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# Solving Equations by Factoring KTIP lesson plan

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interdisciplinary lesson plan w/connection to physics

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### Solving Equations by Factoring KTIP lesson plan

1. 1. KTIP/TPA LESSON PLAN FORMAT<br />Name: Date:Age/Grade Level: 14/9th<br /># of Students: # of IEPs: # of GSSPs: <br /># of LEPs: <br />Subject: Algebra 1Content: FactoringLesson Length: 90 minutes<br />Unit Title: Factoring Patterns Lesson Nbr/Title: Day 5/Solving equations by factoring. <br />ACTIONS – Described prior to observation<br />TECHNOLOGY – CALCULATORS, ALGEBRA TILES, <br />MANIPULATIVES NEEDED - <br />Lesson Objectives – <br /><ul><li>Students will use factoring in solving polynomial equations.
2. 2. Students will solve real world problems by writing and factoring equations.</li></ul>Connections – <br />Common Core Standards (college and career readiness standards for math)<br />Core Practices (4): Look for and make use of structure.<br />Program of Studies <br />MA-HS-AT-S-VEO9<br />Students will factor quadratic polynomials. <br />Kentucky Core Content<br />MA-HS-5.2.1<br />Students will apply order of operations, real number properties (identity, inverse, commutative, associative, distributive, closure) and rules of exponents (integer) to simplify algebraic expressions. <br />MA-HS-5.2.3<br />Students will:<br />add, subtract and multiply polynomial expressions; <br />factor polynomial expressions using the greatest common monomial factor and <br />factor quadratic polynomials of the form ax2 + bx + c, when a = 1 and b and c are integers.<br />MA-HS-5.2.4<br />Students will factor quadratic polynomials, such as perfect square trinomials and quadratic polynomials of the form ax2 + bx + c when a ≠ 1 and b and c are integers.<br />Context – <br />Students are primarily from rural communities and are generally from upper middleclass families. <br />This lesson is taught on day 5 of the Factoring Unit. It continues students learning to understand factoring quadratics when a is an integer other than one. <br />The previous lessons were:<br /><ul><li>Factoring Pattern for x2+bx+c.
3. 3. Factoring Pattern for ax2+bx+c, when a does not equal 1.
4. 4. Factoring by grouping
5. 5. Using several methods of factoring. </li></ul>Resources, media, technology –<br /><ul><li>Projector
6. 6. Computer
7. 7. PowerPoint
8. 8. Guided Notes with examples</li></ul>References – <br />Brown, B. (2000). Algebra Structure and Method Book 1. City: Houghton Mifflin <br />College Div.<br />Dolciani, M. (1992). Algebra 1. City: Houghton Mifflin Company.<br />Dixon, A. (2001). Algebra 1. Paramus: Globe Fearon.<br />Procedures – <br /><ul><li>Warm Up – 5 problems from Days 1-5 of factoring unit (10 minutes)
9. 9. Lesson Development (70 minutes)
10. 10. Lecture from PowerPoint w/guided & individual practice
11. 11. Today we’re going to learn how to use factoring to solve equations and answer real world problems. Before we get started, we need to review the zero product property.
12. 12. Can you tell me what the zero product property is?
13. 13. For all real numbers a and b, ab = 0 if and only if a = 0 or b = 0.
14. 14. Can you put the zero product property in your own words?
16. 16. Example 1.
17. 17. How can we use what we just learned to solve example 1?
18. 18. Either (x + 2) = 0 or (x + 5) = 0
19. 19. How did you solve x + 2 = 0?
20. 20. Add -2 to both sides.
21. 21. How did you solve x + 5 = 0?
22. 22. Add -5 to both sides.
23. 23. What is the solution set?
24. 24. {-2, -5}
25. 25. Next try one with your partner. If you finish early, you may begin to work on the You Try problems. If you need help, please place your book on end on your desk and continue on to another problem.
26. 26. What is the solution set and how did you solve it?
27. 27. {-5, 7}. Add -5 to x + 5 = 0; add -7 to x + 7 = 0
28. 28. Now complete the You Try problems and I will be around to check your work.
29. 29. Example 2.
30. 30. How is example 2 different from example 1?
31. 31. There are three terms on the left hand side.
32. 32. What could we do to solve this problem?
33. 33. Set each term equal to zero.
34. 34. What is the solution set?
35. 35. {0, 3, 4}
36. 36. Next try one with your partner. If you finish early, you may begin to work on the You Try problems. If you need help, please place your book on end on your desk and continue on to another problem.
37. 37. Can you please write the solution on the board?
38. 38. Answers will vary (should be very similar to the PowerPoint)
39. 39. Now complete the You Try problem and I will be around to check your work.
40. 40. Example 3
41. 41. What is different about example 3?
42. 42. It is not in factored form.
43. 43. What can we do to get it into factored form?
44. 44. Transform the equation into standard form by subtracting 12 from both sides.
45. 45. Factor the equation
46. 46. What do we do after we get the equation into factored form?
47. 47. Set each factor equal to 0 and solve.
48. 48. Can you write the solution on the board?
49. 49. Answers will vary but should look like PowerPoint.
50. 50. Next try one with your partner. If you finish early, you may begin to work on the You Try problems. If you need help, please place your book on end on your desk and continue on to another problem.
51. 51. Can you please write the solution on the board?
52. 52. Answers will vary (should be very similar to the PowerPoint)
53. 53. Now complete the You Try problems and I will be around to check your work. If you finish early please attempt the puzzler problems for bonus points.
54. 54. In Physics, often times we need to use factoring to answer questions about movement, height and speed.
55. 55. What variable would be good to use for height?
56. 56. h
57. 57. What variable would be good to use for the rate of speed?
58. 58. r
59. 59. What variable would be good to use for time?
60. 60. t
61. 61. Let’s look at how we use factoring in physics.
63. 63. A ball is kicked upward with an initial speed of 20 m/s. When is it 6 m high?
64. 64. What is step 1?
65. 65. Draw a picture.
66. 66. Can you please draw the picture on the board?
67. 67. Student draws one of the three pictures shown on the slide.
68. 68. Can you draw a different picture on the board?
69. 69. Student draws one of the other pictures shown on the slide.
70. 70. Can you draw the remaining picture on the board?
71. 71. Student draws remaining picture on the slide
72. 72. There are three possibilities for this problem. The ball could be at 6 meters on its way up and its way down. It could be at 6 meters once, or it might never get high enough to be at 6 meters.
73. 73. What are the variables we will use in this problem?
74. 74. h = 6 meters, r = 20 m/s, t = t
75. 75. What is step 3?
76. 76. Write the equation
77. 77. Can you write the equation on the board?
78. 78. Student writes equation on the board
79. 79. What is step 4?
80. 80. Simplify and Solve
81. 81. Can you please simply and solve the equation on the board?
82. 82. Answers will vary. It should look like the slides on the power point.
83. 83. What do we do next?
84. 84. Check all solutions.
85. 85. Which of the three possible pictures was the correct picture?
86. 86. Now work with your partner to solve the next physics problem. If you have a question please place your book on end on your desk. If you finish early you may begin working on the You Try problems. I will come around to help.
88. 88. Student reads the question.
89. 89. Can you please come to the board and draw the problem and identify the variables?
90. 90. Answers will vary. It should look like the PowerPoint.
91. 91. Can you please write an equation for the problem and then simply and solve the equation on the board?
92. 92. Answers will vary. It should look like the PowerPoint.