What is a DOG? These ARE dogs. These ARE NOT dogs. Let students struggle a bit as they define “dog.” The definition might be something like “a dog is a mammal that has four legs, a tail and barks.”

How to write a “good” definition: Classify the term. What is it? A dog is a mammal . . . A snake is a reptile . . . Differentiate the term. What makes it different from others? . . . that has four legs, a tail and barks. . . . that has scales, hisses, has no legs, and it slithers on the ground. Test your definition by looking for a counterexample.

What’s wrong with this definition? A square is a figure with four equal sides. Sketch a counterexample. Write a better definition. Have students give counterexamples and better definitions – sample answers are included on the next slide.

What’s wrong with this definition? A square is a figure with four equal sides. Sketch a counterexample. Write a better definition. A square is a four-sided figure that has all four equal sides and four equal angles.

What is a counterexample? Counterexample: is an example to disprove a statement.

Counterexamples Statement: If it is Saturday then it is the weekend. Counterexample: If it is Sunday then it is the weekend. Statement: If a shape has four sides and all of it’s angles are congruent then it is a square. Counterexample: A rectangle has four sides, and all of it’s angles are congruent.

Examples Statement: If you are listening to music then you are listening to rock and roll. Counterexample: Statement: If you are driving a dodge viper, then you are driving a sports car.

Statement: If I am measuring an angle in a triangle then it will be an acute angle. Counterexample: Statement: If I have a shape with four sides then the two pairs of opposite sides are parallel.