Lesson 1

A Different Kind of Change

Lesson Narrative

In this lesson, students encounter a situation where a quantity increases then decreases. They don’t yet have a name for this new pattern of change, but they recognize that it is neither linear nor exponential, and that the graph is unlike the graph of an exponential function.

Students make sense of this new kind of relationship in a geometric context and describe it in concrete and qualitative ways (MP2). Though some students may choose to represent the relationships with calculations or with expressions, these are not required or emphasized in the lesson. Students will have many opportunities to reason symbolically about quadratic patterns in upcoming lessons.

Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate tools to solve problems, so consider making technology available.

Learning Goals

Teacher Facing

  • Describe (orally and in writing) a relationship that increases then decreases when represented by a graph.
  • Given an interesting context, create drawings, tables, and graphs that represent a quadratic relationship.

Student Facing

  • Let’s find the rectangle with the greatest area.

Required Materials

Required Preparation

Graph paper is optional for the activity Measuring a Garden.

Learning Targets

Student Facing

  • I can create drawings, tables, and graphs that represent the area of a garden.
  • I can recognize a situation represented by a graph that increases then decreases.

CCSS Standards

Building On


Building Towards

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