2Homework Check & REVIEW Class work and HomeworkExercise 1.3.1Pages 5-7P. 14 – 16 Q # 1 - 9
3LEARNING 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.
5We have to be able to “translate” words into expressions What words indicate a particular operation?Add SubtractMinusTake awayDifferenceReduce(d) byDecrease(d) byWithdrawalLess thanFewer (than)Loss ofSumPlusMore thanIncrease(d) byPerimeterDepositGainGreater thanUp (flights of stairs)Total
6We have to be able to “translate” words into expressions What words indicate a particular operation?Multiply DivideTimesProductOfTwice (×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 __ partsCost eachQuotientOne-half (÷2), Third (÷3), Quarter (÷4)IntoPerPercent (out of 100)
7FIRST – 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.
85 + 84 Numerical 3x + 10 Algebraic Expressions An expression is NOT an equationbecause it DOES NOT have an equal sign.There are 2 types of expressions.Numerical3x AlgebraicNotice there are no equal signs in theseexpressions so they are not equations!
95 times 3 plus 8 (5•3) + 8 Expressions A numerical expression contains onlynumbers and symbols and NO LETTERS.5 times 3 plus 8(5•3) + 8
10An algebraic expression contains only numbers, symbols, and ExpressionsAn algebraic expression containsonly numbers, symbols, andvariables. It is sometimes referredto as a variable expression.The product of 3 and x xThe sum of m and m + 8The difference of r and r - 2
11ExpressionsWhat is a variable?A variable represents an unknown value.2) 10 – ?1) 4 + x4) 203) 5yA variable can be any letter of the alphabet since it represents an unknown.
125 • c or 5c 7 • t or 7t 6 • d or 6d Expressions Word Phrases for multiplication are:The product of 5 and a number cSeven times a number t6 multiplied by a number d5 • c or 5c7 • t or 7t6 • d or 6d
13Always write the variable AFTER the number. ExpressionsThe Placement rule for multiplication is:The product of 5 and a number cSeven times a number t6 multiplied by a number d5 • c or 5cAlways write the variable AFTER the number.7 • t or 7t6 • d or 6d
14ExpressionsEvaluate means to find the value of an algebraic expression by substituting numbers in for variables.m = 26 + m ?6 + 28
15ExpressionsEvaluate means to find the value of an algebraic expression by substituting numbers in for variables.r = 37 + r ?7 + 310
16Evaluate the variable expression when n = 6. ExpressionsEvaluate the variable expression when n = 6.1)2)Evaluate just means solve by substitution.
17Evaluate the variable expression when n = 6. ExpressionsEvaluate the variable expression when n = 6.3)4)Evaluate just means solve by substitution.
18Evaluate the algebraic expression when n = 8. ExpressionsEvaluate the algebraic expression when n = 8.1)2)
19Evaluate the expression if a = 3 and b = 4. ExpressionsEvaluate the expression if a = 3 and b = 4.1)2)
20Evaluate the expression if a = 3 and b = 4. ExpressionsEvaluate the expression if a = 3 and b = 4.3)4)
21Evaluate the expression if x = 5 and y = 3. ExpressionsEvaluate the expression if x = 5 and y = 3.2)1)
22TYPES OF EXPRESSIONS#1An 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 + 4ALGEBRAIC EXPRESSION: Contains numbers, symbols, and variables. Also known as a variable expression. Example: m + 8A VARIABLE is a letter or symbol that represents a number. Example: x
23Evaluate means solve. Show the substitution. Circle your answer. #2Substitute & EvaluateEvaluate if x = 3 and y = 4Evaluate means solve.Show the substitution.Show your work down.Circle your answer.Show your work one step at a time down. No equal signs!
24Evaluating 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!
25SUCCESS CRITERIAI can explain what an expression is and provide an example.I can explain the types of expressionI 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.