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Course Profile Mathematics, Locally
Developed, Grade 10, Catholic
Course Overview
Course Profiles are professional development materials designed to help teachers implement the new Grade 10 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. 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 or by the Partnership of School Boards that supported the production of the document.
© Queen’s Printer for Ontario, 2000
Catholic District School Board Writing Teams –
Lead Board
Toronto Catholic District School Board
Project Manager
Wendy Schmidt
Course Profile Writing Team
Cathy Bordignon (Lead Writer), Toronto Catholic District School Board
Julian D’Angela, Bishop Ryan C.S.S. Hamilton Wentworth Catholic District School Board
Gloria Houghton, St. Ignatius High School, Thunder Bay Catholic District School Board
Ruth Hyndman, St. Joseph Scollard Hall, Nipissing Perry Sound Catholic District School Board
Margaret Russo, Madonna C.S.S., Toronto Catholic District School Board
Reviewers
Margaret Sinclair, (Lead Reviewer), Dante Alighieri C.S.S., Toronto Catholic District School Board
Dr. Larry Trafford, Curriculum Branch, OECTA
Dorothy Turner, Sagonaska School
Joanne Shields, W.Ross Macdonald School
Cathy Brown/Joy Vanderzand, The Ernest C. Drury School
Course Overview
Locally Developed Mathematics, Grade 10
This course enables students to consolidate their understanding of key mathematical concepts and to expand their mathematical knowledge through hands-on activities in problem-solving situations. Students will solve problems using a variety of methods for calculation; consolidate the meaning and use of proportionality through applications; use patterning strategies to solve simple problems; collect and analyse data that will result in linear relationships; investigate measurement aspects of two-dimensional figures and three-dimensional objects; and explore geometric relationships. This course prepares students for the Grade 11 Mathematics course, Mathematics for Everyday Life – Workplace Preparation.
This course enables students to develop their mathematical abilities and to gain confidence in using mathematical skills in everyday life. Students are offered an opportunity to demonstrate a confident and positive sense of self in shared activities in the Catholic faith community, while acknowledging and affirming the contribution of individual students. Group activities enable students to demonstrate sensitivity and consideration towards others through mutual co-operation and respect, as contributing members of the Catholic faith community. The explorations allow students to see the beauty and order in God’s creation of the world around us.
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Unit 1 |
Making Sense of Numbers |
27 hours |
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Unit 2 |
Angular and Linear Relationships |
25 hours |
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Unit 3 |
Explorations in Two Dimensions |
28 hours |
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Unit 4 |
Explorations in Three Dimensions |
15 hours |
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Unit 5 |
Summative Assessment |
15 hours |
Time: 27 hours
Description
In this unit, students use investigations in the context of fund raising activities to consolidate numeration skills garnered from the Grade 9 course. Students complete activities integrating the relationships between:
· decimals, fractions, percent, rates and ratios;
· the order of operations;
· estimation and mental computation;
· solving problems related to the design of an experiment.
Strand(s) and Expectations
Ontario Catholic School Graduate Expectations: CGE 2a, 2b, 2c, 2d, 3c, 4a, 4b, 4f, 5a, 5g.
Strand(s): Number Sense, Patterns and Relationships
Overall Expectations: NSV.01, NSV.02, PRV.02.
Specific Expectations: NS1.01, NS1.02, NS1.03, NS1.04, NS1.05, NS1.06, NS1.07, NS1.08, NS2.01, NS2.02, NS2.03, NS2.06, PR2.01, PR2.02, PR2.06.
Time: 25 hours
Description
Numerical, geometrical, and logical patterns abound in the world around us. In this unit, students investigate a variety of patterns that determine mathematical relationships. Using appropriate tools and/or technology, they:
· describe simple geometric patterns;
· determine properties of similar triangles and of parallel lines;
· collect and analyse data to solve simple properties;
· explain the procedures for extending patterns;
· explain the procedures and findings of an experiment.
Strand(s) and Expectations
Ontario Catholic School Graduate Expectations: CGE 2b, 2c, 3c, 4f, 5a, 5e, 5g.
Strand(s): Number Sense, Patterns and Relationships, Measurement and Geometry
Overall Expectations: NSV.02, PRV.01, PRV.02, MGV.01, MGV.02.
Specific Expectations: NS2.04, PR1.01, PR1.02, PR1.03, PR1.04, PR1.05, PR2.03, PR2.04, PR.2.05, PR2.06, MG2.02, MG4.01, MG4.04.
Time: 28 hours
Description
In this unit, students explore the properties of two-dimensional figures in the context of home design. These investigations allow students to:
· reinforce the meanings of key terms associated with angles and triangles;
· calculate the perimeter and area of simple and composite figures;
· investigate the optimal values of measurements;
· use the Pythagorean theorem in practical applications.
Strand(s) and Expectations
Ontario Catholic School Graduate Expectations: CGE 2c, 2d, 3c, 3e, 4a, 4f, 5a, 7i.
Strand(s): Number Sense, Patterns and Relationships, Measurement and Geometry
Overall Expectations: NSV.01, NSV.02, PRV.01, MGV.01, MGV.02, MGV.03, MGV.04.
Specific Expectations: NS1.01, NS1.02, NS1.04, NS1.05, NS1.07, NS1.08, NS2.20, NS2.03, NS2.05, NS2.06, PR1.03, PR2.01, MG1.01, MG1.02, MG1.03, MG2.01, MG 2.02, MG2.03, MG2.04, MG2.05, MG2.06, MG3.01, ME3.02, MG3.03, MG4.01, MG4.02, MG4.03, MG 4.05, MG4.06.
Time: 15 hours
Description
In this unit, students extend their comprehension of geometrical and measurement principles through concrete activities dealing with three-dimensional objects. In the course of investigations, students:
· construct triangular prisms, rectangular prisms, and cubes from their nets;
· solve problems using the formulas for the surface area and volume of triangular prisms, rectangular prisms, cubes, and cylinders;
· solve simple problems involving optimal values.
Strand(s) and Expectations
Ontario Catholic School Graduate Expectations: CGE: 2a, 2c, 3b, 3c, 4a, 4f, 5a, 7i.
Strand(s): Number Sense, Measurement and Geometry
Overall Expectations: NSV.01, MGV.01, MGV.02, MGV.03.
Specific Expectations: NS1.02, NS1.04, NS1.07, NS1.08, NS2.05, NS2.06, MG1.01, MG1.02, MG1.03, MG1.04, MG1.05, MG1.06, MG2.03, MG2.04, MG2.06, MG4.02, MG4.03, MG4.06.
Time: 15 hours
Description
The course concludes with a summative assessment unit consisting of a series of activities and a formal examination or cumulative test. Students will display their knowledge in oral, written, and concrete form through activities that are based on the learning expectations of the course.
Strand(s) and Expectations
Ontario Catholic School Graduate Expectations: CGE: 2b, 2e, 3b, 3c, 4b, 4e, 4f, 5g.
Strand(s): Number Sense, Patterns and Relationships, Measurement and Geometry
Overall Expectations: NSV.01, NSV.02,
PRV.01, PRV.02, MGV.01, MGV.02, MGV.03, MGV.04.
Specific Expectations: NS1.01, NS1.02, NS1.03, NS1.04, NS1.05, NS1.06, NS1.07, NS1.08, NS2.01, NS2.02, NS2.03, NS2.04, NS2.05, NS2.06, PR1.01, PR1.02, PR1.03, PR1.04, PR1.05, PR2.01, PR2.02, PR2.03, PR2.04, PR2.05, PR2.06, MG1.01, MG1.02, MG1.03, MG1.04, MG1.05, MG1.06, MG2.01, MG2.02, MG2.03, MG2.04, MG2.06, MG3.01, MG3.02, MG3.03, MG4.01, MG4.02, MG4.03, MG4.04, MG4.05, MG4.06.
This course has been developed to enable students to consolidate and extend basic mathematical concepts. Many skills are revisited throughout the course to ensure that students attain mastery of the expectations. Appropriate technology and concrete materials are utilized as aids to learning and to provide exposure to related computer skills. Conceptual development is embedded in rich contextual situations to encourage students to attain success and interest in mathematics.
The diversity in student’s mathematical knowledge and learning styles necessitates a variety of teaching strategies. These include:
· whole-class, small group and individual instruction;
· direct instructional presentations and student investigations;
· the use of technological tools;
· suggestions to assist students’ organizational skills;
· modifications to suggested timelines;
· setting skill development in rich, contextual problems;
· integrating literacy development within mathematical investigations;
· segmenting tasks or instructions into smaller components;
· the use of modifications, accommodations, and extensions to the suggested activities.
The student’s Individual Education Plan (IEP) serves as a valuable resource of the learning characteristics of individual students that may necessitate accommodations. Teachers should work in consultation with other teachers, and parents, to accommodate students as they work through the activities in order to achieve the expectations described in the IEP. Suggestions for accommodations include the following.
· Prepared notes should be made available for students who have difficulty taking notes.
· Worksheets may be modified for learning disabled students to allow more space for work.
· Peer tutors or educational assistants may provide support in breaking down the steps required for completing various activities.
· Peer tutors and assistants should circulate among identified students to ensure understanding of concepts.
· Additional time should be permitted for identified students to complete their tasks.
· Individual assistance may be required to identify specific terms or procedures for blind, low vision, deaf and hard of hearing students.
· Charts should be available in Braille or large print for students who are blind or with low vision.
· Computers should be made accessible for the use of blind, low vision, deaf and hard of hearing individuals.
· Blind and low vision students should be provided with tactile grid paper or paper with larger grid lines.
· Tactile aids would assist students with low vision in distinguishing among shapes and in learning the appropriate terms for architectural features.
· Learning disabled, deaf and hard of hearing and blind and low vision, students may require assistance in organizing and structuring their language in the technical manual. The students may prefer to access a word processing program and computer to facilitate the detection of grammatical and spelling errors.
· Concrete manipulatives would assist blind or low vision students in understanding and completing activities.
· Opportunities for enrichment should occur on a regular basis.
Resources to support anti-discrimination education, equity/social justice issues, career goals/cooperative education, community partnerships and faith development also support many of the Ontario Secondary School Policies as well as the Ontario Catholic School Graduate Expectations. The Ontario Secondary Schools, Grades 9 to 12: Program and Diploma Requirements, 1999 maintains that all students are entitled to the opportunity to succeed. Accommodations are therefore recommended to assist individual students in meeting curriculum expectations.
Due to the importance of career awareness, opportunities for providing information about the mathematical concepts related to various careers, should be incorporated throughout the course. Teachers may thus find Career Exploration Activities (Choices Into Action) and Guidance and Career Education Program Policy for Ontario Elementary And Secondary Schools, 1999.) informative. Assessment and evaluation strategies have been designed in compliance with Program Planning and Assessment, 1999.
The curriculum in this course has been designed to reinforce key mathematical concepts from The Ontario Curriculum Grades 1-8 and to develop concepts from The Ontario Curriculum Grades 9 and 10.
In the realm of faith development, teachers may refer to Catholicity Across The Curriculum (Ontario Catholic School Trustees’ Association), Blueprints (Catholic Curriculum Cooperative - Central Region),
This Moment of Promise (Ontario Conference of Catholic Bishops) and Educating the Soul.
Teachers may evaluate this course through a variety of methods. Assessment and evaluation of student achievement should be conducted in tandem with critical reflection on the teacher’s method of instruction and curriculum materials. Evaluation strategies presented in this profile include diverse suggestions for peer and self evaluation. Both formative and summative methods should be invoked. As students are required to meet expectations by the end of the course, information from formative assessment may be used to remediate deficiencies. Teachers are encouraged to network with school-based and external colleagues to share ideas for course improvement. The community (local school and business) may provide instructive suggestions on aspects of this mathematics course.
Strategies and Resources may be summarized as:
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Instructional Strategies Conferencing and Interviewing · Student-to-teacher discussion · Student-to-student discussion Presentations (Student/Teacher) · visual, written, video, oral · construction of models · use of technology · use of manipulatives Application · investigations and discovery activities · field trips · use of technology · use of models and manipulatives · whole class, small group, and individual activities Brainstorming · teacher/student initiated · used for introductory, developmental and summative discussion · hypothesizing steps to problems Co-operative Activities · group learning followed by group sharing · used to develop communication skills · used to assist peers · method of strengthening students’ skills while compensating for difficulties |
Assessment Strategies Personal
Communication · on-going feedback · journals · self and/or peer assessment · student/teacher conference · report cards · parent-teacher conferences · teacher-advisor conference Paper and Pencil Tasks · quizzes · diagnostic tests · unit tests · daily tasks · summative evaluation Technology/Manipulatives · competency on assigned tasks Teacher observations · informal/formal Performance Assessment · presentation (oral, written, model construction) · assigned tasks Assessment Tools · rubrics · peer/teacher conferences · checklists · marking schemes · rating scales · communication and application inventory · learning skills inventory · reflections, self-assessments · observation recording sheet · anecdotal comments |
Math Resources The following resources will support teaching and learning: Geoboards Geometer’s SketchPad™ Graphics Calculator: TI-82, TI-83, TI-83 Plus Interlocking cubes Pattern blocks Spreadsheet software Three-dimensional geometric solids Two-dimensional geometric figures Textbooks and reference materials as outlined in a subsequent section. Mathematics Profiles Essential Mathematics 9 Applied
Mathematics 9 Academic Mathematics 9 Applied Mathematics 10 Academic
Mathematics 10 |
The primary purpose of assessment and evaluation is to improve student learning. In order to ensure that valid, reliable, and equitable assessment and evaluation tools are used, teachers ensure that their methods:
· address both what the students learn and how well they learn;
· are based on categories and the descriptors in the achievement chart;
· are varied in nature, administered over a period of time, and designed to provide opportunities for students to demonstrate the full range of their learning;
· are appropriate for both the learning activities used and the purposes of instruction;
· reflect the needs and experiences of the students;
· accommodate the needs of exceptional students, consistent with the strategies outlined in the Individual Education Plans;
· promote students’ ability to assess their own learning and to set specific goals;
· include the use of samples of students’ work providing evidence of achievement;
· are communicated clearly to students and parents at appropriate points throughout the course.
The following table indicates a variety of strategies for evaluating students.
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A. On-going Assessment and Evaluation Knowledge and understanding assessed
by: · Tests · Quizzes · Interviews/Conferences · Presentations (oral, written) · Daily tasks and activities Thinking, inquiry and problem solving
assessed by: · Presentations (oral, written) · Portfolio · Projects · Journals · Observation · Daily tasks and activities · Tests · Performance Tasks Communication assessed by: · Presentations (oral, written) · Daily tasks and activities · Co-operative activities · Self/peer evaluation · Journals, learning logs · Portfolio · Tests · Performance Tasks Application and making connections
assessed by: · Presentations (oral, written) · Portfolio · Projects · Daily tasks and activities · Tests · Observations |
B. Final Evaluation · Final project 30% (written and/or application, optional final exam) · Tests/unit projects/summative assessments 25% · Quizzes 10% · Portfolio/journal/Co-operative activities 20% · Performance Assessments 15% Over the course of the year, the
evaluation tools listed above must include a balance of all four of the
knowledge and skills categories: · Knowledge and Understanding · Thinking, Inquiry and Problem Solving · Communication · Application and Making Connections |
ClarisWorks (spreadsheet)
Microsoft Works (spreadsheet)
Corel WordPerfect Suite (spreadsheet)
The Geometer’s Sketchpad™ (dynamic geometry software)
Zap-a-Graph (graphing software)
Math Trek (skills and concept development)
Internet sites for Canadian
banking establishments
http://www.bmo.com/
http://www.canadatrust.com/
http://www.cibc.com/
http://www.mortgagestore.com/laurent/eng_page_2.html/
http://www.royalbank.com/
http://www.scotiabank.ca/
http://www.tdbank.ca/index.html/
Internet sites related to travel and distances such as:
http://www.canadiandriver.com/testdrives/
http://maps.excite.com/address/
http://www.freetrip.com/
http://www.transontario.com./
http://www.transontario.com/chart.html/
Internet sites related to transportation such as:
http://aircanada.ca/
http://airontario.com/
http://www.greyhound.ca/
http://www.viarail.ca/
Internet sites for Mathematics
http://archives.math.utk.edu/
Links to teaching materials and software; searchable database
http://forum.swarthmore.edu/
Provides resources organized by mathematics subject area (K-12 and advanced);
key issues in education including assessment issues
http://www.learner.org/
Supplies information on reform initiatives including trends in mathematics
education
http://www.mathgoodies.com/
Links to interactive mathematics lessons, activities, worksheets, and puzzles
http://www.mth.msu.edu/cmp/
Presents teaching materials and suggestions for assessment
Adomeit, J. et al. The Learning Equation Ontario Mathematics 7 Student Refresher, ITP Nelson, 1999.
Adomeit, J. et al. The Learning Equation Ontario Mathematics 7 Teacher’s Manual, ITP Nelson, 1999.
Alexander, R., et al. Minds on Math 8. Addison-Wesley, 1996.
Alexander, R., et al. Minds on Math 9. Addison-Wesley, 1994.
Alexander, R., B. Canton, P. Harrison, R. McLeish, N. Nielson, and M. Sinclair. Mathematics 9. Addison- Wesley, 1999.
Allison, P., et al. The Learning Equation Mathematics 9 Student Refresher, ITP Nelson, 1998.
Bennett, B., et al. Cooperative Learning. Toronto, ON: Educational Connections, 1991.
Bourman, A. 61 Cooperative Learning Activities. Portland, ME: J. Weston Walch, 1989.
Elchuck, L. et al. Interactions 8. Scarborough, ON. Prentice Hall Ginn Canada, 1996.
Flewelling, G., E.G. Carli, and J.S. Telfer. Making Mathematics 9. Gage, 1993.
Hope, et al. Interactions 9 Blackline Masters, Scarborough, ON: Prentice Hall Ginn Canada, 1997.
Jasmine, J. Portfolio Planner. Huntington Beach, CA: Teacher Created Materials, Inc., 1995.
Kelly, B. Alexander, and P. Atkinson. Mathematics 9. Addison-Wesley, 1987.
Knill, G., R. Baxter, D. Dottori, G. Fawcett, M.L. Forest, M. Hamilton, S. Pasko, H. Traini, and M. Webb. Mathpower 9, McGraw-Hill Ryerson, 1999.
Lambdin, D., P.E. Kehle, and Preston, R.V. (Eds.). Emphasis on Assessment. Readings from NCTM’s School-Based Journals. NCTM, 1996.
Lunney, J., B. Rae-Dion, B. Tuck, and Walters. Math Sense Book 1. Nelson Canada, 1991.
Montesanto, R. and D. Zimmer. Numbers and Patterns. D.C. Heath Canada Ltd., 1995.
Newton, D. Basic Occupational Mathematics. J. Weston Walch, 1990.
Spikell, M.A. Teaching Mathematics with Manipulatives: A Resource of Activities for the K-12 Teacher. Boston. Allyn & Bacon, 1993.
Woodward, E. and T. Hamel. Visualized Geometry – A Van Hiele Level Approach. J. Weston Walch, 1990.
Zaslavsky, C. The Multicultural Math Classroom Bringing in the World. Portsmouth, NH. Heinemann, 1996.
D. Zimmer, C, Kirkpatrick, R. Montesanto, K. Farentino, and J. Youngberg. Mathematics 9, ITP Nelson, 1999.
Coded Expectations, Locally Developed Mathematics, Grade 10 - Catholic
NSV.01
– use a variety of methods for calculation when solving problems (e.g., mental mathematics or estimation, calculator, paper and pencil computational method) and apply the method effectively;
NSV.02
– consolidate the meaning and use of proportionality through applications drawn from student experiences and broader contexts.
Applying Calculation Methods Effectively
NS1.01
– use paper and pencil computational methods effectively to evaluate expressions involving fractions decimals, and exponents as they arise in problems through out the course;
NS1.02
– use a scientific calculator effectively to evaluate expressions involving fractions, decimals, percent, exponents and square roots, as they arise in problems throughout the course;
NS1.03
– evaluate expressions involving the rules of operations, by hand and by using calculators;
NS1.04
– use estimation and mental computation to approximate and/or calculate answers to numerical problems as they arise throughout the course;
NS1.05
– apply percents in solving problems (involving aspects such as: discounts, sales tax, commissions, interest, and ratios);
NS1.06
– solve problems involving fractions and decimals using appropriate strategies and calculation methods;
NS1.07
– judge the reasonableness of answers to problems by considering likely results;
NS1.08
– judge the reasonableness of answers produced by a calculator or computer, using mental mathematics and estimation.
Consolidating the Meaning and Use of Proportionality
NS2.01
– demonstrate an understanding of the relationships between decimals, percent, rates and ratios;
NS2.02
– demonstrate an understanding of, and apply unit rate in, problem solving situations;
NS2.03
– solve problems involving ratio, proportion, and scale drawn from familiar applications;
NS2.04
– determine some properties of similar triangles, through investigations using appropriate technology (e.g., dynamic geometry software and/or concrete materials);
NS2.05
– solve problems involving scale, proportionality, and similar figures drawn from familiar applications (e.g., scaling down the dimensions of a baseball diamond for T-ball, building models in construction projects);
NS2.06
– communicate solutions to problems involving rates, proportion, and scale and the results of these investigations using appropriate terminology, symbols, and form.
PRV.01
– use patterning strategies to solve simple problems that arise in activities throughout the course;
PRV.02
– collect and analyse data that will result in linear relationships.
Using Patterning Strategies to Solve Simple Problems
PR1.01
– describe simple number patterns using language in oral and/or written form;
PR1.02
– describe simple geometric patterns using language in oral and/or written form;
PR1.03
– identify and extend simple patterns within problem solving situations;
PR1.04
– use the concept of a variable to write simple algebraic equations to describe a pattern;
PR1.05
– present solutions to patterning problems and explain the thinking behind the solutions.
Collecting and Analysing Data to Solve Simple Problems
PR2.01
– formulate an hypothesis about a relationship between two variables and express the relationship in words and/or symbols;
PR2.02
– collect data using appropriate equipment and/or technology (e.g., measuring tools, graphing calculators, scientific probes);
PR2.03
– organize, display, and analyse data, using appropriate techniques and technology (e.g., graphing calculators, spreadsheets);
PR2.04
– describe trends and relationships in data and compare them to the original hypothesis (e.g., Are the data scattered or do they cluster around the shape of a straight line? What does it mean if the data cluster around a straight line? Can a straight line be used to make predictions? Identify any outlying data points and provide explanations for them. Is the outcome of the experiment consistent with the original hypothesis? Why or why not?);
PR2.05
– explain the procedure for the findings of an experiment in an organized manner;
PR2.06
– solve problems related to the design or the findings of an experiment (e.g., Repeat the experiment under different conditions. Will the results be the same? Why or Why not?).
MGV.01
– solve problems involving the measurement of two-dimensional figures and three-dimensional objects;
MGV.02
– determine the optimal values of various measurements, through investigations using concrete materials, diagrams, and calculators or computer software;
MGV.03
– solve simple problems involving the Pythagorean theorem;
MGV.04
– demonstrate an understanding of the properties of sides and angles in triangles and parallel lines through investigations using concrete materials and appropriate technology (e.g., dynamic geometry software);
Solving Problems Involving the Measurement of Two-dimensional Figures and Three-dimensional Objects
MG1.01
– solve simple problems using the formulas for the perimeter and area of triangles, rectangles, squares and circles;
MG1.02
– calculate the perimeter and area of composite figures (e.g., combinations of triangles, rectangles, squares, and circles;
MG1.03
– substitute into and evaluate measurement formulas as the need arises in problem solving;
MG1.04
– solve simple problems, using the formulas for the volume of triangular prisms, rectangular prisms, cubes, and cylinders;
MG1.05
– construct triangular prisms, rectangular prisms, and cubes from their nets;
MG1.06
– solve simple problems using the formulas for the surface area of triangular prisms, rectangular prisms, cubes, and cylinders.
Investigating the Optimal Values of Measurements
MG2.01
– construct a variety of rectangles for a given perimeter and determine the maximum area for a given perimeter;
MG2.02
– construct a variety of rectangles for a given area and determine the minimum perimeter for a given volume;
MG2.03
– construct a variety of rectangular prisms for a given volume and determine the minimum surface area for the prism with a given area;
MG2.04
– describe applications in which it would be important to know the maximum area for a given perimeter or the maximum volume for a given surface area;
MG2.05
– describe applications in which it would be important to know the minimum perimeter for a given area;
MG2.06
– solve simple problems involving optimal values.
Solving Simple Problems Involving the Pythagorean Theorem
MG3.01
– illustrate the Pythagorean theorem using concrete materials;
MG3.02
– use the Pythagorean theorem to construct right angles in practical situations (e.g., the 3, 4, 5 triangle used by carpenters);
MG3.03
– solve simple problems drawn from familiar applications, using the Pythagorean theorem.
Understanding the Properties of Sides and Angles in Triangles and Parallel Lines
MG4.01
– illustrate the meanings of key terms associated with angles and triangles (e.g., acute angle, obtuse angle, right angle, isosceles triangle, equilateral triangle, right triangle, perpendicular lines, parallel lines) by constructing diagrams;
MG4.02
– estimate the measures of angles and line segments;
MG4.03
– determine the measures of angles and line segments using appropriate tools;
MG4.04
– determine through investigations, some of the properties of the angles of triangles and parallel lines;
MG4.05
– solve simple geometric problems;
MG4.06
– communicate solutions to problems and the results of investigations, using appropriate terminology, symbols, and form.
Ontario Catholic School Graduate Expectations
The graduate is expected to be:
A Discerning Believer Formed in the Catholic Faith Community who
CGE1a -illustrates a basic understanding of the saving story of our Christian faith;
CGE1b -participates in the sacramental life of the church and demonstrates an understanding of the centrality of the Eucharist to our Catholic story;
CGE1c -actively reflects on God’s Word as communicated through the Hebrew and Christian scriptures;
CGE1d -develops attitudes and values founded on Catholic social teaching and acts to promote social responsibility, human solidarity and the common good;
CGE1e -speaks the language of life... “recognizing that life is an unearned gift and that a person entrusted with life does not own it but that one is called to protect and cherish it.” (Witnesses to Faith)
CGE1f -seeks intimacy with God and celebrates communion with God, others and creation through prayer and worship;
CGE1g -understands that one’s purpose or call in life comes from God and strives to discern and live out this call throughout life’s journey;
CGE1h -respects the faith traditions, world religions and the life-journeys of all people of good will;
CGE1i -integrates faith with life;
CGE1j -recognizes that “sin, human weakness, conflict and forgiveness are part of the human journey” and that the cross, the ultimate sign of forgiveness is at the heart of redemption. (Witnesses to Faith)
An Effective Communicator who
CGE2a -listens actively and critically to understand and learn in light of gospel values;
CGE2b -reads, understands and uses written materials effectively;
CGE2c -presents information and ideas clearly and honestly and with sensitivity to others;
CGE2d -writes and speaks fluently one or both of Canada’s official languages;
CGE2e -uses and integrates the Catholic faith tradition, in the critical analysis of the arts, media, technology and information systems to enhance the quality of life.
A Reflective and Creative Thinker who
CGE3a -recognizes there is more grace in our world than sin and that hope is essential in facing all challenges;
CGE3b -creates, adapts, evaluates new ideas in light of the common good;
CGE3c -thinks reflectively and creatively to evaluate situations and solve problems;
CGE3d -makes decisions in light of gospel values with an informed moral conscience;
CGE3e -adopts a holistic approach to life by integrating learning from various subject areas and experience;
CGE3f -examines, evaluates and applies knowledge of interdependent systems (physical, political, ethical, socio-economic and ecological) for the development of a just and compassionate society.
A Self-Directed, Responsible, Life Long Learner who
CGE4a -demonstrates a confident and positive sense of self and respect for the dignity and welfare of others;
CGE4b -demonstrates flexibility and adaptability;
CGE4c -takes initiative and demonstrates Christian leadership;
CGE4d -responds to, manages and constructively influences change in a discerning manner;
CGE4e -sets appropriate goals and priorities in school, work and personal life;
CGE4f -applies effective communication, decision-making, problem-solving, time and resource management skills;
CGE4g -examines and reflects on one’s personal values, abilities and aspirations influencing life’s choices and opportunities;
CGE4h -participates in leisure and fitness activities for a balanced and healthy lifestyle.
A Collaborative Contributor who
CGE5a -works effectively as an interdependent team member;
CGE5b -thinks critically about the meaning and purpose of work;
CGE5c -develops one’s God-given potential and makes a meaningful contribution to society;
CGE5d -finds meaning, dignity, fulfillment and vocation in work which contributes to the common good;
CGE5e -respects the rights, responsibilities and contributions of self and others;
CGE5f -exercises Christian leadership in the achievement of individual and group goals;
CGE5g -achieves excellence, originality, and integrity in one’s own work and supports these qualities in the work of others;
CGE5h -applies skills for employability, self-employment and entrepreneurship relative to Christian vocation.
A Caring Family Member who
CGE6a -relates to family members in a loving, compassionate and respectful manner;
CGE6b -recognizes human intimacy and sexuality as God given gifts, to be used as the creator intended;
CGE6c -values and honours the important role of the family in society;
CGE6d -values and nurtures opportunities for family prayer;
CGE6e -ministers to the family, school, parish, and wider community through service.
A Responsible Citizen who
CGE7a -acts morally and legally as a person formed in Catholic traditions;
CGE7b -accepts accountability for one’s own actions;
CGE7c -seeks and grants forgiveness;
CGE7d -promotes the sacredness of life;
CGE7e -witnesses Catholic social teaching by promoting equality, democracy, and solidarity for a just, peaceful and compassionate society;
CGE7f -respects and affirms the diversity and interdependence of the world’s peoples and cultures;
CGE7g -respects and understands the history, cultural heritage and pluralism of today’s contemporary society;
CGE7h -exercises the rights and responsibilities of Canadian citizenship;
CGE7i -respects the environment and uses resources wisely;
CGE7j -contributes to the common good