Detective Digit and the Slap Happy Computer Caper
This lesson will provide students with a hands-on experience in order to investigate the binary number system.
6th through 9th grades
One 50-minute period
Math Vantage # 21 "Digitizing with Binary Power", Imagine the Universe web site or CD.
Students will explore ancient number systems, use binary numbers to decode data, and count in base 2.
Students should have a basic understanding of binary numbers. See the following web site for additional information about binary numbers: http://www.cs.colorado.edu/~l3d/courses/CSCI1200-96/binary.html.
- Virginia SOL MATH 6.22
- NCTM Standards #4 'mathematical connections' and #10 'statistics' (grades 5-8)
- NSES Content Standard E: Science and Technology
- Social Studies: Ancient Civilizations
A binary number is made up of a combination of only two digits: zeroes and ones. The right most number in a binary code series indicates the number of units (ones). The next digit to the left indicates the number of twos, the next digit, the number of fours; the next, eights; then, sixteens; thirty-twos; and so on doubling each time. To write the numbers 5, 34, 51, and 127 see the following chart:
| ||64 (2^6)||32 (2^5)||16 (2^4) ||8 (2^3)||4 (2^2)||2 (2^1)||1 (2^0)|
The teacher enters the room to detective music (Pink Panther, Hawaii 5-0, Mission Impossible, Batman or some other recognizable mystery music). Announce to the class that an encoded message has been found, and help is needed to decipher it. Tell the students that while rummaging through the trash, a secret decoder was found (code on crumpled paper). Divide students up into groups and have each group decipher a part of the message using the decoder. Once each group finishes decoding their part of the message, bring the groups together, and share in reading the message out loud.
Next, ask students to brainstorm about all the possible codes and their uses. Write a list of these on the board. In addition, show students the symbols for the ancient Egyptian and Babylonian number systems. Ask students to work together to write the number 225 in each symbolic language.
Focus for Viewing
Say: Now that we have translated a coded binary message and attempted to write 225 in different number systems, let's see if we were correct.
- START the video at the beginning, when you see the hostess seated in the sand. PAUSE after the Egyptian symbols are displayed on the top row. Let students check their answers.
- FOCUS: Ask students to look and see if their next translation was correct. RESUME. After Babylonian symbols are shown for 225, PAUSE and let students check answers.
- FOCUS: Say: The Mayan language that we will see next shows us the first use of the number zero. RESUME. When Mayan translation is given, PAUSE.
- FOCUS: Say: What was different about the Babylonian and Mayan number systems? (They were not based on ten. The Babylonian system was based on 60 and the Mayan system was based on 20.) Tell the students that you are going to play part of the next segment with the sound off and see if they can guess which number systems are represented by the pictures. PLAY base 10 with SOUND ON. MUTE when you see the ruler. PAUSE after the gross of eggs, so they can guess which base system they just saw (12).
- FOCUS: Say: Try to guess the next base that you will see. PAUSE after the circle to check guesses (60). Note: do not play the base 12 and base 60 segments with the sound on; they are examples of multiples and could be confusing for students.
- FOCUS: Say: Now you will see the last example. RESUME with the SOUND ON. PAUSE after you view the section about base 2.
- FOCUS: Say: We are going to examine base two in greater detail. At the end of this next segment, our hostess will type "E l l e n" into a computer and translate it into a binary code. Let's write the code they used for each letter and to make it easier on the class, each group will be responsible for writing the symbols for only one of the letters. (Assign each group a letter of her name and have students write the binary symbols for that letter. If you assign one letter's binary code per group, there is enough time for each group to write that six digit code without stopping the video. Assign the first "E" to group one, second letter (l) to group two, etc. up to the fifth letter (n) for group five.) RESUME. STOP When the hostess says "Whoever thought two symbols could do so much."
- Have students discuss the code the computer assigned for the letters E l l e n. Say: Are there any
surprises? The E and e have different codes, why? Have students discover the code used for capital letters vs. lower case letters. Tell students "We have seen some of the applications in which the binary number system is used, let's create our own computer and see how high we can count."
Post-Viewing Activity: A Human Computer
Explain to students that computers receive signals that are either on (1) or off (0). To demonstrate how a computer reads a number, place seven students in a line for the initial demonstration, and have each student wear a different power of 2 on signs around their necks. For example: First student would have a card with 1 (2^0) taped to his or her shirt, second student's card has a 2 (2^1) on it. The third student has a 4 (2^2), the next student has 8 (2^3), the next student has 16 (2^4), next is 32 (2^5), and the last student's card has 64 (2^6). Students are side-by-side with student #1's left hand in his or her pocket. All other students have their left hands facing "palm up" and their right hands facing "palm down". Students' right hands are positioned over the top of their neighbors' left hands. The rule is: do not react unless your left hand has been slapped. If a student's left hand has been slapped, then he or she raises his or her right hand if it is down, or lowers it (slapping the person's hand to his or her right) if it was up. The teacher or a designated student counts out loud numbers from 0 to 32 while the demonstration group models each number. This is very confusing at first and you have to walk students through several numbers before they catch on. After students understand the basics of this activity, ask other groups of seven students to model each number from 0 to 64. (You might want to make this a competition and time each group.) Ask students to notice any patterns. (Student #1 will raise or lower his or her hand every time. His or her hand will be raised for odd numbers and lowered for even numbers.) The second student (2 or 2^1) raises and lowers his or her hand up for two then down for two. The patterns will become
obvious when students look at the table below.
|000000 = 0||010001 = 17||100001 = 33||110001 = 49|
|000001 = 1||010010 = 18||100010 = 34||110010 = 50|
|000010 = 2||010011 = 19||100011 = 35||110011 = 51|
|000011 = 3||010100 = 20||100100 = 36||110100 = 52|
|000100 = 4||010101 = 21||100101 = 37||110101 = 53|
|000101 = 5||010110 = 22||100110 = 38||110110 = 54|
|000110 = 6||010111 = 23||100111 = 39||110111 = 55|
|000111 = 7||011000 = 24||101000 = 40||111000 = 56|
|001000 = 8||011001 = 25||101001 = 41||111001 = 57|
|001001 = 9||011010 = 26||101010 = 42||111010 = 58|
|001010 = 10||011011 = 27||101011 = 43||111011 = 59|
|001011 = 11||011100 = 28||101100 = 44||111100 = 60|
|001100 = 12||011101 = 29||101101 = 45||111101 = 61|
|001101 = 13||011110 = 30||101110 = 46||111110 = 62|
|001110 = 14||011111 = 31||101111 = 47||111111 = 63|
|001111 = 15||100000 = 32||110000 = 48||1000000 = 64|
|010000 = 16|
Have students write a message in binary code. Exchange papers and have other students decipher the given message. Other assessments could include translating base ten numbers to base two and vice versa. Students could continue to find patterns in the table for homework, or write the next 64 numbers.
- Invite an engineer, or computer scientist to your classroom to discuss binary numbers and their use in everyday technology.
- Have the technology department build a binary light box (see Extensions), or create another device that is similar (such as putting different colors of cellophane over two flashlights where one color is assigned the number one, and the other a zero). With this device, students can send signals to each other.
- Invite a member of one of the armed services to come speak about the Morse code.
- In Social Studies classes, students can view old clips of war movies where binary systems, such as the Morse code, were used.
- In Music class, students can simulate messages sent by African tribes using two drums with different pitches.
- Language Arts classes can write poems about binary systems.
- Students can visit the following website to write messages in Egyptian Hieroglyphics: http://www.hbschool.com/activity/cartouche/cartouche.html
- Other lesson plans on Binary numbers and instructions for building a binary light box can be found in
the Space Based Astronomy Teacher's Guide with Activities Publicized by NASA/OSS Astrophysics Division, August 1994.
Key Words Binary Numbers, Bit, Byte, Base 2, Base 10, coding, digitizing, encoding, decryption code, ancient number systems, Morse code
|Solution to Detective Digit's Secret Message:|
|Detective Digit knows the secret of how computers work.Computers view everything in the world as a combination of ones and zeroes!|