MODULE #3

MODULE 3

Module Title: Number Theory

Estimated time to complete: Five 75 minute periods

Module objectives: The student will be able to:

Access and evaluate an elementary level interactive web site.
Demonstrate competencies in understanding divisibility, the relationship between prime and composite numbers, and finding the greatest common factor and least common multiple.
Distinguish the advantages and disadvantages of each method of delivery: text, hands-on manipulatives, and interactive educational sites.

Concept(s) learned in this module:

Accessing and evaluating interactive web sites

Communicating student understanding of different pedagogical styles via journal writing

Demonstrating competencies in understanding divisibility, the relationship between prime and composite numbers, and finding the greatest common factor and least common multiple

Standards addressed in this module:

Praxis:

Mathematics Curriculum, Instruction, and Assessment

Teaching strategies and activities that will aid in the development, delivery, and evaluation of the following:

Curriculum components – for example, scope and sequence of skills and materials; appropriate materials and technology; learner objectives
Use of manipulatives and developmentally appropriate materials; variety and reliability
Concepts related to number theory – for example, factors, multiples, primes and composites, remainders, odd and even
Problem solving – for example, investigate and understand content; formulate problems from everyday situations; develop strategies applicable to a wide range of problems; verify and interpret results; build student confidence; identify and solve problems that are developmentally appropriate
Content specific pedagogy – for example, theories necessary for implementing a sound instructional program such as accessing prior knowledge, constructing knowledge, modeling, informal reasoning, graphic organizers

Conceptual Knowledge and Procedural Knowledge

Demonstrate number sense and operation sense, that is, an understanding of the foundational ideas of numbers, number properties, and operations defined on numbers.

Equivalence: demonstrate an understanding that a number can be represented in more than one way
Computation: perform computations; adjust the result of a computation to fit the context of a problem; identify numbers or information or operations needed to solve a problem

NETS:

Demonstrate the ability to:

Use technology tools and information resources to increase productivity, promote creativity, and facilitate academic learning.
Use content-specific tools (e.g., software, simulation, environmental robes, graphing calculators, exploratory environments, Web tools) to support learning and research.
Use technology resources to facilitate higher order and complex thinking skills, including problem solving, critical thinking, informed decision making, knowledge construction, and creativity.
Use technology to locate, evaluate, and collect information from a variety of sources.
Observe and experience the use of technology in their major field of study.

Technology-enhanced instructional strategies utilized in this module:

Technology-enriched problem-based learning

Computer-based simulations/games/role-playing

Web-based learning

Electronic portfolio development

Technology-enhanced demonstrations

Components	Brief description of module activities	Student Grouping	Materials/ Technology
Engagement	KWL Chart or Concept Map of personal information regarding divisibility, prime and composite numbers, and greatest common factor and least common multiple	Individual or whole class	Word processing
Exploration	Prior to class instruction, students visit a given interactive web site(s) and play a game or complete a task that requires using the specific content objectives. Students complete admit slip reflections on their work at the assigned site.	Individual or in pairs	Computer with internet access
Explanation	Teacher facilitates classroom instruction on objectives incorporating text materials, hands-on manipulatives, and interactive sites as applicable. Students complete learning log questions.	Whole class	Computer with internet access
Extension	Students explore additional web sites pertaining to the topic at hand.	Groups of four	Computer with internet access
Evaluation	Student completes a module summary reflecting one of the content areas covered. Summary to include comparisons of text, hands-on manipulatives and interactive educational sites to enhance learning*.	Individual	Electronic journal entries

Expected module outcomes:

The student will be able to:

Access and evaluate an elementary level interactive web site.
Demonstrate competencies in understanding divisibility, the relationship between prime and composite numbers, and finding the greatest common factor and least common multiple.
Distinguish the advantages and disadvantages of each method of delivery: text, hands-on manipulatives, and interactive educational sites.

Performance-based assessment of module outcomes:

Students will complete a module summary in an electronic journal based on comparisons of text, hands-on manipulatives, and interactive educational sites. This module summary will be used in the culminating unit activity (see Unit Overview).

Module Summary Rubric:

Excellent	Adequate / Good	Fair	Poor
Each bullet is 5 points	Each bullet is 4 points	Each bullet is 3 points	Each bullet is 2 points
Excellent description of the web activity Clearly states content objective(s) including NCTM Standards addressed Compares / contrasts site vs. text vs. manipulative (as applicable) including advantages / disadvantages of each Each question has a substantive response Posted by deadline	Adequate description of the web activity Clearly states content objective(s) Adequate compare / contrast site vs. text vs. manipulative (as applicable) Each question has an adequate response Posted by deadline	Fair description of the web activity States content objective(s) Fair compare / contrast At least two questions have adequate responses Posted by deadline	Poor description of the web activity Minimally states content objective(s) Poor compare / contrast At least one question has an adequate response Posted by deadline
Maximum Points: 25

Unit Description Modules: 1 2 3 4

Unit Description
Modules: 1 2 3 4