Four Linear Patterns  Section 2: Investigation: Finding the nth Term
Finding the nth Term
Lesson 1 of 6
Objective: Students will be able to use inductive reasoning to find the rule for a linear pattern.
Silent Board Game
Since we use both inductive and deductive reasoning extensively throughout this year in geometry, I use the Silent Board Game to introduce students to inductive reasoning while activating some of their pattern recognition skills.
I like to introduce Inductive Reasoning through the Silent Board Game. In the Silent Board Game, there are two rules:
 Everyone must stay silent.
 If I hand a student a marker, the student must come forward to put down a guess. If the answer is correct, it will stay on the board. If the answer is incorrect, I will erase it.
The Silent Board Game allows students to problem solve by looking for patterns, taking risks, and ultimately, finding a general rule (MP1). Additionally, it helps us to create a classroom culture of making mistakes and learning from them, since incorrect guesses often lead us to a better understanding of how x and y relate to each other.
y = 2x+10
x 
0 
2 
4 
1 
1 
10 

y 
10 
14 
18 
12 
8 
30 

y = x^{2}+1
x 
0 
2 
4 
1 
1 
10 

y 
1 
5 
17 
2 
2 
101 

Resources (1)
Resources (1)
Resources
In the Finding the nth Term Investigation, I ask students to look for patterns in the table and to algebraically represent how points on a line divide the line into segments and nonoverlapping rays. After students check in with me about how they expressed the general rule, I give them four different linear patterns for which they will complete a table, and find a general rule that represents the situation. As students get more exposure to linear patterns, they notice the features of linear equations: a constant rate of change and some kind of initial valuein this sense, students express regularity in repeated reasoning (MP8) and look for and make use of structure (MP7).
Resources (2)
Debrief
I debrief the lesson by telling students that rules that generate a sequence with a constant difference are called linear functions. I tell them that inductive reasoning is the process of observing data, looking for patterns, and making generalizations about those patterns.
Exit Ticket: Generalize the pattern to find the expression for the nth term.
Term 
1 
2 
3 
4 
5 
… 
n 
Value 
20 
27 
34 
41 
48 


Similar Lessons
What is Algebra?
Environment: Suburban
Rabbit Run  Day 2 of 2
Environment: Urban
Ahoy team! What can you see? Finding functions.
Environment: Urban
 UNIT 1: Creating Classroom Culture to Develop the Math Practices
 UNIT 2: Introducing Geometry
 UNIT 3: Transformations
 UNIT 4: Discovering and Proving Angle Relationships
 UNIT 5: Constructions
 UNIT 6: Midterm Exam Review
 UNIT 7: Discovering and Proving Triangle Properties
 UNIT 8: Discovering and Proving Polygon Properties
 UNIT 9: Discovering and Proving Circles Properties
 UNIT 10: Geometric Measurement and Dimension
 UNIT 11: The Pythagorean Theorem
 UNIT 12: Triangle Similarity and Trigonometric Ratios
 UNIT 13: Final Exam Review