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Algebra I CM third marking term

This resource provides a structured overview for solving systems of equations in algebra, designed for Wicomico High School Algebra I students under Mrs. J. Austin. Students will engage with a Cognitive Tutor program tailored for self-paced learning, featuring immediate feedback to enhance understanding. The mini-quiz format encourages collaborative learning through two groups with designated day activities. The guide covers graphing, substitution, and elimination methods, ensuring students master the skills needed to find solutions for systems of linear equations.

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Algebra I CM third marking term

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  1. Algebra I CMthird marking term Wicomico High School Mrs. J. Austin 2009-2010 Chapter 7 : System of Equations

  2. Class FormatMiniQuiz: 10 minutes Cognitive Tutor Program on Computer GROUP A DAY 1 GROUP B DAY 2 Textbook Lesson / Practice at Desk GROUP B DAY 1 GROUP A DAY 2

  3. Cognitive Tutor Program • Self-pacing program with immediate feedback. • Log-in using your first name and last name • The lesson will open and to begin you will click on the yellow box in the upper right-hand corner. • The first lesson has eight sections of Solving Equations • On the right-hand side of the screen, there are two drop-down menus. Transformations and Applications • Use the choices to solve the problem • Click Done and the next problem will appear • RED means incorrect. • Use the UNDO button and try again.

  4. Systems of Linear Equations • Two linear equations graphed on the SAME coordinate plane. • What are the THREE things that could happen? • They could CROSS or INTERSECT • They could NEVER CROSS or be PARALLEL • They could be ON TOP OF EACH OTHER or COINCIDE

  5. Solving a System of Linear Equations By Solving a System of Linear Equations, we are asking: • Are there any Values for x and y that will “satisfy” or make BOTH equations TRUE? • Is there a POINT that will make BOTH equations TRUE? • What is the POINT OF INTERSECTION of these two lines? • Find the values for x and y that will make BOTH equations TRUE.

  6. Solving a System By Graphing 7.1 • Transform each equation to Slope-Intercept Form For EACH of the TWO equations: • PLOTthe y – intercept, b • COUNT,rise over run using the Slope, m. • DRAW the straight line.

  7. Solving a System By Graphing 7.1 • Transform each equation into Slope-Intercept Form.

  8. Solving a System By Graphing 7.1 GROUP A: Work Session • Solving Systems using the Graphing Method. Textbook: Pg. 431 (1-28) GROUP B: Computer Session • Cognitive Tutor Unit 19 Solving Equations DAY 1

  9. Solving a System By Graphing 7.1 GROUP B: Work Session • Solving Systems using the Graphing Method. Textbook: Pg. 431 (1-28) GROUP A: Computer Session • Cognitive Tutor Unit 19 Solving Equations DAY 2

  10. Solving a System By Substitution 7.2 • Transitive Property • A variable can be REPLACED with its equivalent. • If two equations equal the SAME thing, they must then EQUAL each other. AND THEN The two equations are SET equal to each other

  11. Solving a System By Substitution • EXAMPLE: • Now we know y=2. • Substitute this into an equations to find x. • Solve the first equation for x. • Substitute the expression in for x in the second equation. • Now SOLVE for y.

  12. Solving a System By Substitution GROUP A: Work Session • Solving Systems using the Substitution Method. Textbook: Pg. 439 (1-28) GROUP B: Computer Session • Cognitive Tutor Unit 19 Solving Equations DAY 1

  13. Solving a System By Substitution GROUP B: Work Session • Solving Systems using the Substitution Method. Textbook: Pg. 439 (1-28) GROUP A: Computer Session • Cognitive Tutor Unit 19 Solving Equations DAY 2

  14. Solving a System By Elimination 7.3 • Transitive Property • Replace a variable with its equivalent. • Set two expressions equal to each other, when they BOTH equal the same thing! • Property of Equality • Add or Subtract two equations to create a new equivalent equation. • Transform the look of an equation by multiplication.

  15. Solving a System By Elimination 7.3 • Using Addition: • ___________ • Write the equations one above the other. Be sure the variables are lined up. • Draw a line under them. • Combine the Like-Terms to create a NEW equation. • Solve for the variable. • Substitute your answer into one of the equations to find the other variable.

  16. Solving a System By Elimination 7.3 • Using Subtraction • _____________ • Write the equations one above the other. Be sure the variables are lined up. • Draw a line under them. • Subtractthe Like-Terms to create a NEW equation. • Solve for the variable. • Substitute your answer into one of the equations to find the other variable.

  17. Solving a System By Elimination 7.3 GROUP A: Work Session • Solving Systems using the Graphing Method. Textbook: Pg. 431 (1-28) GROUP B: Computer Session • Cognitive Tutor Unit 19 Solving Equations DAY 1

  18. Solving a System By Elimination 7.3 GROUP B: Work Session • Solving Systems using the Graphing Method. Textbook: Pg. 443 – 444 (1-35) GROUP A: Computer Session • Cognitive Tutor Unit 19 Solving Equations DAY 2

  19. Solving a System By Elimination7.4 Using Multiplication Before Adding or Subtracting: ___________________ __________________ • Write the equations one above the other. Be sure the variables are lined up. • Multiply the top equation by 4. • Multiply the lower equation by 7. • Draw a line under them. • Distribute through each equation. • CombineorSubtractthe Like-Terms to create a NEW equation.

  20. Solving a System By Elimination7.4 Using Multiplication Before Adding or Subtracting . • What would you MULTIPLY by? • Solve the System. • Did you get the solution: • Solve the System. • Did you get the solution:

  21. Solving a System By Elimination7.4 GROUP A: Work Session • Solving Systems using the Graphing Method. Textbook: Pg. 454 - 455 (1-34) GROUP B: Computer Session • Cognitive Tutor Unit 19 Solving Equations DAY 1

  22. Solving a System By Elimination7.4 GROUP B: Work Session • Solving Systems using the Graphing Method. Textbook: Pg. 454 - 455 (1-34) GROUP A: Computer Session • Cognitive Tutor Unit 19 Solving Equations DAY 2

  23. Special Types of Systems 7.5 • One Solution: • Lines Intersectat one point. • Lines have different slopes. • Lines may be PERPENDICULAR if they cross at 90⁰ angles. • No Solution: • Lines do not intersect. • Lines have the SAME slope and DIFFERENT y-intercepts. • Lines are PARALLEL. • Many Solutions: • Lines touch on every point. • Lines have the SAME slope and SAME y-intercepts. • Line COINCIDE.

  24. Special Types of Systems 7.5 How Many Solutions Does the System Have? . • System: • System: • System: Answer Choices: • One Intersecting Lines • None Parallel Lines • Many Coinciding Lines

  25. Special Types of Systems 7.5 GROUP A: Work Session • Solving Systems using the Graphing Method. Textbook: Pg. 462 – 463 (1-31) GROUP B: Computer Session • Cognitive Tutor Unit 19 Solving Equations DAY 1

  26. Special Types of Systems 7.5 GROUP B: Work Session • Solving Systems using the Graphing Method. Textbook: Pg. 462 – 463 (1-31) GROUP A: Computer Session • Cognitive Tutor Unit 19 Solving Equations DAY 2

  27. Writing and Solving Systems Slope –Intercept Form: • Total Cost scenarios with given rates of change. The movie theater charges $8 per a ticket for its general customers. It offers a movie club discount of $5 per ticket if you join the club for a one-time fee of $15. How many movies would you have to go see to make joining the club beneficial? Write a system. Let x = the number of movie tickets y = total cost

  28. Writing and Solving Systems Standard or General Form: • Two different Items are given. At a grocery store, a customer pays a total of $9.70 for 1.8 pounds of potato salad and 1.4 pounds of coleslaw. Another customer pays a total of $6.55 for 1 pound of potato salad and 1.2 pounds of coleslaw. How much do 2 pounds of potato salad and 2 pounds of coleslaw cost? • Write the system. Let: x = cost of potato salad y = cost of coleslaw.

  29. Writing and Solving Systems High School Assessment Practice Questions: • READ the question ALL the way through. • RE-READ and define the variables. • RE-READ and WRITE two equations to model the scenario. • DECIDE which METHOD you will use to solve the System of Equations. • SOLVE the System. • RE-READ the question. Use YOUR SOLUTION to CONSTRUCT a written ANSWER to the question. 

  30. Solving a System By Writing 7.5 GROUP A: Work Session • Solving Systems using the Graphing Method. Textbook: Pg. 458 (1-6) Pg. 464 ( 36-40) GROUP B: Computer Session • Cognitive Tutor Unit 19 Solving Equations DAY 1

  31. Solving a System By Writing 7.5 GROUP B: Work Session • Solving Systems using the Graphing Method. Textbook: Pg. 458 (1-6) Pg. 464 ( 36-40) GROUP A: Computer Session • Cognitive Tutor Unit 19 Solving Equations DAY 2

  32. Solving Systems of Linear Inequalities 7.6 • Graphing Linear Inequalities: • Graph the first line. • Shade the area defined by the first line. • Graph the second line. • Shade the area defined by the second line. • The SOLUTUION to the System of Linear Inequalities is the AREA OF INTERSECTION. • Re-shade the section of the graph that has been shaded by both of the equations.

  33. Solving Systems of Linear Inequalities 7.6 GROUP A: Work Session • Solving Systems using the Graphing Method. Textbook: Pg. 458 (1-6) Pg. 464 ( 36-40) GROUP B: Computer Session • Cognitive Tutor Unit 19 Solving Equations DAY 1

  34. Solving Systems of Linear Inequalities 7.6 GROUP B: Work Session • Solving Systems using the Graphing Method. Textbook: Pg. 458 (1-6) Pg. 464 ( 36-40) GROUP A: Computer Session • Cognitive Tutor Unit 19 Solving Equations DAY 2

  35. Solving Systems of Linear Inequalities 7.6

  36. Chp7 Review • Two linear functions graphed on a coordinate plane. • They could CROSS, INTERSECT • They could NEVER CROSS, PARALLEL • They could be ON TOP OF EACH OTHER, COINCIDE • Solving a System By Graphing 7.1 • Solving a System By Substitution 7.2 • Solving a System By Elimination 7.3 • Identifying the Point of Intersection • Testing a Solution to a System of Equations • Special Types of Systems • Writing and Solving Systems of Equations

  37. Surveys and Sampling • TAKE A SAMPLE:

  38. Types of Sampling • Simple Random Sampling • Every person has an “equally likely chance of being chosen” and each is independent of the other. • Stratified Random Sampling • The population is divided into groups, then by groups every person has an “equally likely chance of being chosen” and each is independent of the other. • Convenient Sampling • Only people in “your area” get to participate • Self-Selected Sampling • Only people who volunteer to answer your survey get to participate. • Representative Sampling • The people who get to answer your survey match the gender and ethnicity of the population.

  39. Survey Project • STEP 1: Create 5 questions about the given topic. • STEP 2: Create two questionnaires on a half-sheet of paper each. • STEP 3: Decide on your Sampling Technique and how your are going to conduct your survey. • STEP 4: Conduct your Survey of the school population. • STEP 5: You must have a minimum of 30 responses to make the survey VALID. • STEP 6: Compile your results in a table and with a Box-and-Whisker Plot. • STEP 7: Create a POSTER to display your survey, graphics, and findings. • STEP 8:Write a summary and conclusion based on your survey results.

  40. Exponential Functions Chp 8 intro

  41. Graphing Exponential Functions 8.5 • Growth Functions:

  42. Graphing Exponential Functions 8.6 • Decay Functions:

  43. The Laws of Exponents 8.1

  44. The Laws of Exponents 8.2

  45. Negative Exponents 8.3

  46. Exponents and Scientific Notation 8.4

  47. Chapter 8 Review

  48. Simulations

  49. Types of Devices • Dice or Number Cube • Six numbers; evens/odds • Spinners • Any number of sections of EQUAL size can be made • Coins • Two sides, heads/tails • Deck of Playing Cards • Thirteen cards; Four Suits; Two Colors • Colored Chips in a Bag • Any number of chips and colors can be used • Random Number Generator (TI-84 calculator) • Ten digits, any number of choices can be made. • Random Number Table • Ten digits, any number of choices can be made.

  50. Setting Up SimulationsDecide which device will FIT your numbers.

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