Lesson 2

How Does it Change?

Lesson Narrative

In this lesson, students contrast visual patterns that show quadratic relationships with those that show linear and exponential relationships. To analyze the patterns, students generate tables of values, write expressions, and create graphs. They also encounter the term quadratic expression and learn that a quadratic relationship can be written using an expression with a squared term.

Discerning and extending different patterns of change prompts students to look for and make use of structure (MP7). Generating tables of values and generalizing the relationships prompts students to express regularity in repeated reasoning (MP8).

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

Learning Goals

Teacher Facing

• Comprehend that a “quadratic relationship” can be expressed with a squared term.
• Describe (orally and in writing) a pattern of change associated with a quadratic relationship.
• Determine and explain (orally and in writing) whether a visual pattern represents a linear, exponential, or quadratic relationship.

Student Facing

• Let’s describe some patterns of change.

Student Facing

• I can describe how a pattern is growing.
• I can tell whether a pattern is growing linearly, exponentially, or quadratically.
• I know an expression with a squared term is called quadratic.

Glossary Entries

A quadratic expression in $$x$$ is one that is equivalent to an expression of the form $$ax^2 + bx + c$$, where $$a$$, $$b$$, and $$c$$ are constants and $$a \neq 0$$.