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:
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 

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).
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 

