Presentation on theme: "Just the facts: Order of Operations and Properties of real numbers"— Presentation transcript:
1 Just the facts: Order of Operations and Properties of real numbers A GEMS/ALEX SubmissionSubmitted by: Elizabeth Thompson, PhDSummer, 2008
2 Important things to remember Parenthesis – anything grouped… including information above or below a fraction bar.Exponents – anything in the same family as a ‘power’… this includes radicals (square roots).Multiplication- this includes distributive property (discussed in detail later).Some items are grouped!!!Multiplication and Division are GROUPED from left to right (like reading a book- do whichever comes first.Addition and Subtraction are also grouped from left to right, do whichever comes first in the problem.Click to extend information
3 So really it looks like this….. ParenthesisExponentsMultiplication and DivisionAddition and SubtractionIn order from left to rightIn order from left to rightClick to extend information
4 SAMPLE PROBLEM #1 Parenthesis Exponents This one is tricky! Remember: Multiplication/Division are grouped from left to right…what comes 1st?Division did…now do the multiplication (indicated by parenthesis)Click and the operation / next step will appear…keep clicking until the end.More divisionSubtraction
5 SAMPLE PROBLEM Exponents Parenthesis Click and the operation / next step will appear…keep clicking until the end.Remember the division symbol here is grouping everything on top, so work everything up there first….multiplicationDivision – because all the work is done above and below the lineSubtraction
6 Order of Operations-BASICS Think: PEMDAS Please Excuse My Dear Aunt Sally ParenthesisExponentsMultiplicationDivisionAdditionSubtractionClick to extend information
7 Take time to practice Assign problems from text and/or worksheet. Work some problems with the students, allow time for questions.
8 Assignment #1 (When all assigned problems are finished – do for Homework as needed) Remember PEMDAS and “Please Excuse My Dear Aunt Sally”?Make up your own acronym for PEMDAS and post it on the class wiki.Write it on White Paper and Illustrate your acronym.Make sure it is school appropriate.This is a silly but fun assignment. Students get to be creative, all the time thinking of “Order of Operations”.Example: Purple elephants may dance and sing (draw a picture of a singing/dancing purple elephant)Sample 2: People enjoy my daily apple slices (a stick person smiling near apple slices).
9 Lesson Extension Can you fill in the missing operations? 2 - (3+5) = -2* 3 ÷ 3 = 115 * ÷ 2 = 10Teachers: One location for worksheets with ‘blank’ operations isFor an extension of this slide, have each student fold a paper like a card. On the cover of the card, they create a problem with blanks (like the slide) on the inside of the card is the solution. On the back of the card is their name (like you would find a label on a real card). This can be done as homework or a classroom extension.
10 Assignment #2 Create a Puzzle Greeting Fold a piece of paper (white or colored) like a greeting card.On the cover: Write an equation with missing operations (like the practice slide)In the middle: Write the equation with the correct operationsOn the back: Put your name as you would find a companies name on the back of a greeting card.Make a sample for students to see as needed.
11 Part 2: Properties of Real Numbers (A listing) Associative PropertiesCommutative PropertiesInverse PropertiesIdentity PropertiesDistributive PropertyClick for examples of eachAll of these rules apply to Addition and Multiplication
12 Associative Properties Associate = group It doesn’t matter how you group (associate) addition or multiplication…the answer will be the same!Rules:Associative Property of Addition(a+b)+c = a+(b+c)Associative Property of Multiplication(ab)c = a(bc)Samples:Associative Property of Addition(1+2)+3 = 1+(2+3)Associative Property of Multiplication(2x3)4 = 2(3x4)Later we will discuss how these do not apply to subtraction and division.
13 Commutative Properties Commute = travel (move) It doesn’t matter how you swap addition or multiplication around…the answer will be the same!Rules:Commutative Property of Additiona+b = b+aCommutative Property of Multiplicationab = baSamples:Commutative Property of Addition1+2 = 2+1Commutative Property of Multiplication(2x3) = (3x2)The next slide will discuss how these do not apply to subtraction and division.
14 Is (5-2)-3 = 5-(2-3)? Is (6/3)-2 the same as 6/(3-2)? Stop and think!Does the Associative Property hold true for Subtraction and Division?Does the Commutative Property hold true for Subtraction and Division?Is (5-2)-3 = 5-(2-3)? Is (6/3)-2 the same as 6/(3-2)?Leave time to discuss prior to clicking examples.Is 5-2 = 2-5? Is 6/3 the same as 3/6?Properties of real numbers are only for Addition and Multiplication
15 Inverse Properties Think: Opposite What is the opposite (inverse) of addition?What is the opposite of multiplication?Subtraction (add the negative)Division (multiply by reciprocal)Rules:Inverse Property of Additiona+(-a) = 0Inverse Property of Multiplicationa(1/a) = 1Samples:Inverse Property of Addition3+(-3)=0Inverse Property of Multiplication2(1/2)=1
16 Identity Properties Rules: a+0 = a a(1) = a Samples: 3+0=3 2(1)=2 What can you add to a number & get the same number back?What can you multiply a number by and get the number back?0 (zero)1 (one)Rules:Identity Property of Additiona+0 = aIdentity Property of Multiplicationa(1) = aSamples:Identity Property of Addition3+0=3Identity Property of Multiplication2(1)=2
17 Distributive Property If something is sitting just outside a set of parenthesis, you can distribute it through the parenthesis with multiplication and remove the parenthesis.Rule:a(b+c) = ab+bcSamples:4(3+2)=4(3)+4(2)=12+8=202(x+3) = 2x + 6-(3+x) = -3 - xDiscuss/illustrate how arrows can help a student stay on track
18 Take time to practice Assign problems from text and/or worksheet. Work some problems with the students, allow time for questions.
19 Homework Log on to class wiki / discussion thread Follow the directions given:Give an example of each of the properties discussed in class, do not duplicate a previous entry.