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Math 1: Geometry
 
Course Description
    

This on-line course is designed to help teachers with geometry content required in the WV Math I curriculum. Participants will review mathematical content, practice instructional strategies and use some lessons from the Teach21 units. Participants will investigate properties and theorems involving congruent figures to deepen and extend their understanding of geometric content. The Mathematical Practices are embedded in the activities of each session. After completion of this course, participants should have activities and additional resources needed to properly teach the geometry units of Math I.

 

 
Course Syllabus
    

 

Overview

This on-line course is designed to help teachers with geometry content required in the WV Math I curriculum. Participants will review mathematical content, practice instructional strategies and use some lessons from the Teach21 units. Participants will investigate properties and theorems involving congruent figures to deepen and extend their understanding of geometric content. The Mathematical Practices are embedded in the activities of each session. After completion of this course, participants should have activities and additional resources needed to properly teach the geometry units of Math I.

By the end of this course, participants will:
  • know precise definitions of angle, circle, perpendicular line, parallel line and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
  • investigate strategies to develop vocabulary.
  • make use of the definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.
  • represent transformations in the plane and describe transformations as functions that take points in the plane as inputs and give other points as outputs.
  • compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
  • describe the rotations and reflections that carry a figure onto itself.
  • draw the transformed figure using various tools, given a geometric figure and a rotation, reflection or translation.
  • specify a sequence of transformations that will carry a given figure onto another.
  • use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure.
  • use the definition of congruence in terms of rigid motions to show that two triangles are congruent.
  • explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
  • make formal geometric constructions with a variety of tools and methods.
  • construct an equilateral triangle, a square and a regular hexagon inscribed in a circle.
  • use coordinates to prove simple geometric theorems algebraically.
  • prove the slope criteria for parallel and perpendicular lines and use the criteria to solve geometric problems.
  • use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
  • showcase and discuss student work from selected course activities.
  • create a student assessment for Math I Geometry Unit.
Course Organization
This course includes several different activity components, all of which are described below. During each session, you will participate in a unique collection of these activity components, depending on the particular focus of that session.

Read
When you see this icon you will be reading relevant articles, resources, and instructional materials that will help inform your online course development process.

Activities
When you see this icon you will be completing activity-based curriculum and inputting various components of your course content into course project.

Discuss
When you see this icon you will be using the online discussion board to share ideas, resources, and thoughtful conversation with your fellow course participants and facilitator.
Prerequisites

This course is designed for High School Math 1 teachers.

High School Mathematics I Course Description (graphic)
The fundamental purpose of Mathematics I is to formalize and extend the mathematics that students learned in the middle grades. The critical areas, organized into units, deepen and extend understanding of linear relationships, in part by contrasting them with exponential phenomena, and in part by applying linear models to data that exhibit a linear trend. Mathematics 1 uses properties and theorems involving congruent figures to deepen and extend understanding of geometric knowledge from prior grades. The final unit in the course ties together the algebraic and geometric ideas studied. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

Although not a requirement, high speed Internet access definitely enhances the online experience. Participants should be proficient with using email, browsing the Internet and navigating through computer files. Access to Microsoft Office is recommended. Participants who do not have Microsoft Office should click here for some available options.
Prior to Session One course participants at to secure:
1. a WVDE WebTop account.
2. a SAS Curriculum Pathways teacher account.
3. the SAS Curriculum Pathways school account for students.
4. download GeoGebra software from http://www.geogebra.org/cms/download.
5. a scanner for scanning course assignments to be uploaded to the course drop box.

Format and Requirements
This workshop is divided into six one-week sessions which each include readings, activities, and an online discussion among workshop participants. The time necessary to complete each session is estimated to be seven to eight hours.

The outline for the workshop is as follows:
Session One Introduction to Geometry
Session Two Transformations
Session Three Congruence and Rigid Motion
Session Four Construction
Session Five Coordinate Geometry
Session Six Connect, Reflect and Assess
Session 1: Introduction to Geometry
The activities of this session will help participants formalize and extend the geometry that students learned in the middle grades. Participants will investigate strategies for introducing the precise vocabulary of geometry to their students.

Session 2: Transformations
Participants will experiment with transformations in the plane.

Session Three: Congruence and Rigid Motion
Participants will develop the properties of transformations as rigid motions, investigate conjectures about triangle congruencies and define congruence in terms of rigid motion.

Session Four: Construction
Participants will make and verify formal geometric constructions using a variety of tools and methods beginning with paper folding and building to the use of the free geometric software, GeoGebra.

Session 5: Coordinate Geometry
Participants will build on their students' knowledge of the Pythagorean Theorem and use coordinate geometry to find perimeter and area and justify geometric relationships.

Session Six: Connect, Reflect and Assess
Participants will make connections among the different Math I credential courses and sessions within those courses with the development of a Math 1 portfolio and comprehensive student assessment/solution key with work.

Assessment

Workshop participants will complete an orientation six weekly workshop sessions that include readings, activities, and online discussions. There will be a pre-workshop survey and a post-workshop survey. In addition, participants will incrementally develop a Math I portfolio components throughout the duration of the course. The time for completing each session is estimated to be seven to eight hours per session.

Math 1 Portfolio:
Course participants will choose three activities to use in their classroom from those suggested throughout this Math I Geometry course. The activities must be from three different sessions throughout Math I Geometry. Portfolio items are to be selected from the following course activities:

Session Two: Activity #2-Transformational Golf Activity

Session Two: Activity #6-Algebraic Transformations Task

Session Four: Activity #3: Logo Construction Activity and Self-Assessment

Session Four: Activity 4-Transforming Constructions

Session Five: Activity #1 Task #2: Let's Prove It Challenge

Session Five: Activity #2: Going Round in Circles Question Handout

 

Complete the following for each activity to be submitted to your portfolio:

  • Submit two samples of your students’ work that show different levels of understanding.
  • Explain why you selected each sample of student work and describe the level of understanding demonstrated by each student.
  • Discuss how this particular lesson or activity has helped develop your students’ understanding of the mathematics involved.

A total of six student samples are to be included in your portfolio for Math I Geometry.
 

Culminating Assessment:
Course participants will create a Math 1 Geometry culminating assessment for students along with a solution key, complete with all work. This assessment may be used with Math I students to evaluate their conceptual understanding of the Next Generation CSO’s that were targeted in this course. Categories and indicators from the Student Assessment Rubric are to be used to guide the development of the Math 1 Statistics culminating assessment for students.

Self-Assessment of the Culminating Assessment for Students:
Course participants will complete a self-assessment of their Math 1 Geometry student assessment using the Student Assessment Rubric.

Discussion Participation
Participants will be evaluated on the frequency and quality of their participation in the discussion forum. Participants are required to post a minimum of one substantial original posting each session reflecting on the question for that session. They are to read all original postings made by the other workshop participants and reply thoughtfully to at least two of them per session. Participants’ original postings will be evaluated on their relevance, demonstrated understanding of workshop concepts, examples cited, and overall quality. Postings that respond to other participants will be evaluated on relevance, degree to which they extend the discussion, and tone.

Certificate of Completion
Upon successful completion of this course, Math 1 Statistics, and the successful panel portfolio review participants will receive a Certificate of Completion documenting successful completion of the course requirements.
Non-Degree Graduate Credit Information

Participants in this course are eligible to receive non-degree graduate credits from either West Virginia University, Marshall University or Concord University. Credits will be awarded at the end of the semester in which the course occurs. Additional information is available on the course News/Welcome Page.

Content and Technology Standards

This workshop, Math 1 Functions, will help participants meet the ISTE Educational Technology Standards and Performance Indicators for All Teachers (http://edtechleaders.org/documents/NETSAdminTeachers.pdf), especially Standards II, III, IV, and V. For more information about Technology Integration visit: http://www.iste.org

In addition, participants will identify specific WV Content Standards and Objectives (http://wvde.state.wv.us/csos/) as they engage in course content.

About this Course

This workshop was developed for the West Virginia Department of Education (http://wvde.state.wv.us). Original design (before format modifications) by EdTech Leaders Online (http://www.edtechleaders.org), a project of Education Development Center, Inc, © 2007. All rights reserved.