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Lesson 3-1

Learn how to translate verbal sentences into equations and vice versa. Practice using the four-step problem-solving plan and understand the language of math equations.

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Lesson 3-1

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  1. Lesson 3-1 Writing Equations

  2. Transparency 3-1 5-Minute Check on Chapter 2 • Evaluate 42 - |x - 7| if x = -3 • Find 4.1  (-0.5) • Simplify each expression • 3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9) • A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is notgreen? • Which of the following is a true statement Standardized Test Practice: 8/4 < 4/8 -4/8 < -8/4 -4/8 > -8/4 -4/8 > 4/8 A B C D

  3. Transparency 3-1 5-Minute Check on Chapter 2 • Evaluate 42 - |x - 7| if x = -3 • Find 4.1  (-0.5) • Simplify each expression • 3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9) • A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is notgreen? • Which of the following is a true statement 32 -8.2 -4d + 2 -7c + 40 62.5% = 5/8 Standardized Test Practice: 8/4 < 4/8 -4/8 < -8/4 -4/8 > -8/4 -4/8 > 4/8 C A B C D

  4. Objectives • Translate verbal sentences into equations • Translate equations into verbal sentences

  5. Vocabulary • Four-step problem solving plan – “Key Concept” • Step 1: Explore the problem • Step 2: Plan the solution • Step 3: Solve the problem • Step 4: Examine the solution • Defining a variable – letting a variable represent one of the unspecified numbers in the problem • Formula – is an equation that states a rule for the relationship between certain quantities

  6. Language of Math: Equations English expressions that suggest “=“ • is • equals • is equal to • is the same as • is as much as • is identical to

  7. Four-Step Problem Solving Plan • Step 1: Explore the Problem • Identify what information is given (the facts) • Identify what you are asked to find (the question) • Step 2: Plan the Solution • Find an equation the represents the problem • Let a variable represent what you are looking for • Step 3: Solve the Problem • Plug into your equation and solve for the variable • Step 4: Examine the Solution • Does your answer make sense? • Does it fit the facts in the problem?

  8. Answer: The equation is . Example 1 Translate this sentence into an equation. A number b divided by three is equal to six less than c. bdivided by three is equal to six less than c.

  9. 1,2500,000 10,000,000 h Example 2 JellybeansA popular jellybean manufacturer produces 1,250,000 jellybeans per hour. How many hours does it take them to produce 10,000,000 jellybeans? Explore You know that 1,250,000 jellybeans are produced each hour. You want to know how many hours it will take to produce 10,000,000 jellybeans. PlanWrite an equation to represent the situation. Let h represent the number of hours neededto produce the jellybeans. 1,250,000 times hours equals 10,000,000.

  10. 1,2500,000 10,000,000 h Solve Example 2 cont Plan Write an equation to represent the situation. Let h represent the number of hours needed to produce the jellybeans. 1,250,000 times hours equals 10,000,000. Find h mentally by asking, “What number times 125 equals 1000?” h = 8 Answer:It will take 8 hours to produce 10,000,000 jellybeans.

  11. P 4s Answer: The formula is . Example 3 Translate the sentence into a formula. The perimeter of a square equals four times the length of the side. Words Perimeter equals four times the length of the side. VariablesLet P=perimeter and s= length of a side. Perimeter equals four times the length of a side.

  12. a2 3b a squared plus three times b equals c divided by six. Example 4 Translate this equation into a verbal sentence. Answer: a squared plus three times b equals c divided by six.

  13. 1. 2. Example 5 Translate each equation into a verbal sentence. Answer:Twelve divided by b minus four equals negative one. Answer: Five times a equals b squared plus one.

  14. Summary & Homework • Summary: • Equations are the language of Math • Variables are used to represent unknowns when writing equations • Formulas given in sentence form need to be rewritten as algebraic equations • Homework: • pg 124: 14-38 even

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