Sunday, October 24, 2010

Multiplying Integers Using an Alternative Game of Tic-Tac-Toe

Content/concept(s) to be covered:

The purpose of this lesson is to teach the fundamental properties of integer multiplication. Students will use their knowledge of negative and positive integers in an attempt to beat their opponent at a game of tic-tac-toe variation using plus symbols and minus symbols to represent negative and positive numbers.

Instructional objectives:

The objective for each student is, via the process of competition with other students, to recognize the difference in multiplication of negative numbers with other negative numbers as well as negative numbers with positive numbers. At the end of this lesson students should remember that a negative number multiplied by a negative number always yields a positive number. Likewise, at the end of this lesson, the students should remember that a negative number multiplied by a positive number should yield a negative number. The game will involve the use of plus and minus symbols (vs. x and o) on a regular tic-tac-toe board. Each student will have an opponent, the winner of the game ventures onward toward other winners in a game of single elimination. The winner of the all student-to-student games must face the teacher in the finals.

Materials needed for the activities:

• Two different colored markers

• Regular tic-tac-toe worksheet (can be created by students or printed)

• Tally sheet to keep track of eliminated players

Introduction or introductory activity:

1) The educator must begin the lesson with a background of integers and how they differ from counting numbers. Furthermore, the educator should draw a number line labeling zero in order to highlight the difference between a negative number and a positive number.

2) Next, the educator should review the differences between multiplying positive and negative integers by explanation as well as by placing an easy to follow diagram on the overhead or whiteboard

+ = Positive numbers - = Negative numbers

+ times a + = +

+ times a - = -

- times a - = +

- times a + = -

3) Next, the educator should review the game tic-tac-toe in its traditional form by explaining the rules of the game and playing a practice round with a volunteer student

4) Finally, the educator should explain the way the game will be played with its integer variation of positive and negative symbols (Explained more fully below)

Instructional activities:

1) The game is played with the traditional tic-tac-toe board (shown below) but with + and – symbols instead of X and O symbols. The + symbol represents a positive number while the – symbol represents a negative number

2) Before the game is begun have each player decide whom will be the + symbol and whom will be the – symbol.
3) Next, have each student choose a square that they will label theirs, placing negative symbols or positive symbols around the square (shown below).

 4) Explain that any symbol placed in either of these two squares must be multiplied by the symbol already in the square. Thus, if a + symbol is placed in the square surrounded by plus symbols then the ultimate symbol will be a plus symbols (since + times a + = +). However, if a negative symbol is placed in the square surrounded by plus symbols then the ultimate symbol will be a negative (since + times a – = –)

5) Explain to the students that they may ultimately think of choosing a square as placing a trap for their opponent

6) Next, have the student play the game as if they were playing a traditional tic-tac-toe game (shown below)

7) In the scenario above the player using the – symbol believes they are about to win the game by placing their symbol in the upper left-hand corner. However, when they do, they realize that a negative multiplied by a negative numbers is actually a positive number (and thus they fell into their own trap)

8) Ultimately, this game continues without a winner and must be replayed.


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