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5-Minute Check on Activity 1-2

5-Minute Check on Activity 1-2. Problem Solving Techniques: How many steps were Polya’s method? What were the steps? What were some other problem solving strategies?. 4. Understand the problem Devise a plan Carry out the plan Look back at the completed solution. Discussing the problem

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5-Minute Check on Activity 1-2

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  1. 5-Minute Check on Activity 1-2 • Problem Solving Techniques: • How many steps were Polya’s method? • What were the steps? • What were some other problem solving strategies? 4 • Understand the problem • Devise a plan • Carry out the plan • Look back at the completed solution Discussing the problem Organizing information Drawing a picture Recognizing patterns Doing a simpler problem Click the mouse button or press the Space Bar to display the answers.

  2. Activity 1 - 3 Make Me an Offer or Show me the Money!

  3. Objectives • Use the basic steps for problem-solving • Translate verbal statements into algebraic equations • Use the basic principles of algebra to solve real-world problems • Use formulas to solve problems

  4. Vocabulary • Formula – an equation involving letters as variables

  5. Basic Steps in Problem Solving Solving any problem generally requires the following four steps • Understand the problem • Develop a strategy for solving the problem(Devise a plan) • Execute your strategy to solve the problem(Carry out the plan) • Check your solution for correctness (Look back at the completed solution)

  6. Description “Night Train” Henson is negotiating a new contract with his team. He wants $800,000 for the year and an additional $6000 for every game he starts. His team offered $10,000 for every game he starts, but only $700,000 for a base salary. How many games would he need to start in order to make more with the team’s offer? His offer < Team’s offer 800,000 + 6,000S < 700,000 + 10,000S 100,000 < 4,000S 25 < S

  7. Checking Account You need to open a checking account and decide to shop around for a bank. Acme bank has an account with a $10 monthly charge, plus 25 cents per check. Farmer’s bank will charge you $12 per month, with a 20 cent charge per check. How many checks would you need to write each month to make Farmer’s bank the getter deal. 0.25 $10 y = 0.25x + $10 0.20 $12 y = 0.20x + $12 0.25x + 10 ≤ 0.20x + 12 0.05x ≤ 2 x ≤ 40

  8. Perimeter The perimeter of a rectangular pasture is 2400 feet. If the width is 800 feet, how long is the pasture? P = 2(length + width) = 2(L + W) 2400 = 2(L + 800) 2400 = 2L + 1600 800 = 2L 400 = L

  9. Formulas • Choose appropriate letters to represent each variable quantity and write what each letter represents • Use the letters to translate each stated relationship into a symbolic (algebraic) formula • Use the formula to solve the exercise

  10. Extra Work Problems 1 • Net income = Revenue – Cost 11) Net Pay = Gross Income – Deductions • Depreciation = (Ocost – Rvalue)  Est Life = 400,000 – 156,800 = $143,200 = 65,000 – 12,860 = $52,140 = (25,000 – 2,000)  10 = 23,000  10 = 2,300 per year

  11. Extra Work Problems 2 = (9205) + 32 = 68°F 13) F = (9C  5) + 32 a) 20°C b) 100°C 14) C = 5(F – 32)  9 a) 86°F b) 41°F 15) Distance = rate  time a) 50 mph; 5 hr b) 25 km/min; 2 hr = (91005) + 32 = 212°F = 5(86 - 32)  9 = 5(54)  9 = 30 = 5(41 - 32)  9 = 5(9)  9 = 5 = 50  5 = 250 miles = 25  2  60 = 3000 km

  12. 4 Steps in Problem Solving • Understand the problem • Read the problem completely and carefully • Draw a sketch of the problem, if possible • Develop a strategy for solving the problem • Identify and list everything you know about the problem, including relevant formulas. Add labels to diagram • Identify and list what you want to know • Execute your strategy to solve the problem • Write an equation that relates the know quantities and the unknown • Solve the equation • Look back at the completed solution • Is your answer reasonable? • Is your answer correct?

  13. Summary and Homework • Summary • Understand the problem • Develop a strategy for solving the problem • Execute your strategy to solve the problem • Look back at the completed solution • Language of Math is equations • Homework • pg 17; 1-10

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