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T RANSLATING V ERBAL P HRASES

T RANSLATING V ERBAL P HRASES. Verbal Phrase. Expression. The sum of six and a number. Ten times a number. A number decreased by nine. A number plus five. Eight more than a number. Eight. number. more than. number. number. five. plus. +. +. A number increased by seven. seven.

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T RANSLATING V ERBAL P HRASES

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  1. TRANSLATING VERBAL PHRASES Verbal Phrase Expression The sum of six and a number Ten times a number A number decreased by nine A number plus five Eight more than a number Eight number more than number number five plus + + A number increased by seven seven + increased ( ) 10n number nine – decreased number Ten times • 7 Seven number x divided The sum of six and a number 6 + x 6 + x number x + sum six 6 Eight more than a number y + 8 y + 8 y 8 A number plus five n + 5 n + 5 n 5 A number increased by seven x + 7 x + 7 x 7 n – 9 n – 9 A number decreased by nine n 9 (10n) (10 ) 10 •n Ten times a number 10 •n ( ) 10n or n n 10 10 n Seven divided by a number 7 x

  2. USING AVERBAL MODEL In Mathematics there is a difference between a phrase and a sentence. Phrases translate into expressions; sentences translate into equations or inequalities. Phrases Expressions Equations or Inequalities Sentences

  3. is = The sum of six and a number 6 + x The sum of six and a number is 6 + x = < 12 = 12 In this sentence, “is” says that one quantity is equal to one another. Sentence is twelve. Equation The sum of six and a number is twelve. 6 + x = 12 6 + x= 12 number is twelve. is less than twelve. Sentence In this sentence, the words “is less than” indicate an inequality. Inequality 6 + x < 12 6 + x< 12 The sum of six and a number is less than twelve. is less than twelve. USING AVERBAL MODEL Phrase Expression The sum of six and a number 6 + x The sum of six and a number is 6 + x = The sum of six and a number is twelve. 6 + x = 12 The sum of six and a number is less than twelve. 6 + x < 12

  4. USING AVERBAL MODEL Writing algebraic expressions, equations, or inequalities that represent real-life situations is called modeling. The expression, equation, or inequality is a mathematical model. Use three steps to write a mathematical model. WRITE A VERBAL MODEL. ASSIGN LABELS. WRITE AN ALGEBRAIC MODEL.

  5. Writing 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. SOLUTION Understand 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. Writing an Algebraic Model Cost per plate Number of plates Bill LABELS p Tax 25.20 2 2 ALGEBRAIC MODEL – p = 1.20 25.20 1.20 Your group ordered 12 plates of food costing $24.00. VERBAL MODEL – = • Cost per plate = (dollars) Number of plates = (plates) Amount of bill = (dollars) Tax = (dollars) = 2p 24.00 p = 12

  7. Writing an Algebraic Model LABELS ALGEBRAIC MODEL SOLVE CHECK A PROBLEM SOLVING PLAN USING MODELS 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. 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. VERBAL MODEL Assign labels to each part of your verbal problem. Assign labels to each part of your verbal problem. Use 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. Solve the algebraic model and answer the original question. Solve the algebraic model and answer the original question. Check that your answer is reasonable.

  8. Using a Verbal Model JET 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?

  9. Using a Verbal Model Speed of jet Time You can use the formula (rate)(time) = (distance) to write a verbal model. LABELS 2 x 600 ALGEBRAIC MODEL 2 x 600 To arrive in 2 hours, the pilot would have to slow the jet down to300miles per hour. a. At what speed would the jet have to fly to arrive in Chicago in 2 hours? SOLUTION Distance to travel VERBAL MODEL = • Speed of jet = (miles per hour) Time = (hours) Distance to travel = (miles) = x = 300

  10. Using a Verbal Model b. 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.

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