## 101 Equals Five

### Timothy Mark DillehayLee County School District

#### Description

Students enjoy this engaging activity (with a twist) on the binary system. The lesson begins with an intriguing roll playing to gain interest.

#### Objectives

The student expresses base ten numbers as equivalent numbers in different bases, such as base two, base five, and base eight.

#### Materials

-Teacher Question sheet (associated files)
-Binary Ditto (associated files)

#### Preparations

1) Copy of "Binary Ditto" one for each student.
2) One "Teacher Question Sheet"
3) Practice with one student on Steps 1-8 from procedures.

#### Procedures

1) Have prearranged with one student to leave the classroom. Have this student pratice this binary questioning a few days before, so the trick works.

2) Have the students remaining in the class decide on a number between 0 and 32. Make sure everyone in the class knows the number and that it is a secret number from the student outside the class.

3) Bring the student in.

4) The student begins by asking random questions that can only see answered with yes or no. The student can make these up. Some appropiate examples would be, 'Is today Wednesday?' Even if today is Friday, you can answer yes or no according to what the Teacher Question Sheet says to answer for that secret number (question #1). Another good example question could be ,'Am I wearing a red shirt?' Once again, the teacher answers the random question according to what the 'Teacher Question Sheet' says to answer for the second question for that secret number. Y means yes N means no.

5) The teacher will answer that question according to the ōTeacher Question Sheet.ö

6) Repeat this process 5 times. The first question is to be answered relating to if '16' is a part of that binary representation. The second question is to be answered by the teacher, using the teacher question sheet, if '8' is a part of the number. And so on with '4' , '2', and '1'.

7) The student calls out the secret number.

8) Repeat the entire process 1-8 for a second person (optional)

9) Teacher Says, ōWould you like to know how the trick works?ö

10) Have on overhead or board: Define the word Binary: ōIn mathematics, positional numeral system employing 2 as the base and requiring only two different symbols, 0 and 1. The importance of the binary system to information theory and computer technology derives mainly from the compact and reliable manner in which data can be represented in electromechanical devices with two statesŚsuch as ōon-off,ö ōopen-closed,ö or ōgo-noģō

11) Teacher Says, ōSince binary means 2, you start with the number 1, and then double each number to the left of it.ö

12) Teacher Writes: ō64, 32, 16, 8, 4, 2, 1ö Begin writing from the left side.

13) Teacher Says, ōTo make the value of five, we need one four, and just one one. You can only take 1 of each number, no more. 101=5 (have the 1 line up directly below the 4).ö

14) Teacher Says, ōYou can not make 8 by taking two fours. You just take one 8. 1000=8 (have the 1 line up directly under the 8).

15) Evaluate the studentÆs understanding by having a volunteer come to the board and demonstrate the representation of the number 18. Continue with student modeling at the board, until satisfied with understanding.

16) Hand out the ōBinary Dittoö.

17) Choose students to complete one of the remaining numbers from 0-32 on the board.

18) Collect the ōBinary Dittoö

#### Assessments

Use completed "Binary Ditto" (associated file) and class participation to formatively assess the student's ability to represent values in binary.

Criteria:
(1) writing one correct representation on the chalkboard for a selected number.
(2) correct representations for 25 of 32 numbers from the "Binary Ditto".

#### Attached Files

The associated word documents include Teacher Question Sheet     File Extension: pdf

The associated word documents include Binary Ditto     File Extension: pdf