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LESSON 1.4 EVALUATING EXPRESSIONS Slide 2 Homework Check & REVIEW Class work and Homework 1.Exercise 1.3.1 2.Pages 5-7 3.P. 14 16 Q # 1 - 9 Slide 3 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. Slide 4 Slide 5 We have to be able to translate words into expressions What words indicate a particular operation? AddSubtract Sum Plus More than Increase(d) by Perimeter Deposit Gain Greater than Up (flights of stairs) Total Minus Take away Difference Reduce(d) by Decrease(d) by Withdrawal Less than Fewer (than) Loss of Slide 6 We have to be able to translate words into expressions What words indicate a particular operation? MultiplyDivide Times Product Of Twice (2), double (2), triple (3), etc. Half (), Third (), Quarter () 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) Slide 7 1.FIRST replace the variables with the known (given) value. 2.THEN follow the Order of Operations. EVALUATE EXPRESSION To EVALUATE means to FIND THE VALUE OF THE EXPRESSION when the value of the variables are known. Slide 8 An expression is NOT an equation because it DOES NOT have an equal sign. There are 2 types of expressions. 5 + 84 Numerical 3x 3x + 10 Algebraic Notice there are no equal signs in these expressions so they are not equations ! Slide 9 A numerical expression contains only numbers and symbols and NO LETTERS. 5 times 3 plus 8 (53) + 8 Slide 10 An algebraic expression contains only numbers, symbols, and variables. It is sometimes referred to as a variable expression. The product of 3 and x 3x The sum of m and 8 m + 8 The difference of r and 2 r - 2 Slide 11 What is a variable? A variable represents an unknown value. 1) 4 + x 2) 10 ? 3) 5y 4) 20 A variable can be any letter of the alphabet since it represents an unknown. Slide 12 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 Slide 13 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 7 t or 7t 6 d or 6d Always write the variable AFTER the number. Slide 14 Evaluate means to find the value of an algebraic expression by substituting numbers in for variables. m = 2 6 + m ? 6 + 2 8 Slide 15 Evaluate means to find the value of an algebraic expression by substituting numbers in for variables. r = 3 7 + r ? 7 + 3 10 Slide 16 Evaluate the variable expression when n = 6. 1)2) Evaluate just means solve by substitution. Slide 17 Evaluate the variable expression when n = 6. Evaluate just means solve by substitution. 3) 4) Slide 18 Evaluate the algebraic expression when n = 8. 1)2) Slide 19 Evaluate the expression if a = 3 and b = 4. 1)2) Slide 20 Evaluate the expression if a = 3 and b = 4. 3)4) Slide 21 Evaluate the expression if x = 5 and y = 3. 1) 2) Slide 22 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 TYPES OF EXPRESSIONS #1 Slide 23 #2 Show the substitution. Show your work down. Circle your answer. Show your work one step at a time down. No equal signs! Evaluate means solve. Evaluate i f x = 3 and y = 4 Slide 24 Evaluating Expressions 1) Replace each letter in the expression with the assigned value. 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. 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! Slide 25 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.