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A Creative Encounter of the Numerical Kind

 

 A WebQuest for Middle Grades Math Students

 

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The year is 2073 A.D. and the President of the United Nations has

drafted you (because of your famous mathematical brain) to join a

team of mathematical consultants to travel to Zonetia, a recently

discovered planet in a neighboring galaxy. King Zoppo (he's the

green guy on the Home page) of the Zony Tribe on Zonetia insiststhat his primitive society cannot begin to make technological

advancements unless they have guidance to develop a brand-new

base 4 number system to fit the Zonies' two-fingered hands.

That's right; they have two hands just like you, but each hand has

only two fingers. Therefore, they need a specially-tailored

number system with only four symbols. In order to best preserve

Zony culture, King Zoppo, in his wisdom, has requested that the

new number symbols be different than those used on Earth.

Because King Zoppo knows that Earthlings spent thousands

and thousands of years developing the current U.S./European

number system, he wants you to use your experience to assist him

in leading his people through an efficient process, instead of 

leaving them to build their own number system slowly, through

trial and error. There's no time to waste! In exchange for your 

work King Zoppo has promised to send much-needed energyresources to planet Earth. Although the mission is considered

dangerous, the success of your team could bring you fame and

fortune and make life better for billions of Zonies and Earthlings.

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Your big questions are:

Why does our number system have place value?

How does place value work?

By following each step listed on the "process" page you will:

PREPARE FOR YOUR MISSION: While in flight on the

way to planet Zonetia, you will adopt the role of a specialized

math expert and use given Internet sites to research number 

systems, counting, and place value.BECOME A TEAM:

Share your new knowledge with your group;CREATE A NEW NUMBER SYSTEM: Create a base 4

number system with your group (using original symbols and

names) to launch the technological development of the Zony

tribe;TEACH THE ZONIES: As a team, present your new number 

system to the Zony Tribal Council using your choice of visual

aids: a poster, book, Power Point, or Excel spreadsheet.

Part I: Activate Prior Knowledge

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Write down everything you already know about place valuein the "know" column in a chart. Write a question in the"want to know" column of the chart. Feel free to addquestions to this chart as you progress through the

WebQuest.

Part II: Gaining New Knowledge

 Your teacher will assign you to a group of 3 students.As a group decide which of the 3 roles each member of 

your group will assume. Scroll down to your section of detailed instructions and Internet resource links.

Historian

 

Abacus Operator 

 Number SystemsAnalist

 

Historian

1. Open a blank Word document with the title  HistorianResearch Report.

2.  Click on this site Historian Research Report to get thequestions you have to answer 

3. Complete the Historian Research Report as you visitthe Internet sites provided below.

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African Counting Method 37,000 BC

Egyptian Numerals 3,500 BC

Babylonian Numbers Chart, 2,000BC

Mayan Number System, 400AD

Abacus Operator 

1. Open and save a blank Word document with the titleAbacus Operator Report.

2. Click on this site Abacus Operator Report to get thequestions you have to answer 

3. Complete the Abacus Operator Report as you visit the

Internet sites provided below

  The Invention of the Abacus

  Abacus Introduction: The Art of Calculating with Beads

The Abacus History

  Counting in various number systems

Number Systems Analyst

1. Open and save a blank Word document with the titleNumber System Report. 

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2. Click on this site Number System Report. to get thequestions you have to answer 

3. Complete the Number Systems Analyst Report as youvisit the Internet sites provided below.

A Basic Review of Our Base 10 Number System

  What is it? Place Value to 1,000

Racing With Place Value

  Binary--How Does it Work?

Part III: Sharing Your New Knowledge

Meet with your group and teach them what you learned

from your Internet research. Discuss your response to thereflection question on your report. Post at least one thingyou learned onto the chart in the "learned" column.

Part IV: Creating the New Number System

Draw and name 4 new symbols which will become the digits

used in the new number system. Think about how thenumber system will work. Make sure you use place value indesigning the new number system. Will you need a symbolto represent 0? Will you need a symbol to represent 4?Make sure your symbol designs are simple enough to writequickly, because you will be using them over and over.

Part V: Presenting the New Number System

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1. Make sure everyone in your group continues toparticipate as you prepare and present the final project.

2. Agree on a visual aid to use for presenting the new

number system: a book, poster, Power Point, or Excelspreadsheet. Make sure the visual aid includes:

a key with each symbol, name, English translation, and apicture of the number of objects (dots are fine) itrepresents.a rule to tell when you regroup.a chart showing the value of the number one symbol in

each of the first 7 columns/places. The value of eachplace should be shown in the English number system inits expanded form and as an exponent.a counting list with the symbols and pictures (dots arefine) up to 70.

3. Have each member of your team present one part of the

number system to the Zony Tribal Council. Be sure toclearly show the visual aid and the online abacus for counting. Explain why place value is an important conceptin your new number system.

4. Congratulations! Your mission is complete. You arenow free to return to Earth and resume using our good-oldbase 10 number system