Pre-AP Algebra 2 Lesson

Recognizing Linear, Quadratic, and Exponential Relationships

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10th & 11th grade Level IIBTC Style / Thinking Classroomspa2.1.1.150 min

Learning Objective

Students will classify linear, quadratic, and exponential relationships by analyzing patterns in graphs, tables, and verbal descriptions, and justify their classifications using first differences, second differences, and common ratios.

Lesson Overview

Students progress from identifying function families by their graphs to analyzing tables for constant differences/ratios and finally classifying relationships given real-world contexts with mixed representations. Each task changes only one variable — representation, complexity, or context.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors if available)
Pencils and paper for notes
Basic calculator or phone calculator

Scaffolded Task Progression

1Task 1

Three graphs are shown below. Without doing any calculations, match each graph to its family: Linear, Quadratic, or Exponential. Write one observation that helped you decide for each.

[ Interactive graph / diagram, available in the full lesson ]

2Task 2

The table below shows

x

and

y

values. Decide: is this relationship linear, quadratic, or exponential? Show the work that proves it.

$x$	$0$	$1$	$2$	$3$	$4$
$y$	$3$	$6$	$12$	$24$	$48$

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