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Algebraic Modeling

Algebraic Modeling. Solving One-Step Equations. Objectives. Write and solve one-step equations Solve real-world problems including those involving distance, rate, and time. Please Excuse My Dear Aunt Sally. P. Parentheses ( ). E. Exponents 4 3. M D. Multiply x Divide . A

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Algebraic Modeling

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  1. Algebraic Modeling Solving One-Step Equations

  2. Objectives • Write and solve one-step equations • Solve real-world problems including those involving distance, rate, and time

  3. Please Excuse My Dear Aunt Sally P Parentheses ( ) E Exponents 43 M D Multiply x Divide  A S Add + Subtract -

  4. ONE STEP EQUATIONS An equation is like a balance scale because it shows that two quantities are equal. What you do to one side of the equation must also be done to the other side to keep it balanced.

  5. ONE STEP EQUATIONS • What is the variable? To solve one step equations, you need to ask three questions about the equation: • What operation is performed on the variable? • What is the inverse operation? (The one that will undo what is being done to the variable)

  6. ONE STEP EQUATIONS Example 1 Solve x + 4 = 12 What is the variable? The variable is x. Addition. What operation is being performed on the variable? What is the inverse operation (the one that will undo what is being done to the variable)? Subtraction. Using the subtraction property of equality, subtract 4 from both sides of the equation. The subtraction property of equality tells us to subtract the same thing on both sides to keep the equation equal. x + 4 = 12 - 4 - 4 x 8 =

  7. ONE STEP EQUATIONS Example 2 Solve y - 7 = -13 What is the variable? The variable is y. What operation is being performed on the variable? Subtraction. What is the inverse operation (the one that will undo what is being done to the variable)? Addition. Using the addition property of equality, add 7 to both sides of the equation. The addition property of equality tells us to add the same thing on both sides to keep the equation equal. y - 7 = -13 + 7 + 7 y = -6

  8. ONE STEP EQUATIONS Example 3 Solve –6a = 12 What is the variable? The variable is a. What operation is being performed on the variable? Multiplication. What is the inverse operation (the one that will undo what is being done to the variable)? Division Using the division property of equality, divide both sides of the equation by –6. The division property of equality tells us to divide the same thing on both sides to keep the equation equal. –6a = 12 -6 -6 a = -2

  9. ONE STEP EQUATIONS = -10 Example 4 Solve What is the variable? The variable is b. What operation is being performed on the variable? Division. What is the inverse operation (the one that will undo what is being done to the variable)? Multiplication Using the multiplication property of equality, multiply both sides of the equation by 2. The multiplication property of equality tells us to multiply the same thing on both sides to keep the equation equal. = -10 2 • = -10 • 2 b = -20

  10. Example 1: Application Zoology • Justify each step • Subtract both sides by 5033 • Always put your answer in a sentence and label correctly for word problems. • Solve the following equation • 5396 = 5033 + w • 363 = w • The weight of the baby elephant is 363 lbs

  11. Solving Word Problems

  12. “Word Problems scare me!”

  13. “Word Problems make me nervous!”

  14. “Word Problems? I just skip them!”

  15. Don’t Worry! With just 4 easy steps, you can become… a Word Problem Whiz!

  16. Step 1 UNDERSTAND the problem. What are you trying to figure out? Here’s an example:

  17. Yesterday, Alex saw 14 birds in his backyard. Today, he saw 12. How many birds did he see in all? In this problem, what are you trying to figure out?

  18. If you said: “How many birds did Alex see in all?” then… You’re right!

  19. Step 2 Get a PLAN. How will you answer the question? Should you ADD or SUBTRACT?

  20. Look for clues. Here are some CLUE WORDS that will help you decide what to do.

  21. Addition Clue Words in all altogether sum total

  22. Subtraction Clue Words how many more how many are left difference

  23. Let’s look at the example again. Yesterday, Alex saw 14 birds in his backyard. Today, he saw 12. How many birds did he see in all? Do you see any CLUE WORDS?

  24. If you said… “in all,” then… You’re right!

  25. The words “in all” tell us that we should ADD! Now that we UNDERSTAND the problem, and have a PLAN, we’re ready for the next step!

  26. Step 3 SOLVE it! Write a number sentence using the information in the problem, and…

  27. Work it out!

  28. Give it a try! Yesterday, Alex saw 14 birds in his backyard. Today, he saw 12. How many birds did he see in all? Write a number sentence and SOLVE it.

  29. If you wrote… 14 + 12 = 26 then… You’re right!

  30. Step 4 LOOK BACK. Does your answer fit the question?

  31. We had to find out how many birds Alex saw in all. We added the number he saw yesterday and the number he saw today.

  32. Our answer was “Alex saw 26 birds in all.” It makes sense!

  33. We did it! We are Word Problem Whizzes!

  34. Here are the steps once more: Step 1 – UNDERSTAND the problem. Step 2 – Get a PLAN. Step 3 – SOLVE it! Step 4 – LOOK BACK.

  35. Solving one-step equations • In 1975, Bob Hall became the first wheelchair athlete to win the Boston Marathon. He finished the 26.2 mile race in about 178 minutes. Use the following formula to find his average speed, or rate, in miles per minute. • d = rt • (Underline/record important info!!!)

  36. Example 2: d = rt • Important information • Distance = 26.2 mi • Time = 178 min • Rate = is unknown • Plug information into formula • 26. 2 = r(178) • 26. 2 = r(178) • 26. 2 = 178r 178 178 0.15 ≈ r

  37. Charity Walk • You are taking part in a charity walk, and you have walked 12.5 miles so far. Your goal is to walk 20 miles. How many more miles do you need to walk to meet your goal? • (Underline/record important info!!!)

  38. Charity Walk 12.5 + m = 20 • walked 12.5 miles so far • goal is to walk 20 miles • How many left to walk? • Let m = miles left to walk -12.5 = -12.5 m = 7.5 You need to walk 7.5 more miles to reach your goal.

  39. Example: 1 • Lisa is cooking muffins. The recipe calls for 7 cups of sugar. She has already put in 2 cups. How many more cups does she need to put in? • (Underline/record important info!!!)

  40. Example 1: 2 + c = 7 • Calls for 7 cups • Put in 2 cups • How many left? • Let c = unknown cups -2 = -2 c = 5 You need to put in 5 more cups of sugar.

  41. Example: 2 • How many packages of diapers can you buy with $40 if one package costs $8? • (Underline/record important info!!!)

  42. Example 2: 8d = 40 • Your have $40 • Cost is $8 each • How many can you buy? • Let d = unknown diapers 8 8 d = 5 You can buy 5 packages of diapers with $40.

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