Binary Decision Trees

Purpose: to demonstrate a way that logic relates to numbers, to show how logic can be diagrammed, to introduce a measure of efficiency - an abstract rather than physical measurement

Background: these lessons have been introduced in a 1st-2nd grade multiage class.

Reformatted August 2009
 

Generating Binary Numbers with a Logical Process:

This requires a situation that may be discovered through a sequence of questions that may be answered with "yes" or "no."

In the classroom where this was used, a new student was picked each day for certain tasks. The class would determine which student was picked by asking questions: "Is it a girl?" "Is it a student at the red table?" All students would start by standing. If a question eliminated them, they would sit. Questions would be asked until only one student was standing.

Method 1: As each question is asked a "1" is marked if the answer is "yes," a "0" is marked if the answer is "no." Once the final answer is found a binary number exists in the sequence of 1's and 0's. Students who have been exposed to binary may convert this number back to decimal.

Method 2: In this method a student will be picked out as in the example given. As each question is asked, each student marks a "1" if they would answer "yes," and a "0" if they would answer no. For example with "Is it a girl?", all the girls will mark "1" and all the boys will mark "0." Once the end is reached, each student will have a different binary number, distinct from all the other students in the class.

Related pages

 

Generating a Logic Tree:

Diagram the questions in order to show which students are on the yes or no side of each question:

Estimating the Efficiency of the Logical Process:

Follow the same steps as above. Count the number of steps (questions). The lower the number of steps, the higher the efficiency. A complete measure of efficiency will occur when each student in the class (or each element) has a distinct number (method 2 above.) For example, if students ask questions like, "Is it me?" It will take 1 question for every student in class. If they ask questions like, "Is it a girl?" it will take a bout 5 questions for a class of 32.


 

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