Date: February 18, 1999

Grade Level(s): 7, 8, 9, 10, 11, 12

Subject(s):

• Mathematics/Process Skills

Duration: 20-25 minutes

Description: This is a demonstration with physical objects to show why a minus times a minus is a plus, a plus times a plus is a plus, and a plus times a minus is a minus.

Goals: To use physical objects to explain an abstract concept. This is a demonstration for signed numbers.

Objectives: The students will be part of the demonstration. They will manipulate the physical objects. They will understand why a minus times a minus is a plus, a plus times a plus is a plus, and a minus times a plus is a minus.

Materials: A bottle or glass of a healthful drink, a glass of something dreadful such as slop water, a sleeve made from paper that can be put over the arm with one end open, a sleeve made from paper that can be put over the arm with the end stapled shut, a chalk or dry eraser board.

Procedure:
Two sets of words are put on the board. One set is labeled "good" and the other set is labeled "bad". The students are asked for some good words to put under that heading. Such words as healthy, life, and fun, are listed. Then a positive sign is put above the list. These are concepts that we would like to add to our lives.

Then a group of words is derived to put under the "bad" heading. Words such as death, sickness, and pain, are listed under this heading. A negative sign is placed on top of the list as these are thing that we would like to have removed from our lives.

Next we develop two sets of objects to be used in the demonstration. One set is good things to drink or eat such as milk and orange juice. The other set contains bad things such as slop water, glue, and soap water.

Negative symbols are applied to each jar or glass that we would not want to drink and positive symbols are pasted to each drink that we would like to drink.

One of the sleeves is put on a student. The sleeve with the open end will be marked with a plus because the demonstrator can reach through the open end and add to a collection.

The student is asked to reach through the sleeve and grasp the orange juice. The demonstrator asks the student which of the main headings on the board would take place if the student drank the juice. Naturally, a person would expect to be healthy. The demonstrator points out that the sleeve has a plus on it and when the student reaches for a drink from the plus list we know that the final result is healthy from the plus heading on the board.

Then the negative sleeve is put on a student. This sleeve is a staple at the end so the arm can only go in to the stapled end. The student can reach no objects through the sleeve.

The student is asked to reach for the slop water. Of course he can not get his hand through the sleeve to get it. We can point the students' attention to the sign on the sleeve. It is a minus sign. We call the students attention to the negative group of objects. The slop water was in that group.

Since the students with the negative sleeve could not get the slop water (negative group) we can see that a negative times a negative is a positive since he will remain healthy which is with the plus list of words on the chalkboard.

Other students can try the sleeves with different objects and see for themselves why the mathematical rule is true.

Assessment: When the students have done this a number of times, try this short quiz:

A minus times a minus is _________

A plus times a plus is _________

A minus times a plus is _________