Pre-AP Algebra 2 Lesson

Recognizing Linear, Quadratic, and Exponential Relationships

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10th GradeBTC Style / Thinking ClassroomsCCSS.MATH.CONTENT.HSF.LE.A.1, CCSS.MATH.CONTENT.HSF.LE.A.2, CCSS.MATH.CONTENT.HSF.IF.B.650 min

Learning Objective

Students will identify linear, quadratic, and exponential relationships from tables of values by analyzing first differences, second differences, and ratios, and will connect these patterns to their algebraic and contextual representations.

Lesson Overview

Students progress from identifying function families by their defining numerical patterns (constant differences, constant ratios) to classifying real-world contexts and writing equations from tables — changing one variable at a time across six tasks.

Materials

Whiteboard or chart paper and markers
Pencil and paper

Scaffolded Task Progression

1Task 1

Compute the first differences for this table. What do you notice?

$x$	$y$
0	2
1	5
2	8
3	11
4	14

2Task 2

Compute the first differences for this table. Are they constant? If not, compute the second differences. What do you notice?

$x$	$y$
0	1
1	3
2	7
3	13
4	21

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