Lesson 3

Building Quadratic Functions from Geometric Patterns

Lesson Narrative

In an earlier lesson, students reasoned about visual patterns using different representations and wrote expressions to describe the patterns. In this lesson, they continue to work with patterns but begin to see these relationships as quadratic functions and write equations to define them.

Students recognize that different expressions can be used to describe the same function. Previously they learned that an expression like \(n^2+2n\) is a quadratic expression. Here they see that \(n(n+2)\) defines the same function as \(n^2+2n\), so \(n(n+2)\) is also a quadratic expression. The work here is a preview to a more formal exploration of equivalent expressions later.

Learning Goals

Teacher Facing

  • Comprehend that the same quadratic function can be expressed symbolically in different ways.
  • Interpret (using words and other representations) the quadratic relationships in growing patterns as functions, where each input gives a particular output.
  • Write expressions that define quadratic functions.

Student Facing

  • Let’s describe some other geometric patterns.

Learning Targets

Student Facing

  • I can recognize quadratic functions written in different ways.
  • I can use information from a pattern of shapes to write a quadratic function.
  • I know that, in a pattern of shapes, the step number is the input and the number of squares is the output.

CCSS Standards

Glossary Entries

  • quadratic function

    A function where the output is given by a quadratic expression in the input.