came from the title of book Hidab – al – jabr wal – muqubala written in Baghdad about 825 AD by the Arab Mathematician Muhammad ibne Musa al – khowarizmi.

The words jabr (JAH– ber) and muqabalah (moo – KAH – ba – lah) were used by al – khowarizmi to designate two basic operations in solving equations.

Jabr is used in the step x – 2 = 12 becomes x = 14. The left side of the first equation where x is lessened by 2 is restored or completed back to x in the second equation.

Contd.Muqabalah takes us from x + y = y + 7 to x =

7 by cancelling or balancing the two sides of the equation.

DEFINITIONSAlgebra: A branch of mathematics in which symbols

usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.

Variables: They are defined as numbers that can change value or represent a missing value.

Expressions: An expression is a mathematical term or a sum or difference of mathematical term, that may use numbers, variables or both. Example 2, x, 3 + 7, 2 x y + 5, 2 + 6 x (4 – 2)

Learning ObjectivesTo introduce algebraic notations and

expressions.To give idea that different letters represent

different generalized numbers .To do four operations involving algebraic

notations.To simplify the algebraic expressions.

Long Term Objectives

Adopt 21st century teaching approaches. to enhance students appreciation of

mathematics and to help students to develop abstract thinking so that they are able to

apply it in algebraic expressions.

Short Term ObjectivesBy the end of the topic ,the students will

understand the use of letters to represent unknown numbers.

They will be able to write an expression for any given statement.

They will evaluate different expressions involving addition, subtraction, multiplication and division.

They will create a booklet in which they will write their own expressions and write story for those expressions.

TIME LINE1ST Week Algebraic notations and

expressions will be introduced and emphasis will be given to write algebraic expression for the given statement.

2nd Week The four operations in algebra will be done.

3rd Week Worksheets and activities related to algebra will be done.

MethodologyIn the following table letters are used to

represent unknown numbers.Weight of duck (kg)

Weight of goose (kg)

Total weight (kg)

2 3 5

x 3 x+3

4 y 4+y

p q p+q

Contd.A housewife bought m kg of sugar. She used n kg

of it. How much sugar did she have left? ( m-n) kgUmair had 3 packets of pencils. There were b

pencils in each packet. How many pencils did Umair have altogether?

3b pencils Sana has 7 beads more than Zara. If Zara has d

beads, how many beads does Sana have? (d+7) beadsSo m-n, 3b, d+7 are called expressions.

Contd.Make lot of practice so that students are able to write

expressions for any given statement.For addition and subtraction of expressions, only like

terms can be added or subtracted. For example 3b+6b=9b but 3b+4c cannot be added because they are unlike terms.

For multiplication we break the terms and then simplify the numbers. For example 3x2k=3x2xk=6xk=6k

For expressions involving division explain the students to treat the letters like numbers and use their knowledge of fractions to do the simplification. For e.g.4t/2v=4xt/2xv=2t/v

REMEMBERx + x + x + x =4x 4x is a term and 4 is the coefficient of x.2m, 5m, 6m, are like terms since m represent

the same object in each case. You can add like terms.

You can subtract one term from another term like it.

2m, 2o, and 5n are unlike terms, since m, n and o represent different objects.

The sum of two unlike terms, x and y, is x + yThe difference between x and y (if x > y) is x – y.

Contd.The product of x and y is xy.2p + 4q is an algebraic expression.To add two expressions, like terms must be added

together. For example, the sum of (2a + 3b) and (3b + 4a) is :

2a + 3b 4a + 3b

6a + 6b

Contd.To subtract one expressions from another, you

must find the difference of like terms. For example, the difference between (4x +

5y) and (2y + 3x) is : 4x + 5y 3x + 2y

- - 1x + 3y

To multiply an expressions by a given number, each term must be separately multiplied by that number.

For example, (3x + 2y) + (3x + 2y) = 2 x (3x + 2y) = 6x + 4y