Finding the nth Term

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:

1. Everyone must stay silent.
2. 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

y = x²+1

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 non-overlapping 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 value--in this sense, students express regularity in repeated reasoning (MP8) and look for and make use of structure (MP7).