Logic Games

By Nicholas Harth, Megan Perkey  •

Grade Level
11th
Subject Area
Mathematic III
Duration
1 day
Background Knowledge
The students were about to begin learning geometric proofs as part of their logic unit. This lesson is meant to show that the thought process associated with that type of work is relevant in many other parts of our daily lives (as we make decisions, figure things out, etc.) Again the emphasis is on the process of deductive reasoning and was meant to serve as an introduction to it’s mathematical application.
Author
Nicholas Harth, Megan Perkey
 
Summary

This lesson consists primarily of three games. The first is called “Green Glass Door.” The game is played by saying things that fit into the sentence pattern: “You can take _________ through the green glass door, but you can’t take ____________.” The trick is, you can only take words that contain a double letter. For example, “You can take pizza through the green glass door, but you can’t take candy.” You could also say, “You can take the moon through the green glass door, but you can’t take Mars.” The students have to figure out the criteria by asking questions such as, “Can you take _______ through the green glass door?” The teacher then answer yes or no, as the case may be. If someone catches on, they can then start offering examples: “You can take boots through the green glass door, but you can’t take shoes.” It may be helpful to start making two lists on the board, one of things that you can take through the green glass door, and one of things that you can’t.
The second game is called “Traffic Jam.” The object of traffic jam, is that the students must stand in the following order (with the arrow indicating which direction they are facing):

 

There are five standing spaces, but only four people. When the game starts, the middle space is empty. The students can then move, but only one at a time. They must always move into an empty space, and they can not pass more than one person at a time. No one may move backwards at any time. They must move in the direction in which they are facing. At the end of the game, the students should be positioned as illustrated below:

 

When they have figured out a way to do this, the students can then be challenged to do it in as few moves as possible.
The final game is called “Bagels, Pico, Fermi.” This game is also played in groups of three or four. One member of the group chooses a three digit number (all three digits must be different). The rest of the students take turns guessing three digit numbers. If none of the numbers are correct, the leader says “Bagels”. If one of the numbers is correct, but it is not in the correct position, the leader says Pico, and if one of the numbers is correct, and it is in the correct position, the leader says “Fermi.” These phrases can be paired up when appropriate. For example, if the leader’s number is 765, and someone guesses 759, the leader would say “Pico, Fermi.” If the next person then guessed 357, the leader would say “Pico, Pico.” The game ends when someone guesses the correct number, and the leader say “Fermi, Fermi, Fermi.” It is important to remember, that the order in which the leader says the words, in no way indicates which digit is correct or is in the correct location.

 
Objectives
1. To realize how the process of elimination can be used to reach a specific conclusion. (Bagels, Pico, Fermi)
2. To understand the benefits of proactive planning to solve problems and more quickly. (Traffic Jam)
3. To collect and analyze data in order to recognize patterns, and trends that can be used to predict the outcome of future situations. (Green Glass Door)
 
Mateirals Required
None
Documents

Formal Writeup worddoc

Reflection worddoc

All Documents and Pictures zipfile