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X orations Petabyte 0101000001100101011101000110000101100010011110010111010001100101

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Petabyte

X orations

X orations

0101000001100101011101000110000101100010011110010111010001100101

Petabyte 0101000001100101011101000110000101100010011110010111010001100101

© 2013 Make It Real Learningwww.makeitreallearning.com

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With the purchase of this workbook, license is granted for one (1) teacher to copy the activities in this workbook for use in classes and professional development workshops. Copying pages in this workbook for any other use is prohibited without written consent from Make It Real Learning Company. For permissions, visit www.MakeItRealLearning.com and complete the Contact Us form.

© 2013 Make It Real Learningwww.makeitreallearning.com

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© 2013 Make It Real Learningwww.makeitreallearning.com

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Part 1 – What is a Byte?Before we discuss the answer to this question, we have to go back to the smallest unit of data that a computer uses. This is called a bit. The word “bit” comes from putting the words binary digit together. Computers convert all of its inputs, outputs, and processes to a binary system. This means that everything in a computer uses the symbols 0 or 1. A bit can be used to represent two states of information, such as “Yes or No”, “On or Off”, “0 or 1.”

The next unit of data is the byte which is equivalent to 8 bits. A byte can represent 28 = 256 states of information such as numbers or a

combination of numbers and letters. One byte could be equal to one character. Ten bytes could be equal to a word. One hundred bytes would equal an average sentence.

As you are probably well aware, units of data that a computer uses are represented with terms such as kilobyte (kB), megabyte (MB), gigabyte (GB), terabyte (TB), etc.

Petabyte

© 2013 Make It Real Learningwww.makeitreallearning.com

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photos: Robert Couse-Baker

In the 1970’s and 1980’s, computer data was saved to 5-¼-inch floppy disks that could initially hold 100 kilobytes (kB) of data. Later in the 1980’s and into the 1990’s, the standard way to save data was with the 3-½ inch disk (that wasn’t as floppy, but since the disk inside was still flexible, it was considered a floppy disk). It could hold 1.44 megabytes of data. Now, we have flash drives (a.k.a thumb drives, USB drives, or jump drives) that can hold several gigabytes of data. We also have portable disk drives that can hold up to several terabytes of data.

These prefixes (kilo, mega, giga, and tera) tell us how many bytes of data the storage device can hold. Tra-ditionally, the prefixes have the following meanings:

• kilo – one thousand• mega – one million• giga – one billion• tera – one trillion

These prefixes give you some idea of the size of these storage devices. But to really wrap our heads around the amount of data that can be stored is a challenge. The goal of this project is to help you to make sense of these quantities.

© 2013 Make It Real Learningwww.makeitreallearning.com

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Part 2 – How Much Data?As mentioned in Part 1, computers use the binary system and so the actual data storage sizes are based on powers of 2. For example, one byte is equivalent to 23 = 8 bits.

1. Please consider the table and extend the pattern to complete the table. Note that you may need to be flexible in expressing an equivalent number when dealing with the very large numbers. That is, not every-thing has to be based on 1 byte.

Name Equivalent Number1 byte 20 = 1 byte

1 kilobyte 210 = 1,024 bytes

1 megabyte 220 = 1,048,576 bytes

1 gigabyte 230 bytes = 1,024 megabytes

1 terabyte

1 petabyte

1 exabyte

1 zetabyte

1 yottabyte

1 brontobyte

Source: www.whatsabyte.com

© 2013 Make It Real Learningwww.makeitreallearning.com

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2. An average 10 megapixel JPEG image will be about 4.5 megabytes. How many pictures can you store on a 1 gigabyte storage device?

3. How many pictures can you store on a 1 terabyte storage device?

© 2013 Make It Real Learningwww.makeitreallearning.com

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While music file size depends on the length of the song, a typical size is 4 megabytes. In this part of the project, we will determine the time needed to download music files as a way to make sense of the size of the storage device.

1. How many music files (assuming each is 4 megabytes in size) will fit on a 8 gigabyte storage device?

2. If your internet connection is 128 kbps (kilobits per second) and you purchase 8 gigabytes worth of music on the Apple iTunes store, how long would it take to download the music? (use your results from #1 above).

Petabyte

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0101000001100101011101000110000101100010011110010111010001100101

Petabyte 0101000001100101011101000110000101100010011110010111010001100101

© 2013 Make It Real Learningwww.makeitreallearning.com

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Getting Started Each activity (complete with solutions) is ready to print and use immediately; however, you can enhance your experience by doing the following:

PreparationPrint the activity and associated solutions.

1. Make copies of the activity (minus the solutions) for your students.2. Using a blank copy of the activity, solve each problem. During this process, reflect

on the big ideas the student should learn through the activity.3. Compare your answers to the preprinted solutions.

Implementation4. Divide the class into groups of four students.5. Give all class members a copy of the activity.6. Have the class members work in groups to complete the activity. During this time,

move from group to group to address specific learner questions. As needed, pro-vide a mini-lecture to the entire class to help students continue forward progress on the activity.

7. Once the activity is complete, invite students to present their results at the board. 8. Engage the class in a dialogue surrounding the big ideas.

ScoringIf desired, score the activity using the preprinted solutions as a key. Alternatively, you can provide class participation points for students who work the activity regardless of the accu-racy of their work. The latter approach works well if you have already discussed the prob-lems and solutions with the class as a part of the activity.

Common Core Standards

This activity is mapped to the Common Core State Standards for Mathematics (www.core-standards.org). As of June 2012, these learning standards had been adopted by 45 of the 50 states in the United States. A reference document at http://www.makeitreallearning.com/images/Activity_Map_to_Common_Core_Standards.pdf shows the standards that are ad-dressed by this activity.

© 2013 Make It Real Learningwww.makeitreallearning.com

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About the AuthorsAll of the activities in the Make It Real Learning Activity Series are written by award-win-ning authors and accomplished mathematics teachers. The combined experience of the authors represents more than 60 years of teaching experience ranging from K – 12 through college-level.

LicenseWith the purchase of this workbook, license is granted for one (1) teacher to copy the ac-tivities in this workbook for use in classes and professional development workshops. Copy-ing pages in this workbook for any other use is prohibited without written consent from Make It Real Learning Company. For permissions, visitwww.MakeItRealLearning.com and complete the Contact Us form.

© 2013 Make It Real Learningwww.makeitreallearning.com

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Teacher C

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Part 1 – What is a Byte?Before we discuss the answer to this question, we have to go back to the smallest unit of data that a computer uses. This is called a bit. The word “bit” comes from putting the words binary digit together. Computers convert all of its inputs, outputs, and processes to a binary system. This means that everything in a computer uses the symbols 0 or 1. A bit can be used to represent two states of information, such as “Yes or No”, “On or Off”, “0 or 1.”

The next unit of data is the byte which is equivalent to 8 bits. A byte can represent 28 = 256 states of information such as numbers or a

combination of numbers and letters. One byte could be equal to one character. Ten bytes could be equal to a word. One hundred bytes would equal an average sentence.

As you are probably well aware, units of data that a computer uses are represented with terms such as kilobyte (kB), megabyte (MB), gigabyte (GB), terabyte (TB), etc.

Petabyte

© 2013 Make It Real Learningwww.makeitreallearning.com

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photos: Robert Couse-Baker

In the 1970’s and 1980’s, computer data was saved to 5-¼-inch floppy disks that could initially hold 100 kilobytes (kB) of data. Later in the 1980’s and into the 1990’s, the standard way to save data was with the 3-½ inch disk (that wasn’t as floppy, but since the disk inside was still flexible, it was con-sidered a floppy disk). It could hold 1.44 megabytes of data. Now, we have flash drives (a.k.a thumb drives, USB drives, or jump drives) that can hold several gigabytes of data. We also have portable disk drives that can hold up to several tera-bytes of data.

These prefixes (kilo, mega, giga, and tera) tell us how many bytes of data the storage device can hold. Tra-ditionally, the prefixes have the following meanings:

• kilo – one thousand• mega – one million• giga – one billion• tera – one trillion

These prefixes give you some idea of the size of these storage devices. But to really wrap our heads around the amount of data that can be stored is a challenge. The goal of this project is to help you to make sense of these quantities.

© 2013 Make It Real Learningwww.makeitreallearning.com

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Teacher C

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Part 2 – How Much Data?As mentioned in Part 1, computers use the binary system and so the actual data storage sizes are based on powers of 2. For example, one byte is equivalent to 23 = 8 bits.

1. Please consider the table and extend the pattern to complete the table. Note that you may need to be flexible in expressing an equivalent number when dealing with the very large numbers. That is, not every-thing has to be based on 1 byte.

Name Equivalent Number1 byte 20 = 1 byte

1 kilobyte 210 = 1,024 bytes

1 megabyte 220 = 1,048,576 bytes

1 gigabyte 230 bytes = 1,024 megabytes

1 terabyte 240 bytes = 1,024 gigabytes

1 petabyte 250 bytes = 1,024 terabytes

1 exabyte 260 bytes = 1,024 petabytes

1 zetabyte 270 bytes = 1,024 exabytes

1 yottabyte 280 bytes = 1,024 zetabytes

1 brontobyte 290 bytes = 1,024 yottabytes

Source: www.whatsabyte.com

Note that we can be flexible in terms of how they relate the equivalent number.

© 2013 Make It Real Learningwww.makeitreallearning.com

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Formulas and FactsYou may need to use some of the following formulas and facts in working through this project. You may not need to use every formula or each fact.

Area of a rectangle Circumference of a rectangle

Area of a circle

Circumference of a circle Area of a triangle Slope12 inches = 1 foot 5280 feet = 1 mile 3 feet = 1 yard16 ounces = 1 pound 2.54 centimeters = 1 inch 100¢ = \$11 kilogram = 2.2 pounds 1 ton = 2000 pounds 1 gigabyte = 1024 megabytes1 mile = 1609 meters 1 gallon = 3.8 liters 1 square mile = 640 acres1 square yard = 9 sqare feet 1 cubic foot of water = 7.48 gal-

lons1 ml = 1 cubic centimeter

2V r hp= Volume of cylinder V lwh= Volume of rectangular prism

V = 4-3 π r3 Volume of a sphere

Lateral SA = 2π xr xhLateral surface area of cylinder

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242 -±-

=

© 2013 Make It Real Learningwww.makeitreallearning.com

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Common Core Standards (CCS) and Common Core Standards for Mathematical Practices (CCSSMP)

Part 2Question CCS CCSSMP1 6.EE.1, 8.EE.1 MP1, MP2, MP4, MP62 5.MD.1 MP1, MP2, MP4, MP63 5.MD.1 MP1, MP2, MP4, MP6

Part 3Question CCS CCSSMP1 5.MD.1, 7.RP.1 MP1, MP2, MP4, MP62 7.RP.1 MP1, MP2, MP4, MP63 7.RP.1 MP1, MP2, MP4, MP6, MP84 7.RP.2, 8.EE.5 MP1, MP2, MP4, MP65 6.EE.2c MP1, MP2, MP4, MP6, MP7, MP86 6.EE.2c, 7.RP.1 MP1, MP2, MP4, MP6, MP7, MP8

Part 4Question CCS CCSSMP1 5.MD.1, 8.EE.4 MP1, MP2, MP4, MP5, MP6, MP7, MP82 5.MD.1, 8.EE.4 MP1, MP2, MP4, MP5, MP6, MP7, MP8

Part 5Question CCS CCSSMP1 7.RP.1,8.EE.4 MP1, MP2, MP4, MP5, MP6, MP7, MP82 7.RP.1,8.EE.4 MP1, MP2, MP4, MP5, MP6, MP7, MP8

Part 6Question CCS CCSSMP1 7.RP.1,8.EE.4 MP1, MP2, MP4, MP5, MP6, MP7, MP82 7.RP.1,8.EE.4 MP1, MP2, MP4, MP5, MP6, MP7, MP8

Part 7Question CCS CCSSMP1 7.RP.1,8.EE.4 MP1, MP2, MP4, MP5, MP6, MP7, MP8