I. Curricular Framework

Concept:

Systems

Essential Question:

How is the binary system different from the hexidecimal and decimal system?

Bridge:

Base 2 Pantomimes

Content:

Outcomes:

II. Standards Aligned

III. Instruction and Assessment

1. Connect: Connecting to the Concept Experientially

Objective: To interest students in the various numbering systems and in translations.

Activity: 1) Break students into groups of four or five. Ask students to imagine they are system programmers employed by IBM, they are 30 years old, and they are on a company trip to Europe. Using chart paper and markers, brainstorm and write the different numbering systems (bases) they might encounter during the trip. Examples: U.S. money is base 10 (decimal). The clock at the airport is base 60. Gasoline is in liters. Mileage is kilometers, etc. 2) Speak to the students in a combination of Spanish and Pig Latin: "Buenos Dias, Amigos. e-wa are earning-la about ecimal-da, inary-ba, and exi-ha ecimal-da, etc."

Assessment: Students curiosity and reaction to teacher behavior.

2. Attend: Attending to the Connection

Objective: To analyze why we have different numbering systems and how our mind can translate.

Activity: Using chart paper and markers, 1) Students share their lists of the numbering systems encountered on the trip to Europe. 2) Students translate what the teacher said.

Assessment: Quality of group lists.

Assessment, Phase One, Level of Engagement, Fascination:

3. Image: Creating a Mental Picture

Objective: To familiarize students with Base 2 and foster a desire for more information about numbering systems.

Activity: Each group should pantomime an activity or thing that demonstrates a use of Base 2 and/or reminds us of Base 2. Examples: 1. Nod head/shake head ñ Yes/No 2. Flip light switch On/Off 3. Sit/Stand Up/Down 4. Close eyes/open eyes Asleep/Awake 5. Shiver/Perspire Cold/Hot Which example of Base 2 do you think is most like the computer? (On/Off)

Assessment: Level of student contribution to activity.

Assessment, Phase Two, Seeing the Big Picture:

4. Inform: Receiving Facts & Knowledge

Objective: To explain how computers use the binary system. To explain how and why programmers use the hexidecimal system. To explain how to convert from decimal to binary to hexidecimal.

Activity: 1) Tape eight signs to the wall that read "1, 2, 4, 8, etc." Have eight students wear signs that read "0" and "1" and stand under the signs on the wall. The teacher then physically places the eight students into a line and by turning their cards over, constructs binary numbers and explains how to translate those binary numbers into decimal numbers. The teacher can then illustrate how each group of four students is a "nibble," while all eight students represent a "byte." The teacher then uses each nibble to explain how binary can be converted to hexidecimal. 2) Teacher does conventional lecturing and diagramming at the board for emphasis. 3) Students read textbook.

Assessment: Teacher checking for understanding; quality of student questions and involvement in interactive lecture/discussion.

Assessment, Phase Three, Success with Acquiring Knowledge:

5. Practice: Developing Skills

Objective: To gain skill in creating and converting numbers in the three numbering systems.

Activity: There are many interactive worksheets in game formats available on the market which present opportunities for students to convert number systems.

Assessment: Quality of student worksheets.

Assessment, Phase Four, Success with Acquiring Skills:

6. Extend: Extending Learning to the Outside World

Objective: To experiment with binary and/or hexidecimal by creating a project.

Activity: Students create a game (Bingo, Dominoes), card trick, puzzle, picture, poster, model, song, teaching tool, computer program, etc. that utilizes either Base 2 or Base 16. Students are encouraged to use individuality in selection and design of their project.

Assessment: Quality of student project plans.

7. Refine: Refining the Extension

Objective: To critique the project from 3R.

Activity: Students trade projects and another student completes a form listing the strengths and weaknesses of the project.

Assessment: Students' ability to critique the effectiveness of the assignment. Did they understand the concept well-enough to critique another's work?

8. Perform: Creative Manifestation of Material Learned

Objective: To share their knowledge of binary and hexidecimal with others.

Activity: Students play the games, work the puzzles, sing the songs, etc. that were prepared in 3R (and then improved in 4L). (Possible Alternate Activity ñ if the project lends itself, perhaps the presentation of the project could go school-wide on closed-circuit TV.)

Assessment: Student enjoyment of shared learning.

Assessment, Phase Five,Performance, Creative Use of Material Learned: