The Foundation for a Meaningful Life
Kindergarten - Grade 9 in Southborough, MA

Math Takes Flight

Students in math teacher Christina Berthelsen's Algebra 1 Part 1 class applied systems of equations this spring to evaluate and compare the costs of vacations to Mexico and Spain. With their foundational knowledge of linear equations and slope as a constant of proportionality, they tackled the real-world problem of vacation budgeting. Christina's goal was to help students see the practical applications of abstract mathematical concepts. She challenged them to use systems of equations to compare the costs of vacations, considering variables such as the length of stay, flight expenses, and lodging costs. 

The project required students to present a recommended vacation destination, including detailed hotel and flight information based on flights from Boston and a list of attractions, activities, and restaurants to visit. They had a budget of $5,000 for flights and hotels. To evaluate the costs, students had to write equations representing the flight and hotel expenses based on the length of stay. Additionally, they needed to graphically and algebraically demonstrate when the costs of both destinations would be the same. They also had to mathematically prove after how many nights Mexico would be less expensive than Spain, and vice versa. Based on all their data, students had to make a final recommendation on which trip to take, for how many nights, and why. They could present their project in various ways, such as a brochure, Google Slide presentation, website, video, or poster. 

Graphing the equations with Desmos allowed students to appreciate the practical application of the math. "They were able to see each line and what the total cost of a trip would be," says Christina. "Then they grabbed both lines together and saw the intersection as a real-world example of what a solution of a system of equations looks like." An optional extension to the project challenged students to write a system of equations for food, shopping, and entertainment on the trip based on a specified budget and spending ratios.

The project was designed to be particularly engaging for this math class,  which includes five students from Mexico and two from Spain. "The project allowed them to demonstrate their understanding of the math, but it also gave them a chance to talk about places from home that were meaningful to them," says Christina. "In a way, it became a love letter to their home."
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