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# Introduction To Algebra 1

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### Introduction To Algebra 1

1. 1. Welcome to Algebra 1
2. 2. <ul><li>Allow me to share a few thoughts on: </li></ul><ul><li>Class Material </li></ul><ul><li>Prerequisites </li></ul><ul><li>Expectations </li></ul><ul><li>Extra-Credit </li></ul><ul><li>Wisdom (not necessarily my own) </li></ul>
3. 3. I will be the first to admit, some of the material covered in this class is going to be challenging. Unless you have studied in the “Pre-Algebra” course, this is probably going to be your first experience with the “abstract” ideas of Algebra. It is essential that you put forth your best efforts, ask thoughtful questions each step of the way . In this course, we will begin laying the foundation to your entire mathematics career. How well you do in any other math class may be a direct reflection of how well you do in this class. Material
4. 4. We will discuss such things as: The Real Number System, and Properties of Real Numbers. Material
5. 5. We will discuss such things as: The Real Number System, and Properties of Real Numbers. Material Additive Identity - Additive Inverse - Multiplicative Identity - Multiplicative Inverse - Distributive Property -
6. 6. We will discuss such things as: The Real Number System, and Properties of Real Numbers. Material Additive Identity - Additive Inverse - Multiplicative Identity - Multiplicative Inverse - Distributive Property -
7. 7. We will discuss such things as: The Real Number System, and Properties of Real Numbers. Material Additive Identity - Additive Inverse - Multiplicative Identity - Multiplicative Inverse - Distributive Property -
8. 8. We will discuss such things as: The Real Number System, and Properties of Real Numbers. Material Additive Identity - Additive Inverse - Multiplicative Identity - Multiplicative Inverse - Distributive Property -
9. 9. We will discuss such things as: The Real Number System, and Properties of Real Numbers. Material Additive Identity - Additive Inverse - Multiplicative Identity - Multiplicative Inverse - Distributive Property -
10. 10. We will discuss such things as: The Real Number System, and Properties of Real Numbers. Material Additive Identity - Additive Inverse - Multiplicative Identity - Multiplicative Inverse - Distributive Property -
11. 11. We will discuss such things as: Variables and Expressions. Material
12. 12. We will discuss such things as: Variables and Expressions. Material A “variable” is simply a symbol that we put in the place of a number. It can change (or vary), depending on the situation.
13. 13. We will discuss such things as: Variables and Expressions. Material A “variable” is simply a symbol that we put in the place of a number. It can change (or vary), depending on the situation. Example: Your dad is 24 years older than you. You can use a variable to write an expression that represents his age at any time.
14. 14. We will discuss such things as: Variables and Expressions. Material A “variable” is simply a symbol that we put in the place of a number. It can change (or vary), depending on the situation. Example: Your dad is 24 years older than you. You can use a variable to write an expression that represents his age at any time.
15. 15. We will discuss such things as: Variables and Expressions. Material A “variable” is simply a symbol that we put in the place of a number. It can change (or vary), depending on the situation. Example: Your dad is 24 years older than you. You can use a variable to write an expression that represents his age at any time.
16. 16. We will discuss such things as: Variables and Expressions. Material A “variable” is simply a symbol that we put in the place of a number. It can change (or vary), depending on the situation. Example: Your dad is 24 years older than you. You can use a variable to write an expression that represents his age at any time. What is your age? Will it ever change?
17. 17. We will discuss such things as: The Cartesian Coordinate System. Material We will learn how to locate points on the coordinate plane. Then we’ll quickly see patterns that form lines, or linear patterns.
18. 18. We will discuss such things as: Linear Equations and Inequalities Material With Inequalities, one side of the line is the solution set, and the other side of the line is not. Pretty simple, huh?
19. 19. We will study several other topics as well but, that’s enough to get us started for now. Material
20. 20. Prerequisites are the things you should know before entering a class (situation). Prerequisites I expect you to become very comfortable with manipulating, (add, subtract, multiply & divide) fractions!
21. 21. Prerequisites are the things you should know before entering a class (situation). Prerequisites I expect you to become very comfortable with manipulating, (add, subtract, multiply & divide) fractions! I will consistently assign and generate problems that involve fractions.
22. 22. Prerequisites are the things you should know before entering a class (situation). Prerequisites I expect you to become very comfortable with manipulating, (add, subtract, multiply & divide) fractions! I will consistently assign and generate problems that involve fractions. Try this one!
23. 23. Prerequisites are the things you should know before entering a class (situation). Prerequisites I expect you to become very comfortable with manipulating, (add, subtract, multiply & divide) fractions! I will consistently assign and generate problems that involve fractions. Try this one!
24. 24. Prerequisites are the things you should know before entering a class (situation). Prerequisites I expect you to become very comfortable with manipulating, (add, subtract, multiply & divide) fractions! I will consistently assign and generate problems that involve fractions. Try this one!
25. 25. Prerequisites are the things you should know before entering a class (situation). Prerequisites I expect you to become very comfortable with manipulating, (add, subtract, multiply & divide) fractions! I will consistently assign and generate problems that involve fractions. Try this one!
26. 26. Prerequisites are the things you should know before entering a class (situation). Prerequisites I expect you to become very comfortable with manipulating, (add, subtract, multiply & divide) fractions! I will consistently assign and generate problems that involve fractions. Try this one!
27. 27. Prerequisites are the things you should know before entering a class (situation). Prerequisites I expect you to become very comfortable with manipulating, (add, subtract, multiply & divide) fractions! I will consistently assign and generate problems that involve fractions. Try this one!
28. 28. Prerequisites are the things you should know before entering a class (situation). Prerequisites I expect you to become very comfortable with manipulating, (add, subtract, multiply & divide) fractions! I will consistently assign and generate problems that involve fractions. Try this one!
29. 29. Prerequisites are the things you should know before entering a class (situation). Prerequisites You will need to know the multiplication tables almost instantaneously ( without a calculator ).
30. 30. Prerequisites are the things you should know before entering a class (situation). Prerequisites You will need to know the multiplication tables almost instantaneously ( without a calculator ). I suggest you study if you do not know it well already.
31. 31. Prerequisites are the things you should know before entering a class (situation). Prerequisites You will need to know the multiplication tables almost instantaneously ( without a calculator ). I suggest you study if you do not know it well already. Along this same idea, you should be able to recognize the square numbers, 1 – 13, almost as soon as you see them.
32. 32. Prerequisites are the things you should know before entering a class (situation). Prerequisites 1 X 1 = 2 X 2 = 3 X 3 = 4 X 4 = 5 X 5 = 6 X 6 = 7 X 7 = 8 X 8 = 9 X 9 = 10 X 10 = 11 X 11 = 12 X 12 = 13 X 13 = Square Numbers You Need To Know
33. 33. Prerequisites are the things you should know before entering a class (situation). Prerequisites 1 X 1 = 2 X 2 = 3 X 3 = 4 X 4 = 5 X 5 = 6 X 6 = 7 X 7 = 8 X 8 = 9 X 9 = 10 X 10 = 11 X 11 = 12 X 12 = 13 X 13 = 1 4 9 16 25 36 49 64 81 100 121 144 169 Square Numbers You Need To Know
34. 34. Prerequisites are the things you should know before entering a class (situation). Prerequisites (Some) Vocabulary I expect you to know, and use immediately:
35. 35. Prerequisites are the things you should know before entering a class (situation). Prerequisites <ul><li>(Some) Vocabulary I expect you to know, and use immediately: </li></ul><ul><li>Perimeter – </li></ul><ul><li>Area – </li></ul>
36. 36. Prerequisites are the things you should know before entering a class (situation). Prerequisites <ul><li>(Some) Vocabulary I expect you to know, and use immediately: </li></ul><ul><li>Perimeter – </li></ul><ul><li>Area – </li></ul>distance around an object.
37. 37. Prerequisites are the things you should know before entering a class (situation). Prerequisites <ul><li>(Some) Vocabulary I expect you to know, and use immediately: </li></ul><ul><li>Perimeter – </li></ul><ul><li>Area – </li></ul>distance around an object. number of square units contained by an object, surface.
38. 38. Prerequisites are the things you should know before entering a class (situation). Prerequisites <ul><li>(Some) Vocabulary I expect you to know, and use immediately: </li></ul><ul><li>Perimeter – </li></ul><ul><li>Area – </li></ul>distance around an object. number of square units contained by an object, surface. Calculate the perimeter and area of the given rectangle: 7 (units) 3 (units)
39. 39. Prerequisites are the things you should know before entering a class (situation). Prerequisites <ul><li>(Some) Vocabulary I expect you to know, and use immediately: </li></ul><ul><li>Perimeter – </li></ul><ul><li>Area – </li></ul>distance around an object. number of square units contained by an object, surface. Calculate the perimeter and area of the given rectangle: Perimeter = 20 units 7 (units) 3 (units)
40. 40. Prerequisites are the things you should know before entering a class (situation). Prerequisites <ul><li>(Some) Vocabulary I expect you to know, and use immediately: </li></ul><ul><li>Perimeter – </li></ul><ul><li>Area – </li></ul>distance around an object. number of square units contained by an object, surface. Calculate the perimeter and area of the given rectangle: Perimeter = 20 units Area = 21 units 2 7 (units) 3 (units)
41. 41. My expectations are very simple: Expectations
42. 42. <ul><li>My expectations are very simple: </li></ul><ul><li>Work Hard! </li></ul>Expectations
43. 43. <ul><li>My expectations are very simple: </li></ul><ul><li>Work Hard! </li></ul><ul><li>Take responsibility for your self and your education. </li></ul>Expectations
44. 44. <ul><li>My expectations are very simple: </li></ul><ul><li>Work Hard! </li></ul><ul><li>Take responsibility for your self and your education. </li></ul><ul><li>Ask questions when you don’t understand, (during class, before or after school). </li></ul>Expectations
45. 45. <ul><li>My expectations are very simple: </li></ul><ul><li>Work Hard! </li></ul><ul><li>Take responsibility for your self and your education. </li></ul><ul><li>Ask questions when you don’t understand, (during class, before or after school). </li></ul><ul><li>Help others when you can. </li></ul>Expectations
46. 46. <ul><li>My expectations are very simple: </li></ul><ul><li>Work Hard! </li></ul><ul><li>Take responsibility for your self and your education. </li></ul><ul><li>Ask questions when you don’t understand, (during class, before or after school). </li></ul><ul><li>Help others when you can. </li></ul><ul><li>Always act and respond with maturity and integrity . </li></ul>Expectations
47. 47. Everyone asks about “Extra – Credit” at one time or another. So, let’s define what extra-credit IS , and Extra – Credit
48. 48. Everyone asks about “Extra – Credit” at one time or another. So, let’s define what extra-credit IS , and Extra – Credit <ul><li>A different means of helping you learn a mathematical idea. </li></ul>Extra-Credit IS:
49. 49. Everyone asks about “Extra – Credit” at one time or another. So, let’s define what extra-credit IS , and Extra – Credit <ul><li>A different means of helping you learn a mathematical idea. </li></ul><ul><li>A different means for you to express a mathematical idea. </li></ul>Extra-Credit IS:
50. 50. Everyone asks about “Extra – Credit” at one time or another. So, let’s define what extra-credit IS , and Extra – Credit <ul><li>A different means of helping you learn a mathematical idea. </li></ul><ul><li>A different means for you to express a mathematical idea. </li></ul><ul><li>A way for you to enhance an already passing grade. </li></ul>Extra-Credit IS:
51. 51. Everyone asks about “Extra – Credit” at one time or another. So, let’s define what extra-credit IS , and Extra – Credit <ul><li>A different means of helping you learn a mathematical idea. </li></ul><ul><li>A different means for you to express a mathematical idea. </li></ul><ul><li>A way for you to enhance an already passing grade. </li></ul><ul><li>A chance to better learn one of our technologies. </li></ul>Extra-Credit IS:
52. 52. Everyone asks about “Extra – Credit” at one time or another. So, let’s define what extra-credit IS, and what extra-credit IS NOT . Extra – Credit
53. 53. Everyone asks about “Extra – Credit” at one time or another. So, let’s define what extra-credit IS, and what extra-credit IS NOT . Extra – Credit <ul><li>A means of passing an exam or the class, without learning the material! </li></ul>Extra-Credit IS NOT:
54. 54. Everyone asks about “Extra – Credit” at one time or another. So, let’s define what extra-credit IS, and what extra-credit IS NOT . Extra – Credit <ul><li>A means of passing an exam or the class, without learning the material! </li></ul><ul><li>It will not be a “ brain-dead ” activity. It will require a lot of thought and effort. </li></ul>Extra-Credit IS NOT:
55. 55. Everyone asks about “Extra – Credit” at one time or another. Ideas I have for Extra-Credit: Extra – Credit
56. 56. <ul><li>Everyone asks about “Extra – Credit” at one time </li></ul><ul><li>or another. </li></ul><ul><li>Ideas I have for Extra-Credit: </li></ul><ul><li>Make a Movie of a problem (or problems), that we’ve discussed in class. Finally, your project will be placed in your wiki page. </li></ul>Extra – Credit
57. 57. <ul><li>Everyone asks about “Extra – Credit” at one time </li></ul><ul><li>or another. </li></ul><ul><li>Ideas I have for Extra-Credit: </li></ul><ul><li>Make a Movie of a problem (or problems), that we’ve discussed in class. Finally, your project will be placed in your wiki page. </li></ul><ul><li>Create a PowerPoint, explaining some topic that we’ve discussed. Your project can be uploaded to “SlideShare” and placed in your wiki page. </li></ul>Extra – Credit
58. 58. <ul><li>Everyone asks about “Extra – Credit” at one time </li></ul><ul><li>or another. </li></ul><ul><li>Ideas I have for Extra-Credit: </li></ul><ul><li>Make a Movie of a problem (or problems), that we’ve discussed in class. Finally, your project will be placed in your wiki page. </li></ul><ul><li>Create a PowerPoint, explaining some topic that we’ve discussed. Your project can be uploaded to “SlideShare” and placed in your wiki page. </li></ul><ul><li>As long as you understand my overall goal, (your math education), then I am open to other ideas. </li></ul>Extra – Credit
59. 59. Wisdom Ben Franklin was once asked what good a new invention was, he responded:
60. 60. Wisdom Ben Franklin was once asked what good a new invention was, he responded: “ What good is a newborn baby?”
61. 61. Wisdom Ben Franklin was once asked what good a new invention was, he responded: “ What good is a newborn baby?” Translation:
62. 62. Wisdom Ben Franklin was once asked what good a new invention was, he responded: “ What good is a newborn baby?” Translation: What good is mathematics?
63. 63. Wisdom Ben Franklin was once asked what good a new invention was, he responded: “ What good is a newborn baby?” Translation: What good is mathematics? In an immature state, none!
64. 64. Wisdom Ben Franklin was once asked what good a new invention was, he responded: “ What good is a newborn baby?” Translation: What good is mathematics? In an immature state, none! If nurtured and developed properly, there is no limitation.
65. 65. Wisdom Ben Franklin was once asked what good a new invention was, he responded: “ What good is a newborn baby?” Translation: What good is mathematics? In an immature state, none! If nurtured and developed properly, there is no limitation. “ If a man empties his purse into his head, no one can take it away from him. An investment of knowledge always pays the best interest.” Benjamin Franklin