CONFIDENTIAL1 Good Afternoon! Today we will be learning about Number stories & expressions Let’s warm up : Simplify. Follow the order of operations:- 1) 12 – ) ( 8 – 2 ) x ) ( ) ÷ ) ( 3 x 4 ) ) 2 x ( ) + 2

CONFIDENTIAL2 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.

CONFIDENTIAL3 Evaluate x x 2 = 7 x 2 = 14 or x 2 = = 11 Two people may interpreted the problem differently this problem like Here, the correct answer is 11. Let’s see how.

CONFIDENTIAL4 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 Rule 3: Finally, do addition and subtraction in order from left to right There is no more multiplicatio n or division.

CONFIDENTIAL5 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

CONFIDENTIAL6 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.

CONFIDENTIAL7 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)

CONFIDENTIAL8 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.

CONFIDENTIAL9 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.

CONFIDENTIAL10 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 n is replaced by 4. Evaluate the expression 3 x m for m = 5

CONFIDENTIAL11 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.

CONFIDENTIAL12 When converting word problems to equations, certain "key" words tell you what kind of operations to use. WordOperation sumaddition differencesubtraction productmultiplication timesmultiplication less thansubtraction totaladdition more thanaddition

CONFIDENTIAL13 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.

CONFIDENTIAL14 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.

CONFIDENTIAL15 BREAK

CONFIDENTIAL16 GAME Click on the link below for some exciting puzzle puzzles/12-piece-jigsaw/ bunnies.html

CONFIDENTIAL17 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.

CONFIDENTIAL18 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.

CONFIDENTIAL19 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 ?

CONFIDENTIAL20 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)

CONFIDENTIAL21 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

CONFIDENTIAL22 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

CONFIDENTIAL23 Review When converting word problems to equations, certain "key" words tell you what kind of operations to use. WordOperation sumaddition differencesubtraction productmultiplication timesmultiplication less thansubtraction totaladdition more thanaddition

CONFIDENTIAL24 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.

CONFIDENTIAL25 You have done a nice job. See you in the next session.