What Is the Biggest Package You Can Mail? 📦 (Optimization Activity with Polynomials)
Автор: Ashley Mitchell
Загружено: 2026-01-14
Просмотров: 3
Описание:
In this lesson, we explore a real-world optimization activity with polynomials based on U.S. Postal Service size restrictions for packages. Students first attempt the problem on their own with their groups. Then we review and model the situation step-by-step together which is shown here.
The package has a square cross-section, and the condition is that the perimeter of one end plus the length equals 130 inches. From this, students:
• Write a volume function in terms of the width: 𝑉(𝑤)=𝑤^2(130−4𝑤)
• Determine the meaningful domain for the function
• Use a table and/or graphing calculator to estimate the maximum volume
• Interpret their result in the context of the problem
This activity connects polynomial functions, constraints, and real-world interpretation, and serves as an introduction to optimization in Precalculus.
This is ideal for Precalculus and Algebra 2 students learning how to model and analyze real-world situations using functions.
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