CONFIDENTIAL 1

Good Afternoon!

Today we will be learning about Number stories &

expressionsLet’s warm up :

Simplify. Follow the order of operations:-

1) 12 – 3 + 6

2) ( 8 – 2 ) x 5 + 5

3) ( 12 + 4 ) ÷ 8 + 2

4) ( 3 x 4 ) + 15 - 6

5) 2 x ( 18 - 5) + 2

1) 15

2) 35

3) 4

4) 21

5) 28

CONFIDENTIAL 2

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

ARITHMETIC EXPRESSION: It is an expression consisting of numbers, grouping symbols and arithmetic operation symbols.

To evaluate these expressions, a specific Order of Expressions is followed.

When a numerical expression involves two or more operations, there is a specific order in which these operations must be

performed.

4 – (3 + 2) is an arithmetic expression.

Parenthesis, Exponents, (Multiplication/Division) then (Add/Subtract)OR that is, PEMDAS for short .

Please Excuse (My Dear) (Aunt Sally).

This phrase will help you understand the order.

CONFIDENTIAL 3

Evaluate 3 + 4 x 2

3 + 4 x 2 = 7 x 2 = 14

or

3 + 4 x 2 = 3 + 8 = 11

Two people may interpreted the problem differently this problem like

Here, the correct answer is 11.Let’s see how.

CONFIDENTIAL 4

To solve an expression you need to follow the rules for the Order of Operation.

Evaluate: 3 + (3 x 4) - 1

Rule 1:

First, do operations inside the parenthesis ( ).

3 + (3 x 4) - 1

Rule 2:

Then do multiplication and division in order from left to right.

3 + 12 - 1

Rule 3:

Finally, do addition and subtraction in order from left to right.

15 - 1

14

There is no more

multiplication or

division.

CONFIDENTIAL 5

Is 8 x (3 + 6) equal to 7 x (17 - 6) ?

The value 8 x (3 + 6) = 72 is less than 7 x (17 - 6) = 77.

Hence, not equal.

First of all, we evaluate

8 x (3 + 6)

= 8 x 9

= 72

Then, we evaluate

7 x (17 - 6)

= 7 x 11

= 77

CONFIDENTIAL 6

Let’s start with Number stories & expressions

First we will learn 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.

For example, we might say that ‘x’ stands for the side-length of a square.

We now treat ‘x’ as if it were a number we could use.

CONFIDENTIAL 7

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.

In other words, an algebraic expression is a number, variable or combination of the two connected by some mathematical operation like addition, subtraction, multiplication, division,

exponents, and/or roots.

The following are examples of expressions:

2 × y + 5

z + 3 × (8 - z)

CONFIDENTIAL 8

Evaluating an Expression

You can evaluate an expression by replacing the variable with the given number and performing the indicated operation

Value of an Expression

When you are asked to find the value of an expression, that means you are looking for the result that you get when you evaluate the

expression.

Evaluate simply means that we want to find an answer.

CONFIDENTIAL 9

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.

CONFIDENTIAL 10

Evaluate the expression 12 – n for n = 4

Given the expression 12 – n.

Here we will replace the occurrence of n with the number 4

Hence, 12 – n becomes

= 12 – 4

= 8

nis

replaced by 4.

Evaluate the expression 3 x m for m = 5

15

CONFIDENTIAL 11

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.

CONFIDENTIAL 12

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 13

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 14

Translating a Sentence into an Equation

Question: There are 2 more students in the class than yesterday.How many students are there in the class today?

Let us suppose that the number of students in the class yesterday be = k.

Today the number of students in the class is 2 more than yesterday.

2 students more than yesterday will be= k + 2.

So, the number of students in the class today will be = k + 2.

CONFIDENTIAL 15

BREAK

CONFIDENTIAL 16

GAME

Click on the link below for some exciting puzzle

http://www.thekidzpage.com/onlinejigsawpuzzles/kids-jigsaw-puzzles/12-piece-jigsaw/03-27-07-2bunnies.html

CONFIDENTIAL 17

Assignments

1) 4 × y + 12 when y = 6.

2) 3 + 2z when z = 4.

Evaluate the given expressions:

3) 2n - 7 when n = 8.

4) m – 4 when m = 25.

5) ( p x 4 ) + 3 when p = 7.

1) 36

2) 11

3) 9

4) 21

5) 31

CONFIDENTIAL 18

Write an algebraic expression for the following:

6) The sum of 5 and a number.

7) 5 less than a number.

8) The product of 5 and a number.

9) The sum of 3 and a number.

6) a + 5

7) a - 5

8) a x 5

9) a + 3

CONFIDENTIAL 19

10) A car travels down the freeway at 35 miles per hour. Write an expression for the distance the car

will have traveled after “h” hours. If the value of h = 5 hours, then what is the distance traveled ?

10) 35 x h.and

175 miles

CONFIDENTIAL 20

Very Good!Let's Review

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 21

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 22

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 23

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 24

ReviewWrite 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 25

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