5-Minute Check on Activity 1-2

1
5-Minute Check on Activity 1-2

• Problem Solving Techniques
• How many steps were Polyas method?
• What were the steps?
• What were some other problem solving strategies?

4

1. Understand the problem
2. Devise a plan
3. Carry out the plan
4. Look back at the completed solution

1. Discussing the problem
2. Organizing information
3. Drawing a picture
4. Recognizing patterns
5. Doing a simpler problem

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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 teams offer?

His offer lt Teams offer 800,000
6,000S lt 700,000 10,000S
100,000 lt 4,000S 25 lt 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. Farmers 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
  Farmers bank the getter deal.

Bank Checks Monthly Equation
Acme
Farmers
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
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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
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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

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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
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Extra Work Problems 2

• 13) F (9C ? 5) 32 a) 20C b)
  100C
• 14) C 5(F 32) ? 9 a) 86F b)
  41F
• 15) Distance rate ? time a) 50 mph 5
  hr b) 25 km/min 2 hr

(9?20?5) 32 68F
(9?100?5) 32 212F
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
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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