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**LESSON 1.4 EVALUATING EXPRESSIONS**

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**Homework Check & REVIEW**

Class work and Homework Exercise 1.3.1 Pages 5-7 P. 14 – 16 Q # 1 - 9

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**LEARNING GOALS By the end of this lesson, you will be able to:**

Understand the meaning of the term “operations” Understand the meaning of other words related to addition, subtraction, multiplication, division and equal. Understand what “BEDMAS” stands for. Apply BEDMAS to expressions with multiple operations.

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**EVALUATING EXPRESSIONS**

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**We have to be able to “translate” words into expressions**

What words indicate a particular operation? Add Subtract Minus Take away Difference Reduce(d) by Decrease(d) by Withdrawal Less than Fewer (than) Loss of Sum Plus More than Increase(d) by Perimeter Deposit Gain Greater than Up (flights of stairs) Total

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**We have to be able to “translate” words into expressions**

What words indicate a particular operation? Multiply Divide Times Product Of Twice (×2), double (×2), triple (×3), etc. Half (×½), Third (×⅓), Quarter (×¼) Area (by) Percent (of) Square (times itself 2 times) Cube (times itself 3 times) … to the power of ___ (times itself ___ times) Split into __ parts Cost each Quotient One-half (÷2), Third (÷3), Quarter (÷4) Into Per Percent (out of 100)

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**FIRST – replace the variables with the known (given) value.**

To EVALUATE means to FIND THE VALUE OF THE EXPRESSION when the value of the variables are known. FIRST – replace the variables with the known (given) value. THEN – follow the Order of Operations.

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**5 + 84 Numerical 3x + 10 Algebraic Expressions**

An expression is NOT an equation because it DOES NOT have an equal sign. There are 2 types of expressions. Numerical 3x Algebraic Notice there are no equal signs in these expressions so they are not equations!

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**5 times 3 plus 8 (5•3) + 8 Expressions**

A numerical expression contains only numbers and symbols and NO LETTERS. 5 times 3 plus 8 (5•3) + 8

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**An algebraic expression contains only numbers, symbols, and **

Expressions An algebraic expression contains only numbers, symbols, and variables. It is sometimes referred to as a variable expression. The product of 3 and x x The sum of m and m + 8 The difference of r and r - 2

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Expressions What is a variable? A variable represents an unknown value. 2) 10 – ? 1) 4 + x 4) 20 3) 5y A variable can be any letter of the alphabet since it represents an unknown.

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**5 • c or 5c 7 • t or 7t 6 • d or 6d Expressions**

Word Phrases for multiplication are: The product of 5 and a number c Seven times a number t 6 multiplied by a number d 5 • c or 5c 7 • t or 7t 6 • d or 6d

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**Always write the variable AFTER the number.**

Expressions The Placement rule for multiplication is: The product of 5 and a number c Seven times a number t 6 multiplied by a number d 5 • c or 5c Always write the variable AFTER the number. 7 • t or 7t 6 • d or 6d

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Expressions Evaluate means to find the value of an algebraic expression by substituting numbers in for variables. m = 2 6 + m ? 6 + 2 8

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Expressions Evaluate means to find the value of an algebraic expression by substituting numbers in for variables. r = 3 7 + r ? 7 + 3 10

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**Evaluate the variable expression when n = 6.**

Expressions Evaluate the variable expression when n = 6. 1) 2) Evaluate just means solve by substitution.

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**Evaluate the variable expression when n = 6.**

Expressions Evaluate the variable expression when n = 6. 3) 4) Evaluate just means solve by substitution.

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**Evaluate the algebraic expression when n = 8.**

Expressions Evaluate the algebraic expression when n = 8. 1) 2)

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**Evaluate the expression if a = 3 and b = 4.**

Expressions Evaluate the expression if a = 3 and b = 4. 1) 2)

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**Evaluate the expression if a = 3 and b = 4.**

Expressions Evaluate the expression if a = 3 and b = 4. 3) 4)

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**Evaluate the expression if x = 5 and y = 3.**

Expressions Evaluate the expression if x = 5 and y = 3. 2) 1)

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TYPES OF EXPRESSIONS #1 An expression is NOT an equation because it does not have an equal sign. There are 2 types of expressions. NUMERICAL EXPRESSION: Contains only numbers and symbols. Example: 5 • 3 + 4 ALGEBRAIC EXPRESSION: Contains numbers, symbols, and variables. Also known as a variable expression. Example: m + 8 A VARIABLE is a letter or symbol that represents a number. Example: x

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**Evaluate means solve. Show the substitution. Circle your answer.**

#2 Substitute & Evaluate Evaluate if x = 3 and y = 4 Evaluate means solve. Show the substitution. Show your work down. Circle your answer. Show your work one step at a time down. No equal signs!

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**Evaluating Expressions**

1) Replace each letter in the expression with the assigned value. First, replace each letter in the expression with the value that has been assigned to it. To make your calculations clear and avoid mistakes, always enclose the numbers you're substituting inside parentheses. The value that's given to a variable stays the same throughout the entire problem, even if the letter occurs more than once in the expression. However, since variables "vary", the value assigned to a particular variable can change from problem to problem, just not within a single problem. 2) Perform the operations in the expression using the correct order of operations. Once you've substituted the value for the letter, do the operations to find the value of the expression. Don't forget to use the correct order of operations (BEDMAS): first do any operations involving exponents, then do multiplication and division, and finally do addition and subtraction!

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SUCCESS CRITERIA I can explain what an expression is and provide an example. I can explain the types of expression I can explain the difference between the types of expressions. I can describe the meaning of a variable. I can look at an expression and provide a phrase for it. I can make an expression from a word phrase. I can explain the placement rule of multiplication. I can explain the meaning of “substitution”. I am able to solve an algebraic expression when given the value of a given variable(s). I am able to replace each letter in the expression with the assigned value. I am able to perform the operations in the expression using the correct order of operations. I can write a variable expression that models a real life situation.

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Variables and Expressions

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