COURSE OF
MATHEMATICS DEPARTMENT
FEBRUARY 2007
WINEGAR
COURSE OF STUDY
BRIDGE TO GEOMETRY/GEOMETRY
PURPOSE AND
PHILOSOPHY
The Bridge to Geometry/Geometry course is designed to aid students in developing their mathematical abilities to fill in identified gaps in knowledge and complete the Geometry curriculum in a single year. Students will be planed in Bridge to Geometry by teacher recommendation. Students will be engaged in a double period, intensive class incorporating classroom experiences and a self paced computer laboratory for the entire school year. Assessment and review of previous knowledge will allow students to identify their needs while enriching experiences will provide an intensive Geometry experience. Students who are unsuccessful or who need further experience may choose to reenroll in a traditional full year Geometry course.
STUDENT OUTCOMES
Ø Major Goals
At the conclusion of this course, students will have:
v The knowledge and understanding of mathematical ideas, concepts and procedures
v The ability to solve problems within mathematics and in other subject areas
v The ability to use mathematical tools and techniques
v The ability to use mathematics in the world beyond the classroom
v The ability to use mathematics to communicate
v The ability to reason and think critically
Ø Evaluation
v To evaluate student progress, both formal and informal assessment will be used. Homework, quizzes, performance based assessment, computer lab based assessment and tests will compose the formal assessment while group work, notebooks, and technological explorations will comprise the informal assessment. Summary and review at the conclusion of each chapter will serve as an opportunity for pretest and self evaluation. Students will be provided ample opportunity to practice across a variety of learning styles.
OBJECTIVES
This course will cover basic arithmetic topics as well as Geometric topics. (NJCCC 4.2, 4.4, 4.5)
These topics will include:
Ø The Language and Logic of Geometry
Ø Parallel Lines
Ø Congruent Triangles
Ø Inequalities
Ø Quadrilaterals
Ø Similarity
Ø Right Triangles
Ø Circles
Ø Constructions
Ø Area of Plane Figures
Ø Area and Volume of Solids
Ø Coordinate Geometry
Ø Transformational Geometry
In addition review of the following topics previously taught will be embedded in the class through the Bridge Laboratory to provide a firm mathematical basis for all students:
Ø Geometric Figures and their Properties
Ø Area and the Pythagorean Theorem
Ø Probability and Statistics
Ø Volume and Surface Areas
Ø Transformations
Ø Counting Methods and Permutations
LEARNING ACTIVITIES
In order to develop mastery of stated objectives, the following may be used:
Extra practice problems
Cumulative reviews
Technology based activities
Reinforcement exercises
Transparencies
On-line applets for motion and development problems
Maintenance of a notebook and organizational material
Computer assisted instruction
On-line quizzes and exercises
Group explorations and chapter projects
Self assessments
Graphing calculator explorations
ASSESSMENT
To evaluate student progress, homework will be checked by teacher and by peers, written quizzes and chapter tests will be given, projects will be presented, notebooks will be evaluated and a final examination in June will be administered.
ENRICHMENT
There are extensive enrichment readings and instructional materials on line for students who wish to pursue the study of a related concept in greater depth.
SOFTWARE
Students will be engaged on the Bridge to Algebra (part 2 - Geometry) Software in the computer lab on a regular basis (at least 30% of class time) throughout the entire school year. This software is AI based and will allow students to work at their own pacer supplying both remedial skills and enrichment based on the student’s needs.
TEXTBOOK
Bridge to Algebra (part 2). Carnegie Learning (Book, student assignments and accompanying software) 2006.
Geometry. Pearson Prentice Hall (Book and workbook) 1993.
www.phschool.com is available to all students at all times and is keyed to the specific lessons in the Geometry text.
Additional resources are available to the teacher including Solutions Guides, Transparences, and Enrichment Resources.
www.southjerseyacademy.com
is a rich website for projects and activities that are standards and research
based and ready for presentation.
Addendum:
The 7th, 8th and 9th grade curriculums were mapped and, as a result, streamlined to free the teacher from repeatedly teaching the same concepts while running out of time for other concepts because of ordering in the textbooks. As a result of this mapping, the topics were divided into those that must be taught and those that must be reviewed/assessed. It is recommended that the review/assessment be done using performance activities rather than traditional testing.
For this course the following topics must be taught:
Bridge:
Units 3, 7, 8, 11, 13, 15
Algebra 1:
Chapters 3, 5, 6, 7, 8, 9, 4-6, 12-8, 12-9
The following topics have been taught as part of the 7th grade curricula and need only be reviewed/assessed briefly. All of these topics are presented and reviewed in their entirety in the “Bridge to Algebra” software.
Bridge:
Units 1, 2, 4, 5, 6, 9, 10, 12, 14
Geometry:
Chapters 1, 2, 4
Chapters 10 and 11 are covered as new topics in their entirety in Geometry.
It has been shown that units presented with a “hook” (introductory project or big idea) will maintain interest among students. A sample is attached. In addition, there are a tremendous number of these available on CD and on line that will be made available to the teacher. There is no need for the teacher to create their own unless that is desired.
The following are a few suggestions:
“Are You a Solution” as an introductory activity for linear equations (Bridge 13, Algebra Chapter 6)
http://www.princetonol.com/groups/iad/lessons/middle/grid-drawings.htm (Anamorphic Art) as an introduction to Transformations (Bridge 15)
“Stacking Cups” Assessment activity for Linear Equations (Bridge 13)
“Rate of Change” activity for Slope (pick and choose) Algebra Ch 6
“Construction Problems” a huge collection of real life construction problems that would be ideal as an assessment of Bridge Units 2, 4, 5