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Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE

Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE. Click the ‘NEXT’ button to continue. NEXT. introduction.

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Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE

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  1. Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE Click the ‘NEXT’ button to continue NEXT

  2. introduction • Today, in Ms. Stechschulte’s 7th grade class, we will be learning how to solve one-step equations. To navigate through this presentation, click on the arrows and buttons at the bottom of the screen. The arrow labeled ‘NEXT’, will take you to the next slide. The arrow labeled ‘BACK’, will take you back to the previous slide. When you get to the Main Menu, click on the first link to begin the lesson. If you need to go back to the previous lessons to clarify concepts, please do so. • Click the arrow below to continue. NEXT

  3. Goal • Your goal is to learn the concept of solving equations so you are successful answering the quiz questions. You must know the concepts well enough to solve two-step equations for tomorrow’s class. When you are finished with the first 2 Lessons, go to Lesson 3 and play the online math games for the remainder of the class period. • Good luck and have fun  NEXT BACK

  4. What is an equation? • “An equation is a written statement indicating the equality of two expressions” • It consists of a sequence of symbols that are split into left and right sides joined by an equal sign. • For example, 2 + 4 = 6is an equation. http://dictionary.reference.com/browse/equation Left side Right side NEXT BACK

  5. Parts of an equation * Remember * 2x + 3 = 5 Left side Right side Coefficient: the number that is in front of the x. This means that 2 and x are multiplied. Variable: the letter you are solving for; it needs to be isolated on one side of the equation. A variable can be any letter. NEXT BACK

  6. Main menuSolving equations Lesson 1: Using adding & subtracting Lesson 2: Using multiplication & division Lesson 3: Online Math Games Click on the link for Lesson 1 to begin. When finished with Lesson 1, continue with Lesson 2 then 3.

  7. Online math games • Hoop Shoot • Equation Buster • Easy Algebra Equations • Say the ‘2 – steps’: Rags to Riches BACK

  8. Solving Equations is like balancing a scale: x + 1 = 3 To solve an equation you must get x by itself on one side of the equal sign, while keeping the scale balanced 1 1 1 x 1 NEXT BACK =

  9. Solving Equations is like balancing a scale: To get x by itself you have to take away (subtract) 1. However, this will cause the scale to become unbalanced, so you also have to take away 1 from the other side of the equal sign. 1 1 x 1 1 NEXT BACK =

  10. Solving Equations is like balancing a scale: x + 1 = 3 -1 -1 x = 2 After you subtract 1 from both sides of the equal sign, you are left with x = 2 1 1 1 x 1 NEXT BACK =

  11. inverse operation • “Two operations are said to be inverse to each other if one operation undoes the effect of the other operation.” • Addition and Subtraction are inverse operations • Multiplication and Division are inverse operations http://www.icoachmath.com/Sitemap/InverseOperation.html NEXT BACK

  12. Solving equations Inverse operations must be used when solving equations. In the previous example we SUBTRACTED to undo the ADDITION to get x by itself. To solve x – 5 = 3, what operation must you use to get x by itself? NEXT BACK

  13. Solving equations If you said ADDITION you are correct! To undo SUBTRACTION you must ADD. To solve x – 5 = 3 +5 +5 x = 8 Add 5 to both sides to keep the equation balanced. MORE EXAMPLES BACK Begin Quiz 1

  14. More examples x + 2 = 4 To solve an equation get rid of whatever is with the variable (x). What you do to one side, you must also do to the other side. 1 1 1 1 1 x 1 NEXT =

  15. More examples x + 2 = 4 Subtract 2 from both sides to keep the scale balanced 1 1 x = 2 1 1 1 x 1 To Quiz 1 NEXT BACK =

  16. More examples Since 2 is SUBTRACTED from x, you must ADD 2 to both sides to solve x – 2 = 3 +2 +2 x = 5 Add 2 to both sides to keep the equation balanced. To Quiz 1 NEXT BACK

  17. More examples -1 = 7 + x is the same as saying 7 + x = -1 Since 7 is ADDED to x, you must SUBTRACT 7 from both sides to solve -1 = 7 + x -7 -7 -8 = x x = -8 Subtract 7 from both sides to keep the equation balanced. To Quiz 1 BACK

  18. Quiz 1 Question 1: Solve x + 4 = 9 A. x = 13 B. x = 5 C. x = 9 Click on a letter to continue.

  19. Quiz 1 Question 2: Solve x – 5 = 2 A. x = -3 B. x = 2 C. x = 7 Click on a letter to continue.

  20. Quiz 1 Question 3: Solve – 5 = 4 + x A. x = -9 B. x = -1 C. x = 9 Click on a letter to continue.

  21. Correct!! Nice Work! NEXT

  22. Correct!! Great Job! NEXT

  23. Correct!! Fabulous! NEXT

  24. Incorrect Try Again Let’s look at another example NEXT

  25. More examples x + 2 = 4 To solve an equation get rid of whatever is with the variable (x). What you do to one side, you must also do to the other side. 1 1 1 1 1 x 1 NEXT =

  26. More examples x + 2 = 4 Subtract 2 from both sides to keep the scale balanced 1 1 x = 2 1 1 1 x 1 To Quiz 1 BACK =

  27. Incorrect Try Again Let’s look at another example NEXT

  28. More examples Since 2 is SUBTRACTED from x, you must ADD 2 to both sides to solve x – 2 = 3 +2 +2 x = 5 Add 2 to both sides to keep the equation balanced. To Quiz 1

  29. Incorrect Try Again Let’s look at another example NEXT

  30. More examples -1 = 7 + x is the same as saying 7 + x = -1 Since 7 is ADDED to x, you must SUBTRACT 7 from both sides to solve -1 = 7 + x -7 -7 -8 = x x = -8 Subtract 7 from both sides to keep the equation balanced. To Quiz 1

  31. SOLVING EQUATIONS What is the inverse operation of MULTIPLICATION? NEXT BACK

  32. SOLVING EQUATIONS The answer is… DIVISION NEXT BACK

  33. SOLVING EQUATIONS What is the inverse operation of DIVISION? NEXT BACK

  34. SOLVING EQUATIONS The answer is… MULTIPLICATION NEXT BACK

  35. SOLVING EQUATIONS When you have an equation with multiplication or division, you will do the inverse operation to solve! NEXT BACK

  36. examples Since 6 and x are multiplied, to solve, we divide by 6. 6x = 48 6x = 48 6 6 x = 8 Divide by 6 on both sides to keep the equation balanced. NEXT BACK Reminder: When a number is divided by itself, it equals 1.

  37. examples Since x is divided by 4, to solve, we multiply by 4. x = 5 4 (4)x = 5(4) 4 x = 20 Multiply by 4 on both sides to keep the equation balanced. To Quiz 2 MORE EXAMPLES BACK

  38. More examples The inverse operation of MULTIPLICATION is DIVISION, so we divide by 10. 10x = 30 10x = 30 10 10 x = 3 Divide by 10 on both sides to keep the equation balanced. To Quiz 2 NEXT BACK

  39. More examples The inverse operation of DIVISION is MULTIPLICATION, so we multiply by -5. x = 3 -5 (-5)x = 3(-5) -5 x = -15 Multiply by -5 on both sides to keep the equation balanced. To Quiz 2 NEXT BACK ** Remember: Negative times a positive = negative

  40. More examples The inverse operation of MULTIPLICATION is DIVISION, so we divide by -2. -2x = -10 -2x = -10 -2 -2 x = 5 Divide by -2 on both sides to keep the equation balanced. To Quiz 2 BACK ** Remember: Negative times a negative = positive

  41. Quiz 2 Question 1: Solve 5x = 35 A. x = 175 B. x = 30 C. x = 7 Click on a letter to continue.

  42. Incorrect Try Again Let’s look at another example NEXT

  43. Correct!! Super! NEXT

  44. Quiz 2 Question 2: Solve x = 4 -2 A. x = -8 B. x = 6 C. x = -2 Click on a letter to continue.

  45. Incorrect Try Again Let’s look at another example NEXT

  46. Correct!! Fantastic! NEXT

  47. Quiz 2 Question 3: Solve -3x = 6 A. x = 2 B. x = -2 C. x = -18 Click on a letter to continue.

  48. Incorrect Try Again Let’s look at another example NEXT

  49. Correct!! Great Job! NEXT

  50. More examples The inverse operation of MULTIPLICATION is DIVISION, so we divide by 10. 10x = 30 10x = 30 10 10 x = 3 Divide by 10 on both sides to keep the equation balanced. To Quiz 2

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