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Honors Algebra 2

Honors Algebra 2. Spring 2012 Ms. Katz. Day 1: January 30 th. Objective: Form and meet study teams. Then work together to share mathematical ideas and to justify strategies as you represent geometric objects and order a series of connected functions to create a desired output . Seats

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Honors Algebra 2

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  1. Honors Algebra 2 Spring 2012 Ms. Katz

  2. Day 1: January 30th Objective: Form and meet study teams. Then work together to share mathematical ideas and to justify strategies as you represent geometric objects and order a series of connected functions to create a desired output. Seats Problems 1-1 to 1-2 Introduction: Ms. Katz, Books, Syllabus, Index Card Homework Record, Expectations Conclusion Homework: Have Parent/Guardian fill out last page of syllabus and sign; Problems 1-4 to 1-9 AND 1-13 to 1-19; Extra credit tissues or hand sanitizer (1)

  3. Five Point Star

  4. Function Notation The f is the name of the function machine, and the expression to the right of the equal sign shows what the machine does to any input.

  5. Function Notation 25 Which do you prefer to write? Evaluate f when x = 25? OR 5 The f is the name of the function machine and the value inside the parentheses is the input. The expression to the right of the equal sign shows what the machine does to the input.

  6. Function Machines (a) 6 -16 7 121 11

  7. Function Machines (b) 64 8 -36 17 131065

  8. Support • www.cpm.org • Resources (including worksheets from class) • Extra support/practice • Parent Guide • Homework Help • www.hotmath.com • All the problems from the book • Homework help and answers • My Webpage on the HHS website • Classwork and Homework Assignments • Worksheets • Extra Resources

  9. Respond on Index Card: • When did you take Algebra 1? Geometry? • Who was your Algebra 1 teacher? Geometry teacher? • What grade do you think you earned in Geometry? • What is one concept/topic from Algebra 1 that Ms. Katz could help you learn better? • What grade would you like to earn in Algebra 2? (Be realistic) • What sports/clubs are you involved in this Spring? • My e-mail address (for teacher purposes only) is:

  10. Day 2: January 31st Objective: Review expectations for class and homework. Work together to share mathematical ideas and to justify strategies as you order a series of connected functions to create a desired output. THEN Draw complete graphs of functions and identify possible inputs, outputs, and key points for describing those graphs. You will use a graphing calculator and develop presentation skills. HW Check and Correct (in red) Problems 1-10 and 1-12 Problem 1-27 Conclusion Homework: Problems 1-20 to 1-26; GET SUPPLIES; Extra credit tissues or hand sanitizer (1)

  11. Complete Graph y On graph paper: Plot key points accurately (3,0) (-2,0) x Scale your axes appropriately (0,-6) (.5,-6.25) Label the axes (with units if appropriate) When a problem says graph an equation or draw a graph:

  12. Day 3: February 1st Objective: Identify the domain and range of functions while improving your graphing-calculator skills. THEN Find points of intersection using multiple representations and learn how to use the [CALC], [TABLE], and [TBLSET] functions on a graphing calculator. HW Check and Correct (in red) Problems 1-28 to 1-34 Notes Problems 1-42 and 1-46 Conclusion Homework: Problems 1-35 to 1-41 AND 1-47 to 1-53; GET SUPPLIES; Extra credit tissues or hand sanitizer

  13. Vertical Line Test If a vertical line intersects a curve more than once, it is not a function. Use the vertical line test to decide which graphs are functions.

  14. Vertical Line Test If a vertical line intersects a curve more than once, it is not a function. Use the vertical line test to decide which graphs are functions.

  15. Complete Graph y On graph paper: Plot key points accurately (3,0) (-2,0) x Scale your axes appropriately (0,-6) (.5,-6.25) Label the axes (with units if appropriate) When a problem says graph an equation or draw a graph:

  16. Definitions The domain and range help determine the window of a graph.

  17. 1-34: Learning Log Title: Domain and Range Describe everything you know about domain and range. Why are the domain and range important when graphing? What calculator buttons allow us to see the appropriate domain and range of a graph?

  18. Symbols for Number Set Countingnumbers (maybe0, 1, 2, 3, 4, and so on) Natural Numbers: Integers: Positive and negativecounting numbers (-2, -1, 0, 1, 2, and so on) a number that can be expressed as aninteger fraction(-3/2, -1/3, 0, 1, 55/7, 22, and so on) Rational Numbers: Irrational Numbers: a number that canNOTbe expressed as aninteger fraction(π, √2, and so on) NONE

  19. Symbols for Number Set Real Numbers: The set of allrationaland irrational numbers Rational Numbers Integers Irrational Numbers Real Number Venn Diagram: Natural Numbers

  20. Inequality Notation Less than (not included) Greater than (not included) less than or equal (included) greater than or equal (included) < > ≤ ≥ Open Dot and Parentheses ( ) Closed Dot and Brackets [ ]

  21. Graphically and algebraically represent the following: All real numbers greater than 11 Graph: Symbolic: Example: Inequalities 10 11 12 OR

  22. Describe and algebraically represent the following: Description: Symbolic: Example: Inequalities -6 -5 -4 All real numbers less than or equal to -5 OR

  23. Describe and graphically represent the following: Description: Graph: Example: Inequalities OR All real numbers greater than or equal to 1 and less than 5 1 3 5

  24. Graphically and algebraically represent the following: All real numbers less than -2 or greater than 4 Graph: Symbolic: Example: Inequalities -2 1 4 OR

  25. Day 4: February 2nd Objective: Find points of intersection using multiple representations and learn how to use the [CALC], [TABLE], and [TBLSET] functions on a graphing calculator. THEN Investigate a function defined by a geometric relationship and generate multiple algebraic representations for the function. HW Check and Correct (in red) Wrap-Up Notes Problems 1-42 and 1-46 Problems 1-54 to 1-58 Conclusion Homework: Problems 1-60 to 1-71; Get Supplies! Team Test Tuesday (?)

  26. Inequality Notation Less than (not included) Greater than (not included) less than or equal (included) greater than or equal (included) < > ≤ ≥ Open Dot and Parentheses ( ) Closed Dot and Brackets [ ]

  27. Multiple Representations Table Non-Algebraic Rule or Equation Graph Context Algebraic

  28. Solving a System Algebraically Use the equations to solve the following system:

  29. Using a Table to Solve a System Use tables to solve the following system:

  30. Day 5: February 3rd Objective: Investigate a function defined by a geometric relationship and generate multiple algebraic representations for the function. THEN Develop an understanding of what it means to investigate a function as the family of hyperbolas is investigated. HW Check and Correct (in red) Finish Problems 1-57 to 1-58 Problems 1-78 to 1-83 Start Problems 1-99 to 1-104 Conclusion – [Project will be assigned next week] Homework: Problems 1-72 to 1-77 AND 1-84 to 1-90; Supplies! Team Test Monday? Tuesday?

  31. Domain and Range Domain: Domain: All ℝ Range: Range:

  32. Day 6: February 6th Objective: Develop an understanding of what it means to investigate a function as the family of hyperbolas is investigated. THEN Identify what all linear functions have in common and determine whether relationships in tables and situations are linear. HW Check and Correct (in red) Finish Problems 1-78 to 1-83 Problems 1-99 to 1-104 Assign Project and Review Rubric Start notes on Exponents if time Conclusion Homework: Problems 1-91 to 1-98 AND 1-105 to 1-111 Ch. 1 Team Test Tomorrow Ch. 1 Individual Test Friday

  33. Function Investigation Questions What is the domain of the function? What is the range? Does the function have symmetry? What are the important/key points of this function? Why are they important? What is the shape of the graph? Does the function have any “problem points” or asymptotes? Why do they happen?

  34. Hyperbola What to address: • Domain and Range • Key Points (max/min, intercepts, etc) • Asymptotes (a line that the graph of a curve approaches) • Symmetry

  35. Parameter vs. Variable Variable (Multiple Values/Vary) Parameter (Specific/Constant)

  36. Day 7: February 7th Objective: Assess Chapter 1 in a team setting. THEN Identify what all linear functions have in common and determine whether relationships in tables and situations are linear. HW Check and Correct (in red) Chapter 1 Team Test (≤ 50 minutes) Finish Problems 1-99 to 1-104 Review Project Rubric Start notes on Exponents if time Conclusion Homework: Problems 1-113 to 1-119 AND CL1-120 to CL1-124 Ch. 1 Individual Test Friday

  37. Day 8: February 8th Objective: Identify what all linear functions have in common and determine whether relationships in tables and situations are linear. THEN Explore, state, and practice the rules for simplifying exponential expressions. HW Check and Correct (in red) Finish Problems 1-99 to 1-104 Notes on Exponents Practice – “Exponent Mania” Conclusion Homework: Problems CL1-125 to 1-129 AND Exponent Mania Ch. 1 Individual Test Friday Problem 1-112(b) Due Monday, February 13th

  38. 1-104: Learning Log Title: Recognizing Linear Relationships How do you recognize a linear relationship without a graph? How can you recognize a linear equation? How do you recognize a linear table? How do you recognize linear situation? What must the rate of change be for every relationship?

  39. Exponential Notation BaseExponent Base raised to an exponent

  40. Goal To write simplified statements that contain distinct bases, one whole number in the numerator and one in the denominator, and no negative exponents. Ex:

  41. Exploration Evaluate the following without a calculator: 34 = 33 = 32 = 31 = Describe a pattern and find the answer for: 30 = 81 27 9 3 1

  42. Zero Power 1 a0 = Anything to the zero power is one Can “a” equal zero? No. You can’t divide by 0.

  43. Exploration Simplify: =

  44. Product of a Power If you multiply powers having the same base, add the exponents.

  45. Example Simplify: =

  46. Exploration Simplify:

  47. Power of a Power To find a power of a power, multiply the exponents.

  48. Example Simplify: = 8s13t11

  49. Exploration Simplify:

  50. Power of a Product If a base has a product, raise each factor to the power

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