What’s The Problem With Inequalities? - GED
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017What’s the Problem withInequalities?Tuesdays for TeachersApril 25, 2017GEDtestingservice.com GED.comWelcome! Daphne Atkinson, GED Testing Service Debi Faucette, GED Testing Service Bonnie Goonen, Consultant to GEDTS Susan Pittman, Consultant to GEDTS2GEDtestingservice.com GED.comObjectives Discuss using High ImpactIndicators to driveinstruction Review the basics ofworking with inequalities Investigate importance ofstudents’ understanding ofinequalities Share resources and ideas3GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved1
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Skill Sets for High ImpactIndicators in MathematicalReasoningFocusing Instruction4GEDtestingservice.com GED.comHII5GEDtestingservice.com GED.comDescriptors for InequalitiesA.3 Write,manipulate, solve,and graph linearinequalitiesA.3.a Solve linearinequalities in onevariable withrational numbercoefficients.6A.3.b Identify orgraph the solutionto a one variablelinear inequality ona number line.A.3.c Solve realworld problemsinvolvinginequalities.A.3.d Write linearinequalities in onevariable torepresent context.GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved2
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Can your students . . .7GEDtestingservice.com GED.comThe Inequality Ladder of Fame!8GEDtestingservice.com GED.comWhat is aninequality?99GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved3
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017What is an inequality?An inequality is a mathematical sentencethat uses symbols such as , , , or tocompare two quantities.A10BGEDtestingservice.com GED.comWhat is an inequality?An inequality is a math statement thatdefines a range of values.Jeffrey runs at least two milesevery day.On November 28, thetemperature in North Pole,Alaska is expected to begreater than -4 and lessthan 9 T 611GEDtestingservice.com GED.comInequalities – No ProblemUnderstanding and using inequalities in real-life situations12GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved4
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Inequalities are Everywhere13SituationMathematical InequalitySpeed limitLegal speed on the highway 65 miles per hourCredit cardMonthly payment 10% of your balance in thatbilling cycleTextmessagingAllowable number of text messages per month 250Travel timeTime needed to drive from home to school/work 18 minutesGEDtestingservice.com GED.comRecognize the SymbolsPhraseInequality“a is more than b”a b“a is at least b”a b“a is less than b”a b“a is at most b;” or“a is no more than b”a bInequality tells what is “allowable” or “possible.” An inequalityplaces conditions on the value of the variable.14GEDtestingservice.com GED.comLearn the VocabularyTermInequalityCoefficient4a 8Boundary PointA solution that makes theinequality true.Solution SetThe range of values thatmake the inequality trueInclusivea 6Exclusivea 6Inequality tells what is “allowable” or “possible”15GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved5
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Look Back at our GraphsRemember - An inequality is a math statement that defines a range ofvalues.Jeffrey runs at least two milesevery day.On Nov. 28, the temperaturein North Pole, Alaska isexpected to be greater than 4 and less than 9 T 64a 816GEDtestingservice.com GED.comReading InequalitiesHave students read inequalities by startingwith the variable.x 44 x17GEDtestingservice.com GED.comRules for Solving Inequalities1. Make the same changes to both sides of the inequality2. Isolate the variable3. Combine like terms4. Use the inverse operation to remove clutter from thevariable5. If your inverse operation is multiplication or division bya negative number, reverse the inequality sign18GEDtestingservice.com GED.com becomes becomes becomes becomes Copyright GED Testing Service LLC. All rightsreserved6
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Properties of InequalitiesAddition and SubtractionIf a b, then a c b cIf a b, then a - c b – cReal-life situationBecky is older than Janet: b jAdd 10 years: b 10 j 10Subtract 10 years: b – 10 j - 1019GEDtestingservice.com GED.comProperties of InequalitiesMultiplication and DivisionIf a b, then ac bc, if c 0If a b, then ac bc, if c 020GEDtestingservice.com GED.comBut there is one exceptionWhen you multiply or divide each side of an inequality by anegative number, you must reverse the inequality symbol!WHY?Multiplying or dividing both sides of an equation by anegative number changes the sign of each side of theequation. On both sides, what was positive becomesnegative, and what was negative becomes positive.21GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved7
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017But there is one exceptionWhen you multiply or divide each side of an inequality by anegative number, you must reverse the inequality symbol!WHY?Multiplying or dividing both sides of an equation by anegative number changes the sign of each side of theequation. On both sides, what was positive becomesnegative, and what was negative becomes positive.22GEDtestingservice.com GED.comTesting the Property3 2Multiply by -1(-1)(3) 2 (-1)-3 -2FALSE-3 -2TRUEMultiplying by anegative flipped theinequality sign from“greater than” to “lessthan.”23Solving Inequalities4 x 124 x 12(draw wall down inequality)4 x 12(box in variable)4 x 12(minus 4 both sides)-4-4x 8 Copyright GED Testing Service LLC. All rightsreserved8
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Graphing the solution1.x 8Draw a number line. Just need a few numbers oneither side of the solution number.2. Decide if open circle or closed circle. Place it above thesolution number.3. Determine which way your arrow goes by substituting anumber in for the variable to make the statement true.Then draw the arrow pointing in that direction.Solve the Inequality48 8m48 8m886 m(draw wall, box variable)(divide 8 both sides)Graph the Solution1.6 mDraw a number line. Just need a few numbers oneither side of the solution number.2. Decide if open circle or closed circle. Place it above thesolution number.3. Determine which way your arrow goes by substituting anumber in for the variable to make the statement true.Then draw the arrow pointing in that direction. Copyright GED Testing Service LLC. All rightsreserved9
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/20176u 366u 3666u 63 4 5 6 7 83y – 1 53y – 1 5 1 13y 633y 2-10 12 34Solving Inequalities5x 7 3(x 1)5x 7 3(x 1)5x 7 3x 3Since you divided by apositive number, there is noneed to reverse the inequalitysign.2x 7 3-7 3 - 72x - 422x –2orx –2 Copyright GED Testing Service LLC. All rightsreserved10
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Solving Inequalities-2x 5-2x 5-2-2x –5/2x –5/2Since you divided by anegative number, you need toreverse the inequality sign.Solving Real-WorldInequalitiesIt begins with translationGEDtestingservice.com GED.comWhat would your students do?1. Guess2. Select “C”because theyhaven’t usedit in a while3. Skip it4. Sign up for aretest33GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved11
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017What students need to do!1. Read the problem carefully and determine what you aretrying to find2. Assign a variable to the quantity that must be found3. Write down what the variable represents4. Write the inequality5. Solve the inequality6. Test the solution set7. Look back at the problem34GEDtestingservice.com GED.comRecognize the Symbols and WordsInequalityCommonly Known is not equal toOther Words to Knowdoes not equal greater than or equal toat least; no fewer than; aminimum of; no less than less than or equal toat most; no more than; amaximum of; any more than less thanfewer than greater thanmore thanAn inequality places conditions on the value of the variable.35GEDtestingservice.com GED.comYour Turn!Which one is correct?Coach told us we1. N 18needed to complete2. N 18more than 183. N 18repetitions.364. N 18GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved12
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Your Turn!Which one is correct?Children under 12 pay a1. N 12discounted price at the2. N 12movie theatre.3. N 124. N 1237GEDtestingservice.com GED.comYour Turn!Which one is correct?Marie has purchased1. N 12party supplies for a2. N 12maximum of 12 people.3. N 124. N 1238GEDtestingservice.com GED.comStart with the BasicsJennifer has 10 fewer DVDs than Brad.j – 10 b(common answer, but incorrect)Insert the words and see the difference in theequation.j (has) b (fewer) – 10soj b – 1039GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved13
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Build Skills in Vocabulary and Translation40GEDtestingservice.com GED.comStart with Basic TranslationIf s represents the number of books that Sam has, and g represents thenumber of books that Gerard has, which inequality models the situation“Sam has more than twice the number of books as Gerard?”A) g 2s(Gerard has twice the number of books as Sam)B) g 2s(Gerard has than twice the number of books as Sam)C) s 2g(Sam has less than twice books as Gerard)D) s 2g(Twice Gerard’s books is 2 g, s has )GEDtestingservice.com GED.comYour Turn!Keith has 500 in a savingsaccount at the beginning of thesummer. He wants to have atleast 200 in the account by theend of the summer. He uses 25each week for food, clothes, andfun. How many weeks can Keithwithdraw money from hisWhich is correct?1. 500 – 25w 2002. 500 – 25w 2003. 500 – 25w 2004. 500 – 25w 200account?At first glance, you might think that it is supposed to beless than, but Keith wants the amount in the account to be“at least” 200, which means 200 or greater. Thus, you mustuse .42GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved14
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Your Turn!Yellow Cab Taxi charges a 1.75 flat rate in addition to 0.66 per mile. Katie has noWhich is correct?1. .66x 1.75 10more than 10 spend on a2. .66x 1.75 10ride How many miles can3. .66x 1.75 10Katie travel without4. .66x 1.75 10exceeding her limit?The “no more than” can be tricky. It can make you think of“greater than” however, it really means that Katie has tospend 10.00 or less.43GEDtestingservice.com GED.comReal-World ContextA new music downloading software, GotTunes, istrying to compete with iTunes. Though iTunescharges no monthly fee to download music, itcharges 1.25 a song. GotTunes charges a monthlyfee of 30, but a member is free to download musicall month. Write an inequality and solve for howmany songs you have to download to makeGotTunes a better deal than iTunes.44GEDtestingservice.com GED.comWrite, Solve and GraphA new music downloading software, GotTunes, is trying to compete with iTunes. ThoughiTunes charges no monthly fee to download music, it charges 1.25 a song. GotTunescharges a monthly fee of 30, but a member is free to download music all month. Writean inequality and solve for how many songs you have to download to make GotTunes abetter deal than iTunes.What is your unknown?The number of songs downloaded on iTunes at 1.25 per song? 1.25xWhat is the minimum number of songs you would need to download from iTunes toexceed 30 (the monthly fee)1.25x 301.251.25 (divide both sides by 1.25)x 2445You would need to downloadmore than 24 songs a monthfor GotTunes to be a betterdeal.GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved15
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Now Graph the Solution1.x 24Draw a number line. Just need a few numbers oneither side of the solution number.22 23 24 25 26 27 282. Decide if open circle or closed circle. Place it above thesolution number.3. Determine which way your arrow goes by substituting anumber in for the variable to make the statement true.Then draw the arrow pointing in that direction.46GEDtestingservice.com GED.comSample Question from GEDTSWhich is correct?B. 26x 270 1,32547Used with Permission from GED Testing Service GEDtestingservice.com GED.comSample Question from GEDTS48Used with Permission from GED Testing Service GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved16
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Remember, students need to Solve inequalities in one variable Solve an inequality and identify or create a graph on anumber line Analyze relationship between quantities in real-worldproblem and create an inequality Analyze relationship between quantities in real-worldproblem solve the inequalityPractice – Practice – Practice49GEDtestingservice.com GED.comResources for the ClassroomOnline resources that everyone can use50GEDtestingservice.com GED.comResources – Beginning LooksHow to Graph Inequalities for MiddleSchool: Fractions & Other Math Tipshttps://www.youtube.com/watch?v PTDNApjzsMHow to Solve Inequalitieshttps://www.youtube.com/watch?v wYEYeFGxHkI&t 57s51GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved17
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017ResourcesOne-Variable Inequalities – a/one-variable-linear-inequalitiesVirtual Nerds: What is an Inequality?https://www.youtube.com/watch?v wcBwdz-ZBaM52GEDtestingservice.com GED.comResourcesMath is Fun – Solving uality-solving.htmlVery Basics of Graphing Inequalities(on a number line)https://www.youtube.com/watch?v nif2PKA9bXA53GEDtestingservice.com GED.comResourcesSolving and GraphingInequalities (Excellent!) https://www.youtube.com/watch?v EE2qWIyjKD0Math Dude Unit 1-4 h?v 8hhewFQ K0w54GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved18
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Lesson PlanSolving Linear Inequalities– Event Planningwww.floridaipdae.org/index.cfm?fuseaction resources.GEDAHS&cagiid 3EFA989573B6E655GEDtestingservice.com GED.comLesson PlanFlorida IPDAE – GED andAHS LessonsBeginning Algebra –Lessons ion resources.GEDAHS&cagiid A314A7FABD6FAE56GEDtestingservice.com GED.comLesson PlanInequalities in .com GED.com Copyright GED Testing Service LLC. All rightsreserved19
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Lesson PlanInequalities –Solving andGraphinghttp://alex.state.al.us/lesson view.php?id 2903858GEDtestingservice.com GED.comNumber Line MakerGraph Inequality on NumberLine quality-on-numberline.phpNumber Line Maker ne-maker.php 59GEDtestingservice.com GED.comOne More!Cool Math – vinginequalities60GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved20
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Tips for Teaching Inequalities Make it meaningful - start withconcrete examples and real-worldproblems Make your thinking processes visible Solve the problems different ways Show the application Provide time for discussion61GEDtestingservice.com GED.com62GEDtestingservice.com GED.comSchedulePlanningAheadJuly 26, 2017 President’sReception 6:00 p.m.63GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved21
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Tuesdays for TeachersNext Tuesdays forTeachers – June 27th More content-basedinformation More strategies andactivities More resources64GEDtestingservice.com e.com GED.com66GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved22
Mathematical Reasoning: What’s theProblem with Inequalities?4/25/2017Contact Us:Daphne Atkinson,daphne.atkinson@gedtestingservice.comDebi com GED.comThank you!68GEDtestingservice.com GED.com Copyright GED Testing Service LLC. All rightsreserved23
Descriptors for Inequalities 6 A.3 Write, manipulate, solve, and graph linear inequalities A.3.a Solve linear inequalities in one variable with rational number coefficients. A.3.b Identify or graph the solution to a one variable linear inequality on a number line. A.3.c Solve real-world problems involving inequalities. A.3.d Write linear
May 02, 2018 · D. Program Evaluation ͟The organization has provided a description of the framework for how each program will be evaluated. The framework should include all the elements below: ͟The evaluation methods are cost-effective for the organization ͟Quantitative and qualitative data is being collected (at Basics tier, data collection must have begun)
Silat is a combative art of self-defense and survival rooted from Matay archipelago. It was traced at thé early of Langkasuka Kingdom (2nd century CE) till thé reign of Melaka (Malaysia) Sultanate era (13th century). Silat has now evolved to become part of social culture and tradition with thé appearance of a fine physical and spiritual .
On an exceptional basis, Member States may request UNESCO to provide thé candidates with access to thé platform so they can complète thé form by themselves. Thèse requests must be addressed to esd rize unesco. or by 15 A ril 2021 UNESCO will provide thé nomineewith accessto thé platform via their émail address.
̶The leading indicator of employee engagement is based on the quality of the relationship between employee and supervisor Empower your managers! ̶Help them understand the impact on the organization ̶Share important changes, plan options, tasks, and deadlines ̶Provide key messages and talking points ̶Prepare them to answer employee questions
Dr. Sunita Bharatwal** Dr. Pawan Garga*** Abstract Customer satisfaction is derived from thè functionalities and values, a product or Service can provide. The current study aims to segregate thè dimensions of ordine Service quality and gather insights on its impact on web shopping. The trends of purchases have
Chính Văn.- Còn đức Thế tôn thì tuệ giác cực kỳ trong sạch 8: hiện hành bất nhị 9, đạt đến vô tướng 10, đứng vào chỗ đứng của các đức Thế tôn 11, thể hiện tính bình đẳng của các Ngài, đến chỗ không còn chướng ngại 12, giáo pháp không thể khuynh đảo, tâm thức không bị cản trở, cái được
Le genou de Lucy. Odile Jacob. 1999. Coppens Y. Pré-textes. L’homme préhistorique en morceaux. Eds Odile Jacob. 2011. Costentin J., Delaveau P. Café, thé, chocolat, les bons effets sur le cerveau et pour le corps. Editions Odile Jacob. 2010. Crawford M., Marsh D. The driving force : food in human evolution and the future.
Le genou de Lucy. Odile Jacob. 1999. Coppens Y. Pré-textes. L’homme préhistorique en morceaux. Eds Odile Jacob. 2011. Costentin J., Delaveau P. Café, thé, chocolat, les bons effets sur le cerveau et pour le corps. Editions Odile Jacob. 2010. 3 Crawford M., Marsh D. The driving force : food in human evolution and the future.
