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Although middle school students may have learned to identify basic place value in earlier grades, most are developmentally ready to delve into the deeper concepts of counting in other bases and the exponential growth of groupings within each increasing place.  Just as students can more clearly understand the English language by studying a foreign language, math students can better understand our number system by studying other number systems and/or by creating a new one.  Students who construct depth of understanding of place value through exploration will be more fully equipped to expand their mathematical thinking into the realm of decimals and scientific notation.  I have chosen to use the term "number system" for this WebQuest rather than "numeration system," because I think it will more successfully link new ideas to the prior knowledge of the middle school students. 

In order to prepare your students for involvement in this WebQuest, you may want to spend class time in advance reviewing and exploring place value by engaging them in the activities provided through the Internet links below.  You are also welcome to broaden your knowledge of place value and number systems by reading some selected background information, also linked below. 

If you use this WebQuest with your class, I'd love to have your feedback and suggestions.  Please contact me at alicegabbard@yahoo.com or agabbard@newport.k12.ky.us.

Search the NKU WebQuest database for more K12 math & science WebQuests. 

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Materials

Besides computers with Microsoft Office software and Internet access, your students will need:

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group assignments

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KWL wall chart for place value 

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paper

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markers

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poster board

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projector or TV screen connected to a computer

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Links to Introductory Activities

bulletHands-on Activities to Review Base 10 Place Value:
1.  Race to 1000 Using Beans

2.  The Place  Value Game:  How Long Does It Take to Count to a Million?

3.  Place Value Lessons Involving Movement, Music, and Reflection

 
bulletActivities for Thinking in Other Bases:

4.  A Fictional History of Place Value

5.  Hands-on Role Play Activity: Counting the Rice

6.  Learning the Binary Number System Through Guided Questions

7.  The MacCandy Factory (interactive plug-in designed for Mac computers, but the questions and framework are helpful to all computer users).

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Links to Background Information

  1. Place Value:  Problem Solving and Written Assessment Using Digit-Correspondence Tasks
  2. Numeration Systems and Numbers (History/Overview)
  3. Development of the Arabic/Modern Number System

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Curriculum Standards

KY Academic Expectations

1.5:  Students use mathematical ideas and procedures to communicate, reason, and solve problems.

2.7:  Students understand number concepts and use numbers appropriately and accurately.

KY Program of Studies

M-6-NC-4:  Students will develop place value of large and small numbers.

M-6-NC-5:  Students will explore exponents.

KY Core Content for Assessment

MA-M-1.1.4:  Students will describe properties of, define, give examples of, and/or apply to both real-world and mathematical situations: Place value of whole numbers and decimals

MA-M-1.1.5:  Students will describe properties of, define, give examples of, and/or apply to both real-world and mathematical situations: Positive whole number exponents

National Council of Teachers of Math Standards

Standard 1—Number and Operations

Instructional programs from prekindergarten through grade 12 should enable all students to:

bulletUnderstand numbers, ways of representing numbers, relationships among numbers, and number systems.

 Standard 6—Problem Solving

Instructional programs from prekindergarten through grade 12 should enable all students to:

bulletBuild new mathematical knowledge through problem solving;
bulletSolve problems that arise in mathematics and other contexts;
bulletApply and adapt a variety of appropriate strategies to solve problems;
bulletMonitor and reflect on the process of mathematical problem solving.

 Standard 8—Communication

Instructional programs from prekindergarten through grade 12 should enable all students to:

bulletorganize and consolidate their mathematical thinking through communication;
bulletcommunicate their mathematical thinking coherently and clearly to peers, teachers, and others;
bulletanalyze and evaluate the mathematical thinking and strategies of others;
bulletuse the language of mathematics to express mathematical ideas precisely.

 Standard 9—Connections

Instructional programs from prekindergarten through grade 12 should enable all students to:

bulletrecognize and use connections among mathematical ideas;
bulletunderstand how mathematical ideas interconnect and build on one another to produce a coherent whole;
bulletrecognize and apply mathematics in contexts outside of mathematics.

 Standard 10—Representation

Instructional programs from prekindergarten through grade 12 should enable all students to:

bulletcreate and use representations to organize, record, and communicate mathematical ideas;
bulletselect, apply, and translate among mathematical representations to solve problems;
bulletuse representations to model and interpret physical, social, and mathematical phenomena.  

International Society for Technology in Education PERFORMANCE INDICATORS FOR TECHNOLOGY—LITERATE STUDENTS, Grades 6-8

Prior to completion of Grade 8, students will:

4.  Use content-specific tools, software, and simulations (e.g., environmental probes, graphing calculators, exploratory environments, Web tools) to support learning and research. (3, 5)

5.  Apply productivity/multimedia tools and peripherals to support personal productivity, group collaboration, and learning throughout the curriculum. (3, 6)

7.  Collaborate with peers, experts, and others using telecommunications and collaborative tools to investigate curriculum-related problems, issues, and information, and to develop solutions or products for audiences inside and outside the classroom. (4, 5)

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