Class Notes on Ticket Pricing and Linear Equations

Introduction

• Starting with a task related to page 271 in the binder.
• Students to write their names on purple paper and begin the task with calculators provided.

Task Overview

• Students are working with equations related to ticket pricing for children and adults.
• Example equation: 14C + 4A = 96.
• Discussing methods: RREF (Reduced Row Echelon Form) and elimination.

Key Concepts Discussed

Methods of Solving Equations

• RREF and Elimination
  • Can these methods be used with just one equation? No, at least two equations are needed.
  • Students are encouraged to try different combinations of equations to find the best answer.

Understanding the Problem

• Need to find two prices: child and adult tickets.
• Discussed hypothetical scenarios leading to negative ticket sales (e.g., tickets lost or refunded).

Data Collection

• Students asked to add totals up for the first seven days of ticket sales.
• The importance of verifying ticket prices through calculations.

Group Work Highlights

• Students working together to solve equations and verify answers.
• Multiple approaches discussed:
  • Adding totals first, then multiplying by ticket prices.
  • Using equations to derive totals from ticket prices.

Equations and Results

• Example Equations:
  • April 1st: 14C + 4A = 96 (doubling for calculations).
  • April 2nd: Tripling values to find equations.
• Using matrices to derive ticket prices.
• Confirmed that the prices of tickets remained constant at $4 for children and $10 for adults.

Properties of Equations

• Property of Equality:
  • Validates that operations performed on both sides of an equation do not change the solution.
• Students reassured that as long as operations are applied consistently, equilibrium points remain the same.

Creative Stories for Negative Values

• Students encouraged to create narratives for negative ticket sales:
  • Tickets were given away as prizes.
  • Tickets lost or refunded.

Final Remarks

• Summary of learning outcomes: students show understanding of linear equations, ticket pricing, and methods of solving systems of equations.
• Homework assignment includes a new task considering additional pricing for seniors and preparing for an upcoming test on the topic.

Conclusion

• Emphasis on the importance of teamwork and verifying calculations.
• Students reflected on their approaches and shared results.