1. 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.”

2. 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.

3. 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.

4. 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.

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

6. 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.

7. 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.

8. 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.