CAPFM.5.1

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Course Profile Foundations of Mathematics, Grade 9 applied, Catholic

Course Overview

Course Profiles are professional development materials designed to help teachers implement the new Grade 9 secondary school curriculum. These materials were created by writing partnerships of school boards and subject associations. The development of these resources was funded by the Ontario Ministry of Education and Training. This document reflects the views of the developers and not necessarily those of the Ministry. Permission is given to reproduce these materials for any purpose except profit. Teachers are also encouraged to amend, revise, edit, cut, paste, and otherwise adapt this material for educational purposes.

Any references in this document to particular commercial resources, learning materials, equipment, or technology reflect only the opinions of the writers of this sample Course Profile, and do not reflect any official endorsement by the Ministry of Education and Training or by the Partnership of School Boards that supported the production of the document.

©Queen’s Printer for Ontario

Acknowledgments

Lead Board

Ottawa-Carleton Catholic School Board

Sandra Bender, Manager (P1)

Sean Kelly, Manager (P2)

Department: Mathematics

Course Developer(s):

Arlene Corrigan, Renfrew County Catholic District School Board

Dominique Levac, Catholic District School Board of Easterm Ontario

Maureen Vincentine, Algonquin-Lakeshore Catholic School Board

Linda Sloan, Ottawa Carleton Catholic School Board

Carolyn Boyer, Ottawa Carleton Catholic School Board

Tom Steinke, Ottawa Carleton Catholic School Board

Len St.Clair, Catholic District School Board of Eastern Ontario

Nora Buckley, Algonquin-Lakeshore Catholic School Board

Sue Trew, Dufferin-Peel Catholic District School Board

Brian McCudden, Toronto Catholic District School Board

Margaret Sinclair, Toronto Catholic District School Board

David Kurzinger, Toronto Catholic District School Board

Paul Costa, Toronto Catholic District School Board

Lori Goodfriend, Catholic District School Board of Eastern Ontario

Catherine Rea, Ottawa Carlton Catholic School Board

Anne Delahunt, Ottawa Carlton Catholic School Board

Development Date: February/March 1999

Course Revisor(s):

Revision Date: March/April 1999.

Additional Codes:

Eastern Ontario Catholic Curriculum Cooperative

Institute for Catholic Education

Course Overview

Mathematics, Applied, Grade 9

Identifying Information:

School:

Department:

District:

Course Title: Foundations of Mathematics

Grade: 9

Course Type: Applied

Ministry Course Code: MFMIP

Credit Value: 1.0

Course Developer(s): Arlene Corrigan, Dominique Levac Maureen Vincentine, Linda Sloan, Carolyn Boyer, Tom Steinke, Len St. Clair, Nora Buckley, Sue Trew, Brian McCudden, Margaret Sinclair, David Kurzinger, Paul Costa

Development Date: February/March 1999

Course Revisor(s):

Revision Date: March/April 1999.

Description/Rationale

This course enables students to develop mathematical ideas and methods through the exploration of applications, the effective use of technology, and extended experiences with hands-on activities. Students will investigate relationships of straight lines in analytic geometry, solve problems involving the measurement of 3-dimensional objects and 2-dimensional figures, and apply key numeric and algebraic skills in problem solving. Students will also have opportunities to consolidate core skills and deepen their understanding of key mathematical concepts.

How This Course Supports the Ontario Catholic School Graduate Expectations

This course enables students to develop a confident and positive sense of self. Within the setting of a supportive and caring classroom community, the dignity and value of each student is respected and affirmed. Through their personal growth in reason, critical thinking and communication, students come to appreciate their mathematical ability as a God given gift. By sharing their abilities, students contribute to the good of others, in service to the classroom and school community.

Unit Titles (Time and Sequence)

Unit 1	Exploring Relationships	25 hours
Unit 2	Modeling Linear Relationships	35 hours
Unit 3	Exploring Relationships in Geometry	35 hours
Unit 4	Making Connections	15 hours

Unit Organization - Mathematics, Applied, Grade 9

Unit #1: Exploring Relationships

Time: 25 Hours

Description:

In this unit, students and teachers will begin to explore both linear and non-linear relationships arising from meaningful problems. Students will develop numeric and graphic and skills as needed in the context of the activity. Various forms of assessment are built into all the activities.

Ontario Catholic School Graduation Expectations: CGE 3c, 4b, 5a, 7j

Strand(s): Number Sense and Algebra, Relationships

Overall Expectations: NAV.01, NAV.02, REV.01, REV.02, REV.03.

Specific Expectations: NA1.01, NA1.02, NA1.03, NA1.04, NA1.05, NA1.06, NA2.04, NA2.05, RE1.01, RE1.02, RE1.03, RE1.04, RE1.05, RE1.06, RE1.07, RE2.01, RE2.02, RE2.04, RE2.05, RE3.01, RE3.02, RE3.03, RE3.04.

Unit #2 : Modelling Linear Relationships

Time: 35 Hours

Description:

In this unit, students and teachers will explore numerical, graphical and algebraic models (tables, graphs, equations) of linear relationships arising from meaningful problems. Students will develop numeric, graphic and algebraic skills as needed. Various forms of assessment are built into all the activities.

Ontario Catholic School Graduate Expectations: CGE 2b, 3c, 3e, 4f, 5a, 5g

Strands: Number Sense and Algebra, Relationships, Analytic Geometry

Overall Expectations: NAV.01, NAV.02, NAV.03, NAV.04, REV.01, REV.02, REV.03, AGV.01, AGV.02, AGV.03,

Specific Expectations: NA1.01, NA1.02, NA1.03, NA1.04, NA1.05, NA1.06, NA2.04, NA2.05, NA3.01, NA3.02, NA3.03, NA3.05, NA4.01, NA4.02, NA4.03, RE1.01, RE1.02, RE1.03, RE1.04, RE1.05, RE1.06, RE1.07, RE2.01, RE2.02, RE2.03, RE3.01, RE3.02, RE3.04, AG1.01, AG1.02, AG1.03, AG2.01, AG2.02, AG2.03, AG2.04, AG3.01, AG3.02, AG3.03, AG3.04, AG3.05.

Unit #3: Exploring Relationships in Geometry

Time: 35 Hours

Description:

In this unit, students and teachers will explore and model relationships in measurement and geometry numerically and graphically in the context of optimization problems. This is an extension of the study of non-linear relationships introduced in Unit 1. Students will also explore geometric relationships using dynamic geometry software.

Ontario Catholic School Graduation Expectations: GE 2b, 5a, 5b

Strand: Number Sense and Algebra, Relationships, Analytic Geometry, Measurement and Geometry Overall Expectations: NAV.02, NAV.03, REV.01, REV.02, REV.03, MGV.01, MGV.02, MGV 03.

Specific Expectations: NA2.01, NA2.02, NA2.03, NA2.04, NA2.05, NA2.06, NA3.01, NA3.02, NA3.03, NA3.04, NA3.05, NA3.06, RE1.01, RE1.02, RE1.03, RE1.04, RE1.05, RE1.06, RE1.07, RE2.01, RE2.04, RE3.02, RE3.03, RE3.04, AG3.01, MG1.01, MG1.02, MG1.03, MG1.04, MG2.01, MG2.02, MG2.03, MG2.04, MG2.05, MG3.01, MG3.02, MG3.03, MG3.04.

Unit #4: Making Connections

Time: 15 Hours

Description: In this unit, students will engage in a few, large assessment activities. These activities will capture the essence of the grade 9 course. One activity will serve as a culminating assessment task, which will be used in conjunction with a final exam as a final assessment.

Ontario Catholic School Graduation Expectations: CGE 2b, 5a, 5b.

Strand: Number Sense and Algebra, Relationships, Analytic Geometry, Measurement and Geometry

Overall Expectations: NAV.01, REV.01, REV.02, REV.03, AGV.01, AGV.02, AGV.03, MGV.01, MGV.02.

Specific Expectations: NA1.01, NA1.02, NA1.03, NA1.04, NA1.05, RE1.01, RE1.02, RE1.03, RE1.04, RE1.05, RE1.06, RE1.07, RE2.01, RE2.02, RE2.03, RE2.04, RE2.05, RE3.02, RE3.03, RE3.04, AG1.01, AG1.02, AG1.03, AG2.01, AG2.02, AG2.03, AG2.04, AG3.01, AG3.02, AG3.03, AG3.04, AG3.05, AG3.06, MG1.01, MG1.02, MG1.03, MG1.04, MG2.01, MG2.03, MG2.04, MG2.05.

Course Notes

“It is expected that in developing detailed courses of study from this document, teachers will weave together related expectations from different strands ...” (page 5, The Ontario Curriculum, Grades 9 and 10, Mathematics, 1999). This course profile has been constructed with a common theme of relationships that connects all the units. Below is a chart which displays the “weaving” we have done:

	Number Sense and Algebra	Relationships	Analytic Geometry	Measurement and Geometry
1. Exploring Relationships	Ö	Ö
2. Exploring Linear Relationships	Ö	Ö	Ö
3. Exploring Relationships in Geometry	Ö	Ö		Ö
4. Making Connections	Ö	Ö	Ö	Ö

“Skill acquisition is an important part of the program: skills are embedded in the contexts offered by various topics in the mathematics program and should be introduced as they are needed.” (page 4, The Ontario Curriculum, Grades 9 and 10, Mathematics, 1999). We have endeavoured to ensure that skill development is truly embedded in the activities we have designed.

“The philosophy of the Grade 9 courses is consistent with that of the elementary program and facilitates a seamless transition from elementary school, because it reflects the belief that students learn mathematics effectively when they have initial opportunities to explore through hands-on experiences, followed by careful guidance into an understanding of the abstract mathematics involved.” (page 4, The Ontario Curriculum, Grades 9 and 10, Mathematics, 1999). All the activities give students initial opportunities to explore, through hands-on experiences followed by a thoughtful journey through various, appropriate representations. The bridge to the algebraic representation is one that must by crossed carefully to ensure all students develop a true understanding of this abstract representation. The activities in unit 2 allow students to initially explore relationships numerically and graphically. The linear regression capabilities of graphing calculators provide a bridge for all students to develop an initial algebraic model. Dynamic Geometry Software is a powerful tool to allow all students to explore the connection between graphical and algebraic models.

Many activities require the use of technology: “The development of sophisticated yet easily used calculators and computers is changing the role of procedure and technique in mathematics. Operations that have been an essential part of a procedures-focused curriculum for decades can now be accomplished quickly and effectively using technology, so that students can now solve problems that were to time consuming to attempt, and can focus underlying concepts. This curriculum integrates appropriate technologies into the learning and doing of mathematics ...” (page 3, The Ontario Curriculum, Grades 9 and 10, Mathematics, 1999).

In the area of assessment it is essential that examples of student work be provided to paint a clearer picture of the meanings of the levels and their descriptors for students, parents, and teachers.

Mathematics, Applied, Grade 9

Strategies and Resources

Teaching and Learning Strategies

Teaching and learning strategies will include the following:

Hypothesize - students will formulate hypotheses associated with relationships

Explore/Investigate- through hands-on investigations of relationships

Model/Formulate- students develop numeric, graphic, algebraic and geometric models for exploring relationships, dependencies and constraints

Transform/Manipulate- students will develop numeric, graphic and algebraic skills as needed in the context of their investigations to allow them to move within and between representations

Infer/Conclude - students will re-evaluate their hypotheses in light of their learning and make inferences to extend their learning

Communicate- students, individually and in groups, orally and in writing, communicate the findings of their investigations by defending their mathematical models and explaining their reasoning

Assessment Strategies

The assessment plan will include the following:

Personal Communication

• journals

• self/peer assessment

• student-teacher conferences

Paper and Pencil

• tasks

• unit tests

• final exam

• reports

Observation

• formal and informal

Performance Assessment

• oral presentations

• culminating assessment task

• written reports

Assessment tools will include:

• checklists

• rubrics

Main Resources

The following resources are required to support teaching and learning:

Textbooks

Student Textbook

NCTM Standards

Videotapes

Life By the Numbers, PBS, 1998

Computer Software

Spreadsheet and Word processor (Corel Suite 8, Microsoft Office)

Dynamic Geometry Software (Cabri, Geometer’s SketchPad, TI92)

Graphing Software

(Graphmatica or Zap-A-Graph)

Websites

http://www.ti.com/calc/docs

http://www.statcan.ca

http://forum.swarthmore.edu/

Technology and Manipulatives

Graphing Calculators (TI82/83/83Plus),

Data Collection Devices

(CBR, CBL and scientific probes)

Manipulatives

Mathematics, Applied, Grade 9

Evaluation of Student Achievement

Knowledge/Skill Category Weighting

Final Examination

Focus on:

• Knowledge/Understanding

• Application/Making Connections

Final Assignment: Culminating Assessment Task

Focus on:

• Thinking/Inquiry/Problem Solving

• Communication

Written Reports

Focus on:

• Thinking/Inquiry/Problem Solving

• Communication

Oral Presentations

Focus on:

• Communication

Paper and Pencil Tasks

Focus on:

• Knowledge/Understanding

• Application/Making Connections

Unit Tests

Focus on:

• Knowledge/Understanding

• Application/Making Connections

Course Grade Weighting

Final Examination

Culminating Assessment Task

Written Reports

Oral Presentations

Paper and Pencil Tasks Unit Tests

Course Grade

___

100

Coded Expectations: Foundations of Mathematics, Applied Grade 9

Number Sense and Algebra

Overall Expectations

NAV.01 consolidate numerical skills by using them in a variety of contexts throughout the course;

NAV.02 demonstrate understanding of the three basic exponent rules and apply them to simplify expressions;

NAV.03 manipulate first-degree polynomial expressions to solve first-degree equations;

NAV.04 solve problems, using the strategy of algebraic modelling.

Specific Expectations

Consolidating Numerical Skills

NA1.01 determine strategies for mental mathematics and estimation and apply these strategies throughout the course;

NA1.02 demonstrate facility in operations with integers, as necessary to support other topics of the course (e.g., polynomials, equations, analytic geometry);

NA1.03 demonstrate facility in operations with percent, ratio, rate and rational numbers, as necessary to support other topics of the course (e.g. analytical geometry, measurement);

NA1.04 use a specific calculator effectively for applications that arise throughout the course;

NA1.05 judge the reasonableness of answers to problems by considering likely results within the situation described in the problem;

NA1.06 judge the reasonableness of answers produced by a calculator, a computer, or pencil and paper, using mental mathematics and estimation.

Operating Elements

NA2.01 elevate numerical expressions involving natural-number exponents with rational-number bases;

NA2.02 substitute into and evaluate algebraic expressions involving exponents, to support other topics of the course (e.g., measurement, analytical geometry);

NA2.03 determine the meaning of negative exponents and of zero as an exponent from activities involving graphing, using technology, and from activities involving patterning;

NA2.04 represent very large and very small numbers, using scientific notation;

NA2.05 enter and interpret exponential notation on a scientific calculator, as necessary in calculations involving very large and very small numbers;

NA2.06 determine, from the examination of patterns, the exponent rules for multiplying and dividing monomia