Presentation on theme: "The sum of six and a number The sum of six and a number number 6 + x"— Presentation transcript:
1The sum of six and a number The sum of six and a number number 6 + x TRANSLATING VERBAL PHRASESVerbal PhraseExpressionThe sum of six and a numberThe sum of six and a numbernumber6 + x6 + xsumsixx6+Eight more than a numberEight more than a numberEightmore thannumbery + 8y + 8+y8A number plus fiveA number plus fiveplusnumberfiven + 5n + 5+n5A number increased by sevenA number increased by sevenincreasedx + 7x + 7+numbersevenx7A number decreased by nineA number decreased by ninedecreasedn – 9n – 9–numberninen9Ten times a number(10n)Ten times a numbertimes10 • n10 • n(10 )Tennumber•( )10n( )10n10nor10nn7xSeven divided by a numberdivided7Sevennumberx
2MODEL AND SOLVE REAL-LIFE PROBLEMS In Mathematics there is a difference between a phrase and a sentence. Phrases translate into expressions; sentences translate into equations or inequalities.PhrasesExpressionsSentencesEquations or Inequalities
3The sum of six and a number The sum of six and a number 6 + x 6 + x MODEL AND SOLVE REAL-LIFE PROBLEMSPhraseExpressionThe sum of six and a numberThe sum of six and a number6 + x6 + xThe sum of six and a number is6 + x =The sum of six and a number isis6 + x ==In this sentence, “is” says thatone quantity is equal to one another.SentenceEquationThe sum of six and a number is twelve.6 + x = 12The sum of six and a number is twelve.number is twelve.6 + x = 12is twelve.6 + x = 12= 12In this sentence, the words “is less than” indicate an inequality.SentenceInequalityThe sum of six and a number is less than twelve.6 + x < 12is less than twelve.6 + x < 12The sum of six and a number is less than twelve.6 + x < 12< 12is less than twelve.
4WRITE AN ALGEBRAIC MODEL. MODEL AND SOLVE REAL-LIFE PROBLEMSWriting algebraic expressions, equations, or inequalities that represent real-life situations is called modeling.The expression, equation, or inequality is amathematical model.Use three steps to write a mathematical model.WRITE AVERBAL MODEL.ASSIGN LABELS.WRITE AN ALGEBRAIC MODEL.
5Writing an Algebraic Model You and three friends are having a dim sum lunch at a Chinese restaurant that charges $2 per plate. You order lots of plates. The waiter gives you a bill for $25.20, which includes tax of $1.20. Use mental math to solve the equation for how many plates your group ordered.SOLUTIONUnderstand the problem situation before you begin. For example, notice that tax is added after the total cost of the dim sum plates is figured.
6– – • = = = = Your group ordered 12 plates of food costing $24.00. Writing an Algebraic ModelVERBALMODELCost perplateNumber of plates•=–BillTaxLABELSCost per plate =2(dollars)ALGEBRAICMODELpNumber of plates =(plates)Amount of bill =25.20(dollars)Tax =1.20(dollars)2=p25.201.20–2p=24.00p=12Your group ordered 12 plates of food costing $24.00.
7Assign labels to each part of your verbal problem. Writing an Algebraic ModelA PROBLEM SOLVING PLAN USING MODELSVERBALMODELAsk yourself what you need to know to solve the problem. Then write a verbal model that will give you what you need to know.Ask yourself what you need to know to solve the problem. Then write a verbal model that will give you what you need to know.LABELSAssign labels to each part of your verbal problem.Assign labels to each part of your verbal problem.ALGEBRAICMODELUse the labels to write an algebraic model based on your verbal model.Use the labels to write an algebraic model based on your verbal model.SOLVESolve the algebraic model and answer the original question.Solve the algebraic model and answer the original question.CHECKCheck that your answer is reasonable.
8Using a Verbal ModelJET PILOT A jet pilot is flying from Los Angeles, CA to Chicago, IL at a speed of 500 miles per hour. When the plane is 600 miles from Chicago, an air traffic controller tells the pilot that it will be 2 hours before the plane can get clearance to land. The pilot knows the speed of the jet must be greater then 322 miles per hour or the jet could stall.a. At what speed would the jet have to fly to arrive in Chicago in 2 hours?b.Is it reasonable for the pilot to fly directly to Chicago at the reduced speed from part (a) or must the pilot take some other action?
9Using a Verbal Modela. At what speed would the jet have to fly to arrive in Chicago in 2 hours?SOLUTIONYou can use the formula (rate)(time) = (distance) to write a verbal model.VERBALMODELSpeed ofjetDistance totravel•Time=LABELSSpeed of jet =x(miles per hour)ALGEBRAICMODELTime =2(hours)Distance to travel =600(miles)2x=600x=300To arrive in 2 hours, the pilot would have to slow the jet down to 300 miles per hour.
10Using a Verbal Modelb.Is it reasonable for the pilot to fly directly to Chicago at 300 miles per hour or must the pilot take some other action?It is not reasonable for the pilot to fly at 300 miles per hour, because the jet could stall. The pilot should take some other action, such as circling in a holding pattern, to use some of the time.