Polynomial and Rational Functions: Building Boxes

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In this math lesson, learners explore polynomial and rational function patterns. Learners investigate the relationships between the x-intercepts, factors, and roots of polynomial functions using a graphing calculator. Learners also explore rational functions, identifying the roots, asymptotes, and holes in graphs. Finally, learners construct boxes of various dimensions using graphing paper. Learners use the height and volume data from these boxes to create a scatterplot in order to determine the height of the box with the maximum volume.

Quick Guide

Preparation Time:
Under 5 minutes
Learning Time:
45 to 60 minutes
Estimated Materials Cost:
1 cent - $1 per group of students
Age Range:
Ages 14 - 18
Resource Types:
Activity, Lesson/Lesson Plan
Language:
English

Materials List (per group of students)

Keywords

Subjects

  • Mathematics
    • Algebra
      • Equations and Inequalities
      • Patterns
      • Variables and Expressions
    • Data Analysis and Probability
      • Data Analysis
      • Data Collection
      • Data Representation
    • Measurement
    • Number and Operations
      • Multiples and Factors
    • Reasoning and Proof
    • Representation
  • The Nature of Technology
    • The Design Process
      • Problem Solving
  • Physical Sciences
    • Structure and Properties of Matter
      • Volume and Density

Audience

To use this activity, learners need to:

  • see
  • read
  • touch

Learning styles supported:

  • Involves teamwork and communication skills
  • Involves hands-on or lab activities

Other

This resource is part of:

Access Rights:

  • Free access

By:

Rights:

  • All rights reserved, PBS, 2012

Funding Source:

  • US Department of Education