Quadratic Functions: Toothpicks and Transformations


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In this math lesson, learners explore transformations and quadratic functions through toothpick patterns. Learners examine the mathematical pattern that emerges as they build a geometric design with toothpicks. The pattern is quadratic, and the learners determine the mathematical model in several different forms. Learners investigate the recursive nature of the relationship. An explicit model for the relation is developed, and a third model is developed by examining the scatterplot and determining the equation from the transformations. Finally, the group uses graphing calculators to develop another model and to verify that all of the models--factored form, vertex form, and general form--are equivalent.

Quick Guide


Preparation Time:
Under 5 minutes

Learning Time:
45 to 60 minutes

Estimated Materials Cost:
$1 - $5 per group of students

Age Range:
Ages 14 - 18

Resource Types:
Activity, Lesson/Lesson Plan

Language:
English

Materials List (per group of students)


Subjects


  • Mathematics
    • Algebra
      • Equations and Inequalities
      • Patterns
    • Data Analysis and Probability
      • Data Analysis
      • Data Collection
      • Data Representation
    • Geometry
    • Reasoning and Proof
    • Representation
  • The Nature of Technology
    • The Design Process
      • Problem Solving

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


Includes assesments for student learning:

This resource is part of:

Access Rights:

  • Free access

By:

Rights:

  • All rights reserved, PBS, 2012

Funding Source:

  • US Department of Education