CONFIDENTIAL 1

Good Afternoon!

Today we will be learning about Variables & equations

Let’s warm up :

Write an algebraic expression for the following:

3) The sum of 9 and a number.

4) 3 more than twice of a number.

1) 6a + 7 when a = 5.

Evaluate the given expressions:

2) ( b + 9 ) x 2 when b = 3.

CONFIDENTIAL 2

Let’s first review what we learnt in the previous sessions before proceeding further.

We learnt about the following terms:

Variable: It is a letter that represents a number.

Since a variable represents a number, it is treated just like a number when doing various mathematical

operations .

x is a very common variable that is used in algebra, but you can use any letter (a, b, c, d, ....) to be a variable.

Algebraic expression: It is a mathematical statement which contains at least one number and at least one variable along with at least one

arithmetic operation.

The following are examples of expressions:

2 × y + 5

z + 3 × (8 - z)

CONFIDENTIAL 3

Evaluate the expression 3a for a = 4

STEP 1:Write the expression.

3a.

STEP 2:

Replace a with 4.3 x 4.

STEP 3:

Simplify the expression.

3 x 4.= 12.

So, the value of the expression is 12.

Review

CONFIDENTIAL 4

Translating an  English Phrase Into an  Algebraic Expression

Sometimes, you will be having to write out your own algebraic expression based on the wording of a problem.

In that situation, you should: 

read the problem carefully,

pick out key words and phrases and determine their equivalent mathematical meaning,

replace any unknowns with a variable, and

put it all together in an algebraic expression.

Review

CONFIDENTIAL 5

Review

When converting word problems to equations, certain "key" words tell you what kind of operations to use.

Word Operation 

sum addition

difference subtraction

product multiplication

times multiplication

less than subtraction

total addition

more than addition

CONFIDENTIAL 6

Review

Write an algebraic expression for the sum of n and 5.

The word sum means add.

So the algebraic expression would be ( n + 5 ).

This is an algebraic expression because it contains at least one number (5), at least one variable (n), and at

least one arithmetic operation (subtraction).

Write an algebraic expression for the difference of n and 5.

CONFIDENTIAL 7

Let’s start with Variables & equations

We know that variable is a letter that represents a number.

Equation: It is a mathematical statement that has an expression on

the left side of the equals sign (=) with the same value as the

expression on the right side.

The examples of an equation is:

5 + x = 12

2t - 29 = 7

CONFIDENTIAL 8

One of the terms in an equation may not be known and needs to be determined.

The unknown term may be represented by a letter such as “x”. (e.g. 2 + x = 4).

The equation is solved by finding the value of the unknown “x” that makes the two sides of the equation have the same value. Use the Inverse Operations to find the value of the variable in the addition equations.

Solution A value, such that, when you replace the variable with it, it makes

the equation true. (the left side comes out equal to the right side)

CONFIDENTIAL 9

The equality of two expressions gives an equation.

If two expressions are not equal, an inequality is created.

The inequality symbols used at this grade level are ≠ (is not equal to), > (is greater than), and < (is less

than).

It may also be stated that an equation is ‘two expressions set equal to each

other’.

Solution A value, such that, when you replace the variable with it, it makes

the equation true. (the left side comes out equal to the right side)

CONFIDENTIAL 10

Solve: n + 5 = 9

WAY 1:

WAY 2:

There are different ways of to solve a problem.

Use an addition fact.

n + 5 = 9

n = 4

n + 5 = 9

n + 5 -5 = 9 – 5

n = 4

Use the Inverse Operations.

Subtract 5 from each side.

Think:4 + 5 = 9

So ‘n’ must be

4.

CONFIDENTIAL 11

Solve: 3m = 18

WAY 1:

WAY 2:

Use a related multiplication fact.

3m = 18

m = 6

3m = 18

3 x m ÷ 3 = 18 ÷ 3

m = 6

Use the Inverse Operations.

Divide each

side by 3.

Think:3 x 6 =

18So ‘m’

must be 6.

CONFIDENTIAL 12

We need to use the Inverse Operations to find the value of the variable in the equations.

If the problem has Addition, use Subtraction to solve.

a + 4 = 7a + 4 - 4 = 7 - 4

a = 3

If the problem has subtraction , use Addition to solve.

b - 4 = 5b - 4 + 4 = 5 + 4

b = 9

If the problem has Multiplication ,

use Division to solve.

5c = 155c ÷ 5 = 15 ÷ 5

c = 3

If the problem has Division , use Multiplication to solve.

d ÷ 4 = 4d ÷ 4 x 4 = 4 x4

d = 16

Remember to Use Inverse Operations

CONFIDENTIAL 13

The sum of twice a number and 13 is 75. Find the number.

Translating a Sentence into an Equation

Here the word is means equals.

The word and means plus.

Therefore, you can rewrite the problem like the following:

The sum of twice a number plus 13 equals 75.

Using numbers and a variable, you can write an equation that means the same thing as the original problem.

CONFIDENTIAL 14

STEP1: Let the number be denoted by “n”.

So, the equation will be as follows:2n + 13 = 75

STEP2: Solve the equation.

2n + 13 = 75

2n + 13 - 13 = 75 -13

2n = 622 2

n = 31

Divide both sides

by 2.

Subtract 13 from

both sides.

Hence, the number is 31.

CONFIDENTIAL 15

BREAK

CONFIDENTIAL 16

GAME

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CONFIDENTIAL 17

Assignments

Evaluate:

1) a + 10 = 27

2) b - 11 = 5

3) c × 7 = 63 

4) 15 = 3  d

CONFIDENTIAL 18

5) Three times a number is 15.

6) 20 is ten more than the number.

7) A number divided by 3 is 24.

8) A number subtracted from 10 is 6.

Write the equations and then solve it.

CONFIDENTIAL 19

9) Oliver made 6 sweaters. This is half as many as Sam made. How many sweaters did Sam make. Write and solve

an equation.

CONFIDENTIAL 20

10) In Mrs. Roman’s class, there are 35 students. There are 19 boys in the class. How many girls are in the class?

CONFIDENTIAL 21

Very Good!Let's Review

We know that variable is a letter that represents a number.

Equation: It is a mathematical statement that has an expression on

the left side of the equals sign (=) with the same value as the

expression on the right side.

The examples of an equation is:

5 + x = 12

2t - 29 = 7

CONFIDENTIAL 22

The equality of two expressions gives an equation.

If two expressions are not equal, an inequality is created.

The inequality symbols used at this grade level are ≠ (is not equal to), > (is greater than), and < (is less

than).

It may also be stated that an equation is ‘two expressions set equal to each

other’.

Solution A value, such that, when you replace the variable with it, it makes

the equation true. (the left side comes out equal to the right side)

Review

CONFIDENTIAL 23

Solve: n + 5 = 9

WAY 1:

WAY 2:

There are different ways of to solve a problem.

Use an addition fact.

n + 5 = 9

n = 4

n + 5 = 9

n + 5 -5 = 9 – 5

n = 4

Use the Inverse Operations.

Subtract 5 from each side.

Think:4 + 5 = 9

So ‘n’ must be

4.

Review

CONFIDENTIAL 24

Review

We need to use the Inverse Operations to find the value of the variable in the equations.

If the problem has Addition, use Subtraction to solve.

a + 4 = 7a + 4 - 4 = 7 - 4

a = 3

If the problem has subtraction , use Addition to solve.

b - 4 = 5b - 4 + 4 = 5 + 4

b = 9

If the problem has Multiplication ,

use Division to solve.

5c = 155c ÷ 5 = 15 ÷ 5

c = 3

If the problem has Division , use Multiplication to solve.

d ÷ 4 = 4d ÷ 4 x 4 = 4 x4

d = 16

Remember to Use Inverse Operations

CONFIDENTIAL 25

ReviewThe sum of twice a number and 13 is 75. Find the

number.

STEP1: Let the number be denoted by “n”.

So, the equation will be as follows:

2n + 13 = 75

STEP2: Solve the equation.

2n + 13 = 75

2n + 13 - 13 = 75 -13

2n = 622 2

n = 31

Divide both sides

by 2.

Subtract 13 from

both sides.

Hence, the number is 31.

CONFIDENTIAL 26

You have done a nice job.See you in the next session.