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.”

These are not “widgets.” These are “widgets.” These are not “widgets.” Which of these is a “widget”? What is a “widget”? Again, let students struggle a bit with this. Example A is the widget. Ask “What characteristics do all the widgets have in common?” “What characteristics do widgets have that others do not have?” Eventually, students should notice that all widgets have colorful bodies with nothing else inside and two tails, one like a crescent moon and the other like an eyeball.

How to write a “good” definition: Classify the term. What is it? A dog is a mammal . . . A widget is a made-up shape . . . Differentiate the term. What makes it different from others? . . . that has four legs, a tail and barks. . . . that has a colorful, empty body and two tails, one like a crescent moon and one like an eyeball. 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.