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MJ2A Ch 1.3 Variables & Expressions Bellwork • 1. 2. 3. 4. Write a numerical expression for each verbal phrase Six minus three Nine multiplied by five Eleven more than fifteen The cost of three notebooks at $6 each Before we begin… • Please take out your notebook and get ready to work! • On Friday we looked at words that mean the mathematical operations of add, subtract, multiply and divide…. • Today we will increase out understanding of expressions incorporating variables… • But first what is a variable and what do they represent?....raise you hand if you know the answer The answer… • A variable is a letter used in an expression or equation to represent some unknown number. • Most often the variable represents one number….however, in some instances the variable can represent a range of numbers called a solution set…. Objective • Students will evaluate expressions containing variables and translate verbal phrases into algebraic expressions Evaluating Expressions • To evaluate expressions use the following process: 1. Write the expression 2. Substitute 3. Do the math Example Evaluate the expression: x + y – 9 if x = 15 and y = 26 1. x + y – 9 2. 15 + 26 – 9 3. 41 – 9 32 Note: 1. Write the expression 2. Substitute 3. Do the math When “doing the math” use the order of operations Substitution Property of Equality • Replacing a variable with a number demonstrates the Substitution Property of Equality which states: • If two quantities are equal then one quantity can be replaced by the other • Example: If a = b, then a may be replaced by b Multiplication & Algebra • At this level you are required to be able to recognize and work with the various forms of multiplication in Algebra. • Because the variable x is used often in algebra the multiplication sign (x) that you learned in elementary school is not used. Here are the forms of multiplication: 2x 2∙x 2(x) mn Your Turn • • 1. 2. 3. In the notes section of your notebook write and solve the following: Evaluate each expression if x = 3, y = 4, and z = 7 6x – 4y (z – x) y 5z + (x + 4y) – 15 Translating Verbal Phrases • The first step to translating variable phrases it to identify the variable • After identifying the variable choose a letter to represent the variable in the expression. • Lets see what that looks like… Example • Verbal Phrase: Twelve points more than the Dolphins scored • In this phrase the variable is the Dolphins…Lets use p to represent the dolphins Twelve points more than the Dolphins scored 12 + p The algebraic expression for the verbal phrase becomes: 12 + p Comments • When choosing a variable you may use any letter. • The key to translating verbal phrases is identifying the variable • You can use different strategies to help you like circling, highlighting, or boxing the variable in the sentence • Lets look at another example.. Example • Four times a number decreased by six. • Let x represent the variable “a number” • Four times means multiply 4 times the variable • Decreased by six means subtract 6 4x - 6 Your Turn • In the notes section of your notebook write the verbal phrase and translate it into an algebraic expression 1. Eight more than the amount Kira saved 2. Five goals less than the Pirates scored 3. The quotient of a number and four, minus five Summary • In the notes section of your notebook summarize the key concepts covered in today's lesson: • Today we discussed: • Evaluating variable expressions • The process for evaluating expressions • Translating verbal phrases into algebraic expressions • Identifying the variable in a verbal phrase Assignment • Text p. 20 # 20 – 30 & 33 – 40 • This assignment is due tomorrow • Check your answers to the odd problems in the back of the book. • If you didn’t get the same answer…you need to figure out why! • Reminder…I do not accept late assignments!