text: Math Portal Home > Middle School Lesson Plans > Wacky Water World: Teacher Notes
  
  Wacky Water World: Teacher Notes
  
  MA.912.A.3.8
  MA.912.A.3.11
  MA.912.A.3.13
  MA.912.A.3.15
  
  Conceptual Knowledge
  
  Linear Equations
  Graphing Calculators
  Interpret Data
  
  Procedural Knowledge
  
  y = mx + b
  Graphing Linear Equations
  Graphing Calculator Commands
  Make Predictions
  
  Problem Solving
  Reasoning
  Communication
  Connections
  Representation
  
  It is Saturday and the new water theme park has just opened. You and your friends are making plans to attend. You check the plans at the ticket counter, and since you have a limited amount of money, you want the best buy.
  
  Students work individually or in pairs
  
  Graphing Calculator
  
  Study the two plans below and then decide which plan you will recommend to your friends.
  
   Plan A Plan B \$ 5.00 admission \$ 10.00 admission \$ 1.00 per ride \$      .50 per ride
  
  Which plan will you recommend? ___________
  Why? (be specific and write complete sentences)
  ____________________________________________________________________________
  ____________________________________________________________________________
  ____________________________________________________________________________
  
  Calculate the total cost under both plans for riding 0, 1, 2, 3, 4, 5, and 6 rides. Do this without a calculator.
  
   Plan A Plan B Rides Total Cost Rides Total Cost 0 0 1 1 2 2 3 3 4 4 5 5 6 6
  
  Describe how to find the total cost of going under Plan A and riding any number of rides.
  The total cost will equal _____ plus _____ times the number of rides.
  Describe how to find the cost using symbols only!
  Use Y to equal the total cost and X to equal the number of rides.
  Y = _____ + _____X
  
  Describe how to find the total cost of going under Plan B and riding any number of rides.
  The total cost will equal _____ plus _____ times the number of rides.
  Describe how to find the cost using symbols only!
  Use Y to equal the total cost and X to equal the number of rides.
  Y = _____ + _____X
  
  Now use the graphing calculator to see the graphs of the equations that you have written.
  Press [Y=] and type in your equation for Plan A next to Y1 =.
  Press [ENTER] and type in your Plan B equation next to Y2 =.
  Press [ZOOM] 6 to see the graphs of the equations.
  Press [ZOOM] 8 [ENTER] to see the equations in an integer window.
  
  Now press [TRACE] and use the arrow keys to trace along the equations. The left and right arrow keys trace along a graph and the up and down arrow keys change the graph that is being traced. If you do not see and equation at the top left corner of the screen, press [2nd] [ZOOM], highlight ExprOn, and press [ENTER]. Press [GRAPH] to see the lines. The equation tells you which graph you are currently tracing, Plan A is Y1 and Plan B is Y2.
  
  Trace along the appropriate line and answer the following questions using your graphs.
  
  1. If I ride 9 rides under Plan A, it will cost ______ .
  2. If I ride 9 rides under Plan B, it will cost ______ .
  3. If I ride 30 rides under Plan A, it will cost ______ .
  4. If I ride 30 rides under Plan B, it will cost ______ .
  5. If I spent \$15 under plan A, how many rides did I ride? _______
  6. If I spent \$20 under plan B, how many rides did I ride? _______
  7. When would it cost the same under both plans?
  ________________________________________________________________________________
  8. Explain what you see on the graph that shows you this.
  ________________________________________________________________________________
  9. When would it cost more under Plan A?
  ________________________________________________________________________________
  10. Explain what you see on the graph that helps you to determine this.
  ________________________________________________________________________________
  ________________________________________________________________________________
  11. When would it cost less under Plan A?
  ________________________________________________________________________________
  12. Explain what you see on the graph that helps you to determine this.
  ________________________________________________________________________________
  ________________________________________________________________________________
  13. Comparing the graphs of Plan A and B, which of the lines is steeper and what does this mean as it relates to the total cost?
  ________________________________________________________________________________
  ________________________________________________________________________________
  14. Predict what the line would look like if you graphed the following situations:
  1. a plan that has no admission price and each ride is \$3.00
  ____________________________________________________________________________
  ____________________________________________________________________________
  2. a plan that has \$25 admission price and no charge for the rides
  ____________________________________________________________________________
  ____________________________________________________________________________
  3. a plan that has \$5 admission price for 3 free rides, then \$1 for each additional ride
  ____________________________________________________________________________
  ____________________________________________________________________________
  
  As a result of this activity, students will learn how a system of equations can be used to find the best use of information to make decisions in real world situations.
  
   Math Portal Home > Middle School Lesson Plans > Wacky Water World: Teacher Notes
explanation: The document is a teacher's guide for a lesson plan on linear equations and graphing, specifically focusing on a scenario where students compare two pricing plans for a water theme park. The document contains a series of questions and tasks for students to complete, including calculating costs, graphing equations, and interpreting the results. The questions are designed to help students understand the relationship between linear equations and real-world scenarios.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
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distilabel_metadata.role: system
distilabel_metadata.content: Math Portal Home > Middle School Lesson Plans > Wacky Water World: Teacher Notes
  
  Wacky Water World: Teacher Notes
  
  MA.912.A.3.8
  MA.912.A.3.11
  MA.912.A.3.13
  MA.912.A.3.15
  
  Conceptual Knowledge
  
  Linear Equations
  Graphing Calculators
  Interpret Data
  
  Procedural Knowledge
  
  y = mx + b
  Graphing Linear Equations
  Graphing Calculator Commands
  Make Predictions
  
  Problem Solving
  Reasoning
  Communication
  Connections
  Representation
  
  It is Saturday and the new water theme park has just opened. You and your friends are making plans to attend. You check the plans at the ticket counter, and since you have a limited amount of money, you want the best buy.
  
  Students work individually or in pairs
  
  Graphing Calculator
  
  Study the two plans below and then decide which plan you will recommend to your friends.
  
   Plan A Plan B \$ 5.00 admission \$ 10.00 admission \$ 1.00 per ride \$      .50 per ride
  
  Which plan will you recommend? ___________
  Why? (be specific and write complete sentences)
  ____________________________________________________________________________
  ____________________________________________________________________________
  ____________________________________________________________________________
  
  Calculate the total cost under both plans for riding 0, 1, 2, 3, 4, 5, and 6 rides. Do this without a calculator.
  
   Plan A Plan B Rides Total Cost Rides Total Cost 0 0 1 1 2 2 3 3 4 4 5 5 6 6
  
  Describe how to find the total cost of going under Plan A and riding any number of rides.
  The total cost will equal _____ plus _____ times the number of rides.
  Describe how to find the cost using symbols only!
  Use Y to equal the total cost and X to equal the number of rides.
  Y = _____ + _____X
  
  Describe how to find the total cost of going under Plan B and riding any number of rides.
  The total cost will equal _____ plus _____ times the number of rides.
  Describe how to find the cost using symbols only!
  Use Y to equal the total cost and X to equal the number of rides.
  Y = _____ + _____X
  
  Now use the graphing calculator to see the graphs of the equations that you have written.
  Press [Y=] and type in your equation for Plan A next to Y1 =.
  Press [ENTER] and type in your Plan B equation next to Y2 =.
  Press [ZOOM] 6 to see the graphs of the equations.
  Press [ZOOM] 8 [ENTER] to see the equations in an integer window.
  
  Now press [TRACE] and use the arrow keys to trace along the equations. The left and right arrow keys trace along a graph and the up and down arrow keys change the graph that is being traced. If you do not see and equation at the top left corner of the screen, press [2nd] [ZOOM], highlight ExprOn, and press [ENTER]. Press [GRAPH] to see the lines. The equation tells you which graph you are currently tracing, Plan A is Y1 and Plan B is Y2.
  
  Trace along the appropriate line and answer the following questions using your graphs.
  
  1. If I ride 9 rides under Plan A, it will cost ______ .
  2. If I ride 9 rides under Plan B, it will cost ______ .
  3. If I ride 30 rides under Plan A, it will cost ______ .
  4. If I ride 30 rides under Plan B, it will cost ______ .
  5. If I spent \$15 under plan A, how many rides did I ride? _______
  6. If I spent \$20 under plan B, how many rides did I ride? _______
  7. When would it cost the same under both plans?
  ________________________________________________________________________________
  8. Explain what you see on the graph that shows you this.
  ________________________________________________________________________________
  9. When would it cost more under Plan A?
  ________________________________________________________________________________
  10. Explain what you see on the graph that helps you to determine this.
  ________________________________________________________________________________
  ________________________________________________________________________________
  11. When would it cost less under Plan A?
  ________________________________________________________________________________
  12. Explain what you see on the graph that helps you to determine this.
  ________________________________________________________________________________
  ________________________________________________________________________________
  13. Comparing the graphs of Plan A and B, which of the lines is steeper and what does this mean as it relates to the total cost?
  ________________________________________________________________________________
  ________________________________________________________________________________
  14. Predict what the line would look like if you graphed the following situations:
  1. a plan that has no admission price and each ride is \$3.00
  ____________________________________________________________________________
  ____________________________________________________________________________
  2. a plan that has \$25 admission price and no charge for the rides
  ____________________________________________________________________________
  ____________________________________________________________________________
  3. a plan that has \$5 admission price for 3 free rides, then \$1 for each additional ride
  ____________________________________________________________________________
  ____________________________________________________________________________
  
  As a result of this activity, students will learn how a system of equations can be used to find the best use of information to make decisions in real world situations.
  
   Math Portal Home > Middle School Lesson Plans > Wacky Water World: Teacher Notes
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a teacher's guide for a lesson plan on linear equations and graphing, specifically focusing on a scenario where students compare two pricing plans for a water theme park. The document contains a series of questions and tasks for students to complete, including calculating costs, graphing equations, and interpreting the results. The questions are designed to help students understand the relationship between linear equations and real-world scenarios.
  
  Label: multiple-question-and-answer