Patterns and Inductive Reasoning (1)
You can use inductive reasoning in recognizing patterns. Can you find any pattern in counting the number of handshakes of a given number of people in a certain party or gathering? Work on the following activity:
Activity
| 1. |
Work in groups. Each group should have 8 members. Shake hands with everyone in your group. Count how many handshakes there are for 1, 2, 3, 4, 5, 6, 7, 8 persons. Record the data in a table similar to the one below
|
| 2. |
Use mathematical modeling in solving the problem by representing the number of persons with points, and the number of handshakes with line segments connecting these points. See the examples below.
|
|
Record the results in a table similar to the one below.
|
| 3. |
Use dots to model the number of handshakes and arrange them in a triangular pattern. Make a conjecture on finding the number of handshakes in a group of n persons. Check if your conjecture is correct for 10 and 12 persons.
|
| 4. |
Count the number of line segments that can be drawn from each vertex but note that you are counting each segment twice. Recognize the pattern and formulate a conjecture on counting the number of handshakes for n persons.
|
