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Number Concept Syllabus


1. PROGRAM TITLE: InterMath - Number Concept                           

2. GOALS ADDRESSED

    Participants will:

  • Expand and strengthen their mathematical knowledge and capabilities, specifically in the domain of number concepts by investigating challenging problems
  • Engage in problem solving by identifying patterns, forming conjectures, and developing proofs through the use of technology
  • Use mathematics-specific technologies such as dynamic geometry software, graphing programs, spreadsheets, and the Internet to explore number concept investigations
  • Write and post online solution processes to the investigations using web page development software
  • Develop middle school mathematics instructional activities and strategies that incorporate technology-enhanced mathematical investigations
  • Develop a network of peer educators available for continued support during and following the workshop

3. IMPROVEMENT PRACTICES

Participants will gain knowledge and practice in developing instructional activities and strategies for teaching number concepts in the middle school classroom in order to positively affect student achievement. Participants will also improve their own mathematical competencies in the area of arithmetic.

4. COMPETENCIES

    Participants will be able to:

  • Select and use appropriate technological software to explore, analyze, and represent arithmetic problems
  • Communicate their mathematical thinking by expressing their reasoning, analysis, and extensions of the mathematical concepts associated with an investigation in written, verbal, and visual forms
  • Modify arithmetic investigations for appropriate use in the middle school classroom
  • Make connections between InterMath experiences and standards-based reform documents, such as the NCTM standards

5. PERFORMANCE INDICATORS

    As a result of this course, participants will demonstrate their ability to:

  • Incorporate technology into the learning and teaching of number concepts
  • Communicate mathematical understanding of a variety of number concepts in the form of an online portfolio of investigation solutions
  • Plan middle school instructional activities based on InterMath experiences

6. PREPARATION PHASE

Dates: Fall 2002
Instructor: Dr. Wilson/Dr. Gootman
Location: UGA campus
Strategies: Internet exploration, electronic and classroom discussions, lectures, exploration of mathematical investigations, investigation write-ups, collaborative brainstorming, lesson planning, presentations

 

7. ASSESSMENT

Participants will be assessed on the content and quality of their online portfolios. Feedback and suggested modifications for a select number of write-ups will be provided throughout the workshop. Assessment will be based on use of representation, analysis, appropriate selection and use of technological tools, creation of extensions, and accuracy of mathematics. In addition to the investigation write-ups, the participants will also create a mathematics lesson that integrates technology and number concepts for use in their own classroom. An end-of-course exam will be given to assess students on their mastery of mathematical abilities in the area of number concepts.

8. COURSE OUTLINE

I. Class 1

A. Introduction to InterMath
B. Introduction to Technology
C. Work through a number concept investigation as a whole class using technology
D. Discuss the components and structure of a write-up (including extensions)

II. Class 2

A. Discussion of History of Numeration
B. Participants begin their first web page write-ups to include in their online portfolios

C. Continued technological teaching and support (especially with Excel and the structure of a write-up)

III. Class 3

A.  Participants engage in investigations focused on Sets of Numbers
B.  Participants continue their web page write-ups to include in their online portfolios

C.  Continued technological teaching and support

IV. Class 4

A. Participants engage in investigations focused on order relationships, square roots, and mathematical induction
B. Participants add write-ups to their online portfolios
 

V. Class 5

A. Participants engage in investigations focused on enjoyment/beauty of numbers, countable, uncountable, large, and small numbers
B. Participants add write-ups to their online portfolios
 

VI. Class 6

A. Introduction of Graphing Program
B. Class works through an investigation together that uses the graphing program technology and graphing calculators

C. Participants engage in investigations of divisibility rules, greatest common factor, and least common multiple
D. Participants add write-ups to their online portfolios

VII. Class 7

A. Participants engage in prime, composite, abundant, deficient, and perfect numbers
B. Participants add write-ups to their online portfolios

VIII. Class 8

A. Participants engage in investigations focused on operations on sets of numbers, identity elements, and inverse operations
B. Participants add write-ups to their online portfolios

IX. Class 9

A. Participants engage in investigations of alternative algorithms, other bases, and modular arithmetic
B. Discuss and brainstorm ideas about modifying InterMath experience for a middle school mathematics classroom

C.  Participants add write-ups to their online portfolios

X. Class 10

A. Introduction of Geometer's Sketchpad Program (GSP)
B. Class works through an investigation together that uses the GSP technology

C. Participants engage in investigations of proportional reasoning
D. Participants add write-up to their online portfolios
E. Adapt an InterMath investigation into an instructional activity for middle school students – Whole class or small group activity

XI. Class 11

A. Introduction to Computer Based Laboratory (CBL)

B. Class works through an investigation together that uses the CBL

C. Participants engage in investigations focused on Pascal's Triangle, Fibonacci sequence, and Gauss strategy for computation
D. Participants add write-ups and middle school lesson plan to their online portfolios

XII. Class 12

A. Participants engage in investigations focused on Pythagorean Triples, figurate numbers, and historical aspects of number theory
B. Participants add write-up to their online portfolios

XIII. Class 13

A.   Each participant creates a technology-enhanced mathematical investigation for their own classroom

B.   Participants are encouraged to collaborate with each other for ideas and feedback

C.   Participants add middle school lesson plan to their online portfolios

XIV. Class 14

A. Each participant presents their instructional activity to the entire class

B. If the activity was implemented in the classroom, participant will discuss what went well, what was difficult, what can be improved, etc.

C. Class will provide feedback on the lesson plan

D.  Each participant will take a mathematics exam

9.  MATHEMATICAL CONTENT EXPLORED THROUGH THE INVESTIGATIONS
(Click Here to see a list of selected InterMath investigations clustered for Number Concepts )

Integers
o Model and solve contextualized problems using various representations, such as graphs, tables, and equations
o Recognize, investigate, analyze, extend, and generalize numeric patterns
o Generalize integer patterns using symbolic algebra, a table of results, and/or supporting pictures/diagrams
o Formulate a rule for a pattern
o Assign and describe variables to align with a problem situation
o Translate verbal expressions into numeric expressions/sentences and vice versa
o Evaluate expressions and solve equations (single and multi-variable)
o Explore problems associated with exponents and properties of exponents
o Investigate divisibility rules
o Analyze problems involving the sum, difference, product, and/or quotient of integers
o Express understanding and use the concepts of multiples and factors to solve problems
o Explore problems related to prime numbers
o Consider patterns and relationships associated with perfect square and perfect cube numbers
Fractions & Decimals
o Work with terminating and non-terminating decimals
o Calculate equivalent fractions
o Convert between fractions and decimals
o Investigate division by zero
o Solve problems involving unit fractions
o Investigate the four basic operations of addition, subtraction, multiplication, and division to calculate with fractions and decimals
o Plot fraction and decimal values on a number line
o Compare quantities (greater than, less than, equal to)
o Represent fractions and decimals in picture form
o Work with proper and improper fractions
Ratio, Proportion, & Percent
o Explore the properties of geometric sequences and series
o Determine equivalent forms of proportions
o Investigate methods of adding ratios
o Consider the concept of slope as a rate of change
o Write proportional relationships in geometry problems
o Learn how to use a Calculator-Based Laboratory (CBL)
o Analyze and solve problems involving applications of ratio and proportion
o Explore percent problems

Click Here to see a list of InterMath investigations clustered for Number Sense