labby - binary numbers - reach for the starsgk12.ciera.northwestern.edu/classroom/2012/labby -...

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Binary Numbers – Kristin Labby Adapted from Computer Science Unplugged Activity 1: “Count the Dots-‐ Binary Numbers”

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 you think 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 Code, 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.

I also like this objective 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: 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.)

2 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 worksheet, clear sheet projectors, set of

binary number cards (5 index cards, sharpie marker). • ASCII tables (within this file) • Activity 2 worksheet, one copy for each student • Activity 3 worksheet, one copy for each student • Attached files include: Activity 1 worksheet, Activity 2 worksheet, Activity 3 worksheet,

Additional activities, ASCII Tables

Preparation Make 5 large cards for the in class demo- on 8 ½” x 11” cardstock, use marker to make 1, 2, 4, 8 or 16 dots:

4 Photocopiable for classroom use only. © 2005 Computer Science Unplugged (www.unplugged.canterbury.ac.nz)

Binary Numbers

Introduction

Before giving out the worksheet on page 5, it can be helpful to demonstrate the principles to the whole group.

For this activity, you will need a set of five cards, as shown below, with dots on one side and nothing on the other. Choose five children to hold the demonstration cards at the front of the class. The cards should be in the following order:

Discussion

What do you notice about the number of dots on the cards? (Each card has twice as many as the card to its right.)

How many dots would the next card have if we carried on to the left? (32) The next…?

We can use these cards to make numbers by turning some of them face down and adding up the dots that are showing. Ask the children to make 6 (4-dot and 2-dot cards), then 15 (8-, 4-, 2- and 1-dot cards), then 21 (16, 4 and 1)…

Now try counting from zero onwards.

The rest of the class needs to look closely at how the cards change to see if they can see a pattern in how the cards flip (each card flips half as often as the one to its right). You may like to try this with more than one group.

When a binary number card is not showing, it is represented by a zero. When it is showing, it is represented by a one. This is the binary number system.

Ask the children to make 01001. What number is this in decimal? (9) What would 17 be in binary? (10001)

Try a few more until they understand the concept.

There are five optional follow-up extension activities, to be used for reinforcement. The children should do as many of them as they can.

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) and tuck into sheet protector. Have powerpoint/ internet browser and projector or document camera to show students the ASCII code table. (Alternatively 1 photocopy per group).

Prerequisites None.

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. Minimal familiarity with computers (ex. Typing in word processor and “saving” a file).

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Teaching Notes Students will learn about binary numbers in a series of activities. This is adapted from CS Unplugged (http://csunplugged.org/). I found my 6th and 7th graders needed clearer instructions on the worksheets, so I modified them to hopefully be more straightforward.

1. Assess prior knowledge. I did this by following the students “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, and 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.

(Guide students toward the idea that if we need to store lots of information, we can maximize storage by encoding it into “switches” of 1s or 0s.)

2. Demo with 5 volunteers and large binary cards. 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.)


Binary Numbers

Introduction



Discussion










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 2 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 Activity 1: 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 Activity 2 worksheet, “Working with Binary Code”. I photocopied and shrank it so students could paste into their notebooks after their title, 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: symbols, letters or numbers get translated to binary numbers. Explained real computers are 8-bit; this dot-card system is 5-bit.

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Use chalkboard to draw out 8 bit examples. Start with 8 blank “cards”, ask students how they should be filled in. (From right to left : 1, 2, 4, 8, 16, 32, 64, 128.) Ask students: what’s the maximum decimal number you can count to in 8-bit binary? On the chalkboard, practice a few conversions between decimal and 8-bit binary. Put up ASCII table, explain the columns: focus on “decimal” “binary” and “symbol”. If time, go through some examples of translating 8-bit binary to decimals, then to the corresponding letters/ symbols.

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 science 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- intro and recap/ASCII. • Questions students ask during “group work” time; teacher can circle and watch student progress

during “Group work time on Activity 1”. • Activity 3 worksheet graded as homework.

Additional Information http://csunplugged.org/binary-numbers Great website, contains a lot of information, even has videos!

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Activity 1: Binary Numbers Adapted from CS Unplugged: page 5, “Worksheet Activity: Binary Numbers” Instructions:

1. Working in your small group, clear some workspace and take out the index cards from your packet and lay them out with the 16-dot card on the left as shown below:

Photocopiable for classroom use only. 5 © 2002 Computer Science Unplugged (www.unplugged.canterbury.ac.nz)

!"#$%&''()*+(,-,(./)0,12#.)3456'#%)

7'2#1,18)&"9)(")+"41()So, you thought you knew how to count? Well, here is a new way to do it!

Did you know that computers use only zero and one? Everything that you see or hear on the computer—words, pictures, numbers, movies and even sound is stored using just those two numbers! These activities will teach you how to send secret messages to your friends using exactly the same method as a computer.

:1%(#4+(,"1%)Cut out the cards on your sheet and lay them out with the 16-dot card on the left as shown here:

Make sure the cards are placed in exactly the same order.

Now flip the cards so exactly 5 dots show—keep your cards in the same order!

Find out how to get 3, 12, 19. Is there more than one way to get any number? What is the biggest number you can make? What is the smallest? Is there any number you can’t make between the smallest and biggest numbers?

Extra for Experts: Try making the numbers 1, 2, 3, 4 in order. Can you work out a logical and reliable method of flipping the cards to increase any number by one?

Make sure the cards are in the same order as shown above. (This probably seems backwards to you since in English, we read words from left to right! In binary codes the lowest number is on the right and we count up towards the left.)

2. Flip the cards to show exactly 5 dots:


!"#$%&''()*+(,-,(./)0,12#.)3456'#%)

7'2#1,18)&"9)(")+"41()So, you thought you knew how to count? Well, here is a new way to do it!

Did you know that computers use only zero and one? Everything that you see or hear on the computer—words, pictures, numbers, movies and even sound is stored using just those two numbers! These activities will teach you how to send secret messages to your friends using exactly the same method as a computer.

:1%(#4+(,"1%)Cut out the cards on your sheet and lay them out with the 16-dot card on the left as shown here:

Make sure the cards are placed in exactly the same order.

Now flip the cards so exactly 5 dots show—keep your cards in the same order!

Find out how to get 3, 12, 19. Is there more than one way to get any number? What is the biggest number you can make? What is the smallest? Is there any number you can’t make between the smallest and biggest numbers?

Extra for Experts: Try making the numbers 1, 2, 3, 4 in order. Can you work out a logical and reliable method of flipping the cards to increase any number by one?

Remember to keep the cards in the same order.

3. Now flip the card to make the number 9. Write how you did this in your notebook like this:

9 =


Binary Numbers

Introduction



Discussion










4. Do the same to find out how to get the numbers 3, 12 and 19. Sketch these in your notebook too.

5. Answer these questions in your notebook. Remember to use complete sentences. a. Is there more than one way to make any number? b. What is the biggest number you can make? c. What is the smallest number you can make? d. Is there any number you can’t make between the biggest and the smallest numbers?

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Activity 2: Working with Binary Code Adapted from CS Unplugged: page 7, “Worksheet Activity: Working with Binary” The binary system uses zero and one to represent whether a card is face up or not. 0 shows that a card is hidden, and 1 means that you can see the dots. For example, for the number 9:


!"#$%&''()*+(,-,(./)!"#$,01)!,(&)2,03#.)The binary system uses zero and one to represent whether a card is face up or not. 0 shows that a card is hidden, and 1 means that you can see the dots. For example:

Can you work out what 10101 is? What about 11111?

What day of the month were you born? Write it in binary. Find out what your friend’s birthdays are in binary.

4#.)(")5"#$)"6()(&'%')+"7'7)0689'#%/)

Extra for Experts: Using a set of rods of length 1, 2, 4, 8 and 16 units show how you can make any length up to 31 units. Or you could surprise an adult and show them

how they only need a balance scale and a few weights to be able to weigh those heavy things like suitcases or boxes!

We call the series of 0s and 1s binary numbers, while 9 that is represented is called a decimal number. Questions: (use your 5 binary cards to help if needed)

1. Can you work out what 10101 is as a decimal number? _________

2. What is 11111 in decimal? _________

3. What date of the month were you born in (in decimal)? ________

What is that in binary numbers? ___ ___ ___ ___ ___

4. Write the birthdays of two friends too (decimal and binary):

_____ = ___ ___ ___ ___ ___ _____ = ___ ___ ___ ___ ___

5. Try to work out these coded numbers. Some are 5 bit binary codes; some are only 4-bit, 3-bit, 2-bit or 1-bit. Its important to remember that in binary we count up from the right, not the left. Write the decimal number next to the “ = ”. Translate the codes to 0s and 1s first if it helps you.


!"#$%&''()*+(,-,(./)!"#$,01)!,(&)2,03#.)The binary system uses zero and one to represent whether a card is face up or not. 0 shows that a card is hidden, and 1 means that you can see the dots. For example:

Can you work out what 10101 is? What about 11111?

What day of the month were you born? Write it in binary. Find out what your friend’s birthdays are in binary.

4#.)(")5"#$)"6()(&'%')+"7'7)0689'#%/)

Extra for Experts: Using a set of rods of length 1, 2, 4, 8 and 16 units show how you can make any length up to 31 units. Or you could surprise an adult and show them

how they only need a balance scale and a few weights to be able to weigh those heavy things like suitcases or boxes!

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Activity 3: Use Binary Code to Send Secret Messages! Adapted from CS Unplugged: page 8, “Worksheet Activity: Sending Secret Messages”


!"#$%&''()*+(,-,(./)0'12,13)0'+#'()4'%%53'%)Tom is trapped on the top floor of a department store. It’s just before Christmas and he wants to get home with his presents. What can he do? He has tried calling, even yelling, but there is no one around. Across the street he can see some computer person still working away late into the night. How could he attract her attention? Tom looks around to see what he could use. Then he has a brilliant idea—he can use the Christmas tree lights to send her a message! He finds all the lights and plugs them in so he can turn them on and off. He uses a simple binary code, which he knows the woman across the street is sure to understand. Can you work it out?

6) 7) 8) 9) :) ;) <) =) >) 6?) 66) 67) 68)

5) @) +) 2) ') A) 3) &) ,) B) $) C) D)69) 6:) 6;) 6<) 6=) 6>) 7?) 76) 77) 78) 79) 7:) 7;)

1) ") E) F) #) %) () G) -) H) I) .) J)

Directions: Tom’s building is shown below. Each row is a floor of 5 rooms. Decode Tom’s message by first translating each floor into binary, then into decimal numbers. Finally, use the decoding table at the bottom to translate the decimal numbers into letters. Binary Decimal Letters

= _0_ _1_ _0_ _0_ _0_ = __8__ = _h__

Decimal Letter Code:



6) 7) 8) 9) :) ;) <) =) >) 6?) 66) 67) 68)

5) @) +) 2) ') A) 3) &) ,) B) $) C) D)69) 6:) 6;) 6<) 6=) 6>) 7?) 76) 77) 78) 79) 7:) 7;)

1) ") E) F) #) %) () G) -) H) I) .) J)



6) 7) 8) 9) :) ;) <) =) >) 6?) 66) 67) 68)

5) @) +) 2) ') A) 3) &) ,) B) $) C) D)69) 6:) 6;) 6<) 6=) 6>) 7?) 76) 77) 78) 79) 7:) 7;)

1) ") E) F) #) %) () G) -) H) I) .) J)



6) 7) 8) 9) :) ;) <) =) >) 6?) 66) 67) 68)

5) @) +) 2) ') A) 3) &) ,) B) $) C) D)69) 6:) 6;) 6<) 6=) 6>) 7?) 76) 77) 78) 79) 7:) 7;)

1) ") E) F) #) %) () G) -) H) I) .) J)

8 Extra for Experts: (from CS Unplugged worksheets)

Activity 1: Try making the numbers 1, 2, 3, 4 in order. Can you work out a logical and reliable method of flipping the cards to increase any number by one? Activity 2: Using a set of rods of length 1, 2, 4, 8 and 16 units show how you can make any length up to 31 units. Or you could surprise an adult and show them how they only need a balance scale and a few weights to be able to weigh those heavy things like suitcases or boxes! (these ideas –weights or rods – could be expanded into additional activities)

See CS Unplugged pages 9, 10 , 11 and 12 for additional worksheets relating to this lesson. Other extensions: could extend ASCII table, make a “coded message” in Binary, have students translate to the letters and numbers via ASCII. Could have students define vocabulary words: binary numbers, decimal numbers, ASCII table.

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Taken from: http://www.ascii-code.com/

labby - binary numbers - reach for the starsgk12.ciera.northwestern.edu/classroom/2012/labby -...

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