Module Overview
Logic and Reasoning

x-shaped and o-shaped blocks

Imagine that you and a friend are about to begin a game of tic-tac-toe. You have decided to use X's to mark your spots on the board, and you have the privilege of going first. Where will you place your first X? Do you think you will have a better chance of winning the game if you place your first X in the center? Or how about in one of the corners? How will you decide where to go first?

While tic-tac-toe may not be considered a mathematical game, playing the game does involve some strategy and logic, which are certainly mathematical concepts. Logic can be described as the way you think, or reason, your way through a problem. In geometry, logic is the basis for the rules and definitions that are used to arrive at a solution.

Getting Started

Getting started iconTake a moment to examine this logic puzzle. In this puzzle, nine dots are arranged in a three-by-three square. The goal is to attempt to connect all of the dots in the puzzle using only four straight lines without picking up your pen. You can create this puzzle on a sheet of paper or access the Dot Puzzle Printable to find the solution. When you are ready, you can view the solution in this non-graded interactivity. Click the player button to get started.

Dot Puzzle     Puzzle Solution Interactivity

Key Vocabulary

Glossary iconTo view the definitions for these key vocabulary terms, visit the course glossary.

biconditional
compound statement
conclusion
conditional
conjecture
conjunction
contrapositive
converse
counterexample
deductive reasoning
disjunction
hypothesis
if-then statement
inductive reasoning
inverse
law of contrapositive
law of detachment
law of syllogism
negation
postulate
theorem