Binary+Numbers

= Binary Numbers  = Adapted from Computer Science Unplugged Activity 1: “Count the Dots- Binary Numbers”


 * Author: ** Kristin Labby, 2011

Purpose
This lesson introduces students to computation thinking (I am using it as the first of several lessons for 6th and 7th graders about computational thinking.) This lesson aims to introduce students to binary numbers and binary code as a computer’s “language” of storing information. If this is a first lesson in computational thinking / computer science. A goal of the introduction discussion is to assess students’ prior knowledge of computers.

Overview
Students will learn about binary numbers in a series of activities.
 * 1) // Assess prior knowledge // : how do computers store information?
 * 2) // Demo with 5 volunteers and large binary cards //.
 * 3) // Worksheet Activity 1: Binary Numbers, // in small groups//.//
 * 4) // Worksheet Activity 2: Working with Binary, // individually
 * 5) // Brief re-cap/ discussion: ASCII. //
 * 6) // Worksheet Activity 3: Sending Secret messages, // individually (homework/assessment).

Student Outcomes
Using addition and pattern recognition skills, students will be able to count and encode decimal numbers into binary (and vice versa) in the 5 bit system used first. In the 8 bit system introduced later, students will translate binary codes (using the ASCII code) to numbers and letters, like computers do.

From CS unplugged: “to understand that technological systems are represented by symbolic language tools and understand the role played by the “black box” in technological system.

Illinois State Science Standards identified 11.A.3a Formulate Hypotheses. (Students never really test the hypothesis, but discover the answer through these activities.) 13.B.3a Scientific knowledge and economics drive technological development. (To minimize store space needed, binary numbers and 8-bit code is used. Discussed how computers get smaller and smaller.)

Time
60 minutes (Could cut some activities or turn into more lessons by using more of the CS Unplugged worksheets. “Extra for Experts” could be done too.)

Level
6th and 7th grade science

Materials and Tools

 * Projector and computer to display ASCII table to students (if not available, could print copies of the pdf and distribute 1 to each group).
 * Large binary numbers cards (1, 2, 4, 8, 16 dots): 5 sheets of cardstock, Sharpie marker. See preparation.
 * Activity 1 packet: (1 per group) Photocopies of activity 1, clear sheet projectors, set binary number cards (5 index cards, sharpie marker).
 * ASCII table pdf
 * Activity 2 worksheet, one copy for each student
 * Activity 3 worksheet, one copy for each student
 * ** Attached files include ** : Activity 1 worksheet, ASCII table pdf, Activity 2 worksheet, Activity 3 worksheet.

[|activity1.pdf] [|activity2.pdf] [|activity3.pdf] [|extra.pdf]

Prerequisites
Activities, or alternative activities, that should have been done before

Background
No major background requirements. Addition skills are needed to “count the dots”, pattern recognition skills are needed too. If students have the skills, they may recognize a power series (2n), but not necessary. No prior knowledge of computers needed.

Preparation
Make 5 large cards for the in class demo- cardstock with 1, 2, 4, 8 or 16 dots:



If doing Activity 1 in small groups, photocopy 1 worksheet for each group, put in plastic sheet protector. Make small sets of cards (same as above, but smaller) for each group (index cards and sharpie is fastest, could photocopy and cut out). Have powerpoint/ internet browser or document camera to show students the ASCII code table. (Alternatively 1 photocopy per group).

Teaching Notes
Students will learn about binary numbers in a series of activities.

I did this by following their “science journal format”. The title of the lesson is Binary Numbers and the key question: “How do computers store information?” (write these out on chalkboard. (Students copy this into their notebooks, then write their hypothesis). The question is very open ended, but the title of the lesson is Binary Numbers, so some students put it together and describe what they know or have heard about binary numbers, others may give very vague answers.) If time could do think-pair-share, or have students write their hypothesis on notecards, or just have a discussion.
 * // 1. Assess prior knowledge //** **.**

// Good questions to ask // : (guide students toward the idea that if we need to store lots of information, we can maximize by encoding it into “switches” of 1s or 0s.)

Explain that computers use just ones and zeros to store numbers and letters. (I made the analogy to a switch. Only two states on or off.) Have the 5 volunteers hold their large binary cards (I made my own quickly out of cardstock and a Sharpie marker, see image above of the binary cards.)
 * // 2. Demo with 5 volunteers and large binary cards //** **.**

Ask the following questions:

What do you notice about the number of dots on the cards? How many dots should the next card have if we carried on to the left? We can use these cards to make numbers by turning some of them face down, and adding up the dots that are showing. How can we make “6”? “15”? “21”? Lets count up from zero. Did you notice (maybe ask the 1 dot or 1 dot volunteer) how often the cards flip while we count up from zero? Now lets go from binary to numbers: what number is 01001? What is “17” in binary? Repeat with different students, or continue with similar questions.


 * // 3. Worksheet Activity 1: Binary Numbers //**

Have the students work in small groups (3 or 4) to work through CS Unplugged “Activity: Binary Numbers”. I made one copy for each group and put it in a clear page protector and tucked in a set of 5 index cards with dots (I made them rather than photocopying and cutting. Faster for me that way, and didn’t waste time having students cut cards.) I had them continue writing their answers in their science notebooks or on a loose-leaf sheet of paper.


 * // 4. Worksheet Activity 2: Working with Binary //**

Students worked individually on CS Unplugged “Working with Binary”. I photocopied and shrank it so students could paste into their notebooks after their question, hypothesis and Activity 1.


 * // 5. Re-cap/ discussion of ASCII table : //**

After this activity, I brought the class back together, showed them ASCII code, how computers //really// store data (letters or numbers) in binary numbers. Explained real computers are 8-bit; this dot-card system is 5-bit.


 * // 6. //// Worksheet Activity 3: Sending Secret messages. //** Could be used as an assessment. Work on in class if time allows or at home as homework. (shrink the copy to be pasted in to notebook if desired.


 * // 7. If time allows: //** do “extra for experts” activities or use other CS unplugged worksheets.

Assessment

 * Feedback from the class during discussions.
 * Questions students ask during “group work” time; teacher can circle and watch student progress during “Group work time on Activity 1”.
 * Activity 3 worksheet.

Additional Information
Any other explanations necessary of data, technology development, resources.

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