“Three things cannot be long hidden: the sun, the moon, and the truth.” – Budda
A counterexample is an example that shows a statement is false. Counterexamples are very important as they can be used to disprove a proposition. For example, given the proposition: “All prime numbers are odd”, 2 serves as a counterexample that disproves the proposition. 2 is a prime number, but it is not odd. It is important to realize that although counterexamples can be used to disprove propositions, examples can not be used to prove propositions.
The Counterexample Game is really straight forward. Given a statement, say whether it’s TRUE or FALSE. If it’s FALSE, then give a counterexample that shows that the proposition is FALSE. What’s great about the Counterexample Game is that it gets you thinking. It’s a great quick game that can be used as a starter for a group (in a classroom environment) or rapid-fire with individuals. The other great feature is that the subject does not have to be math. It can be based on nearly all subjects. Make a statement and if it’s false, just ask for a counterexample.
Below is a five statement counterexample game. Within this game four of the five statements are FALSE, so only one is TRUE (so it doesn’t have a counterexample).
1. All of the state names in the United States contain the letter “e”.
2. All rectangles are squares.
3. All multiples of 3 are odd.
4. All multiples of 2 are even.
5. Connecting three unique dots will always make a triangle.
These statements are from varied subjects (spelling, geometry and arithmetic). You can gear the statement(s) to the subject matter being reviewed or studied. Regardless of the subject matter, make it fun. Challenge the students to think beyond their immediate response. “I don’t know” is not allowed – encourage thinking. Reward originality and accomplishment.
Good luck and have fun. Please comment if you like these. I plan on generating more of these to be used in classrooms.