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Course Profile   Mathematics for Everyday Life (MEL4E), Grade 12, Workplace Preparation, Combined

 

Course Overview

 

Policy Document:  The Ontario Curriculum, Grades 11 and 12, Mathematics, 2000.

Prerequisite:  Mathematics for Everyday Life, Grade 11, Workplace Preparation

Course Description

This course enables students to broaden their understanding of mathematics as it is applied in important areas of day-to-day living. Students will use statistics in investigating questions of interest and apply principles of probability in familiar situations. They will also investigate accommodation costs and create household budgets; solve problems involving estimation and measurement; and apply concepts of geometry in the creation of designs.

How the Course Supports the Ontario Catholic School Graduate Expectations

This course encourages the Catholic learner to develop his/her gifts and abilities to promote growth toward personal responsibility in preparation for their role in society. Throughout the course, emphasis should be placed on moral, ethical, and realistic decision-making in an effort to build responsible citizenship. The classroom environment should instill a spirit of cooperation and foster a collaborative sense of community. Students will be expected to acknowledge and respect the opinions of others as they work effectively as interdependent team members.

Course Notes

This Course Profile encourages the development of the critical thinking skills that are required to analyse choices and make informed decisions. This course provides an opportunity for students to explore the link between mathematics and everyday life. Emphasis is placed on making informed decisions about statistics, household finances, and design principles. The units in this profile have been clustered into three groups: data collection and analysis, household considerations (everyday financing), and measurement and design. In Units 1 and 2, students investigate, analyse and represent information using a variety of graphical forms and apply principles of probability in familiar situations. Units 3 and 4 focus on accommodation costs and living expenses, which are investigated and represented within various household budgets. Units 5 and 6 deal with basic measurement (estimation, area, perimeter, etc.), and the mathematical processes involved in home improvement projects (construction and design). A summative unit provides an opportunity to link each of these themes to practical applications. Assessment and evaluation using a wide variety of strategies will allow students to demonstrate learning. The use of technology, e.g., graphing calculators, spreadsheets, drawing software, dynamic geometry software, throughout the course will assist student learning.

This Course Profile represents the collective effort of Catholic and Public writing teams. The fully developed units are Units 2 and 6. In addition to these two complete “model” units, a less-detailed Unit Overview Chart for each of the remaining units offers a recommended clustering of expectations and provides a starting point from which teachers can plan the course. It is suggested that students be encouraged to develop and maintain a glossary of terms as they proceed through each of the units.

Successful implementation of this profile will involve:

Developing Students’ Employability Skills

This course recognizes and supports the student who is preparing to enter the workplace. Employability skills should be fostered by a classroom environment that emphasizes regular and punctual attendance, teamwork, and appropriate communication among teachers and peers. Practical problem solving activities provide the opportunity for students to demonstrate initiative and apply their decision-making skills.

Creating a Positive Learning Environment

This course recognizes that many students will bring years of math anxiety to the classroom. It is important for teachers to maintain a positive environment that recognizes student success and accommodates student needs.

Linking Curriculum Concepts to Practical Applications

This course provides many opportunities for students to appreciate the relevance of math in their lives. Concrete applications, such as designing rooms, home-improvement projects and budgets, allow students to make this connection.

Using Technology as a Tool for Learning

The use of technology reinforces student understanding and facilitates problem solving by providing a visual connection to concepts. Technology can also provide students access to problems and mathematics that may have otherwise been beyond their skill level. Appropriate technological tools (scientific and graphing calculators, spreadsheets, budgeting software, Internet, etc.) should be incorporated wherever applicable. It is recommended that teachers ensure that the probability simulation application is loaded on all graphing calculators before beginning Unit 2 (see Activity 2.5 for instructions).

Units:  Titles and Time

Unit 1

Information Processing

12 hours

* Unit 2

Take a Chance

20 hours

Unit 3

Finding a Place of Your Own

13 hours

Unit 4

Making Ends Meet

16 hours

Unit 5

Measure by Measure

15 hours

* Unit 6

By Design

22 hours

Unit 7

Making Your Mark (Summative)

12 hours

* These units are fully developed in this Course Profile.

Unit Overviews

Unit 1:  Information Processing

Time:  12 hours

Unit Description

The link between the collection, representation, and interpretation of data is investigated in this unit. Data collection and survey methods are explored by having the students gather information about a topic of interest to them. Since student-generated data is more relevant, this provides a practical context for this unit. While conducting surveys, students must be instructed to accept “no comment” as a valid answer to any question, and to respect that people may choose not to respond at all. Teachers should be sensitive to the personal nature of some students’ experiences and support them in avoiding disclosure and discussion of sensitive issues. Information collected from various surveys may be applicable to
Unit 2 where statistics and probability are studied. In addition, students investigate a variety of graphical forms and develop the ability to effectively present their data, with and without the use of technology. Through graphical analysis, students recognize and explain the trends in the data and form valid conclusions. Again, the visual representation of this data may be used in the discussion of statistics in Unit 2. A summative activity might involve the interpretation and representation of given data in both word and graphical form. Students could be required to present their interpretation with the appropriate justification for their choices.

Unit Overview Chart

Cluster

Learning Expectations

Assessment Categories

Focus

1

SPV.01, SP1.01, SP1.02
CGE2b, CGE2c

Knowledge/Understanding
Application

Constructing Graphs

2

SPV.01, SP1.03
CGE3c, CGE5a

Knowledge/Understanding
Communication
Application

Interpreting Graphs

3

SPV.02, SP2.01, SP2.02
CGE2c, CGE4f, CGE5e

Knowledge/Understanding
Application
Communication

Data Collection using Surveys

4

SPV.02, SP2.03, SP2.04
CGE3c, CGE5e

Application
Communication
Thinking/Inquiry/Problem Solving

Interpretation of Surveys

5

SPV.01, SPV.02, SP1.01, SP1.03, SP2.02, SP2.03

Knowledge/Understanding
Application
Communication
Thinking/Inquiry/Problem Solving

Summative: Interpret Given Data in Words and Graphical Form

 

Unit 2:  Take a Chance

Time:  20 hours

Unit Description

Since choices are part of everyday life, this unit provides an opportunity for students to investigate the basics of probability as they relate to common events, such as coin tossing, choosing your favourite coloured candy from a bag, playing the lottery, etc. Throughout the unit, the relevance to practical situations is emphasized. Simple probability experiments and simulations provide the opportunity to predict and explore outcomes. The link between the number of trials and statistical validity is emphasized using technology. Students apply critical thinking skills to interpret the results of probability experiments in order to make informed decisions, e.g., How many times must the coin be flipped before the desired result is achieved? The examination of statistics in the media provides an opportunity to link the skills from Unit 1 to the theory from this unit. Discussions about the representation of data create an awareness of how mathematics is involved in many aspects of our lives.

Unit Overview Chart

Cluster

Learning Expectations

Assessment Categories

Focus

1

SPV.03, SP3.01, SP3.02
CGE2b, CGE2c, CGE3c, CGE4f, CGE5a

Knowledge/Understanding
Communication

Expressions of Probability

2

SPV.04, SP4.01, SP4.02
CGE2a, CGE2e

Communication
Thinking/Inquiry/Problem Solving

Discussion of Statistics in the Media

3

SPV.03, SP3.03, SP3.04
CGE3c, CGE4f

Knowledge/Understanding
Application
Communication

Probability Experiments

4

SPV0.3, SP3.03, SP3.04, SP3.05
CGE3c, CGE4f

Knowledge/Understanding
Communication

Probability Simulations

5

SPV.03, SPV.04, SP3.01, SP3.02, SP4.01, SP4.02

Knowledge/Understanding
Application
Communication
Thinking/Inquiry/Problem Solving

Summative: Analysis of a Marketing Report

 

Unit 3:  Finding a Place of Your Own

Time:  13 hours

Unit Description

To create an awareness of the options, students investigate the costs of accommodation in their local community using current resources such as newspapers, Internet, etc. Accommodation alternatives are explored with an emphasis on comparing renting to owning. Students need to focus on the practical aspects of making accommodation decisions, e.g., budget considerations, location, etc. The monthly costs involved in maintaining both types of accommodation are examined. Emphasis should be placed on examining affordable accommodations. The information collected in this unit can be used in Unit 4 to create realistic budgets.

Unit Overview Chart

Cluster

Learning Expectations

Assessment Categories

Focus

1

EFV.01, EF1.02, EF1.03
CGE2c

Knowledge/Understanding
Communication

Accommodation Alternatives: Rights and Responsibilities

2

EFV.01, EF1.01, EF1.04
CGE5a

Knowledge/Understanding
Thinking/Inquiry/Problem Solving

Renting and Maintaining an Apartment

3

EFV.02, EF2.01, EF2.02, EF2.03, EF2.04
CGE2c, CGE4g, CGE5b

Knowledge/Understanding
Application
Communication
Thinking/Inquiry/Problem Solving

Buying and Maintaining a House

4

EFV.01, EFV.02, EF1.01, EF1.04, EF2.02, EF2.03, EF2.04
CGE3c, CGE4f, CGE4g

Knowledge/Understanding
Application
Communication
Thinking/Inquiry/Problem Solving

Summative: Where Will You Live?

 

Unit 4:  Making Ends Meet

Time:  16 hours

Unit Description

Key features of household budgets are identified and appropriate budgets are designed for given case studies. Students determine necessary adjustments to these budgets in response to changing incomes, family responsibilities, and long-term goals. Accommodation information obtained in Unit 3 may be used to help create various budgets in this unit. Technology, such as spreadsheets and budgeting software, aids students in investigating and organizing data. In the summative activity, the creation of relevant personal budgets by each student provides a practical application of the theory studied in this unit. These budgets can be based on current part-time jobs or possible future employment and include possible scenarios that must be considered, e.g., a layoff, car repair, etc.

Unit Overview Chart

Cluster

Learning Expectations

Assessment Categories

Focus

1

EFV.03, EF3.01, EF3.02
CGE2c, CGE3c

Knowledge/Understanding
Thinking/Inquiry/Problem Solving

Budget Considerations

2

EFV.03, EF3.03, EF3.04
CGE2b, CGE2c

Application
Communication
Thinking/Inquiry/Problem Solving

Developing Budgets

3

EFV.03, EF3.05
CGE3c, CGE4b

Application
Thinking/Inquiry/Problem Solving

Adapting Budgets

4

EFV.03, EF3.03, EF3.04
CGE3c, CGE4f

Application
Thinking/Inquiry/Problem Solving
Communication

Creating a Personal Budget

 

Unit 5:  Measure by Measure

Time:  15 hours

Unit Description

Since estimation and measurement are two of the most widely used mathematical skills in daily life, it is important for students to become familiar and adept with these skills. A practical application is provided in Unit 6 where students are required to design various household improvements. Using appropriate tools and personal referents, e.g., the width of a finger being approximately 1 cm, students demonstrate a working knowledge of the metric and imperial systems. Emphasis is placed on the ability to estimate and calculate common measurements, such as distance, volume, perimeter, and area of regular and irregular figures. To provide practical contexts for this unit, students estimate and measure various objects and rooms around the school. The Pythagorean theorem is also explored as students solve problems involving measurement and design. Connections to the use of these skills at home and at work should be provided throughout the entire unit. A summative activity could involve the estimation and calculation of how many objects, e.g., basketballs, or people would be required to completely fill a particular room in the school (gymnasium).

Unit Overview Chart

Cluster

Learning Expectations

Assessment Categories

Focus

1

AMV.01, AM1.01, AM1.02
CGE2b

Knowledge/Understanding
Application

Applying the Metric and Imperial Systems

2

AMV.01, AMV.02 AM1.03, AM1.04, AM1.05, AM2.08
CGE3c, CGE5h

Knowledge/Understanding
Application
Communication
Thinking/Inquiry/Problem Solving

Estimation of Quantities

3

AMV.02, AM2.02, AM2.03
CGE3c, CGE5a

Knowledge/Understanding
Application
Communication

Perimeter Calculations

4

AMV.02, AM2.02, AM2.03, AM2.04
CGE3c, CGE5a

Knowledge/Understanding
Application
Communication
Thinking/Inquiry/Problem Solving

Area Calculations

5

AMV.02, AM2.01
CGE4f

Knowledge/Understanding
Thinking/Inquiry/Problem Solving

Pythagorean Theorem

6

AMV0.1, AMV.02, AM1.02, AM1.03, AM1.04, AM2.02, AM2.03
CGE3c, CGE4f, CGE5a

Knowledge/Understanding
Application
Communication
Thinking/Inquiry/Problem Solving

How Much Can We Really Put in There?

 

Unit 6:  By Design

Time:  22 hours

Unit Description

Students apply their understanding of measurement and geometry to two-dimensional and three-dimensional constructions and symmetrical designs. Drawing software is used to create two-dimensional scale drawings and three-dimensional drawings of a room. Spreadsheet software is used to plan and evaluate project costs in a household improvement. Students are provided class time to apply their understanding of scale to the construction of a three-dimensional scale model of an area of personal interest such as a garden or bridge. The geometric properties of tiling designs and logos are investigated using drawing software and concrete materials. Students complete these investigations with the construction of a personal logo and tiling designs. The summative activity provides an opportunity for students to demonstrate their understanding of the decision-making processes involved in planning, designing, and costing a household improvement.

Unit Overview Chart

Activity

Learning Expectations

Assessment Categories

Focus

1

AMV.02, AM2.09
CGE4f

Knowledge/Understanding
Thinking/Inquiry/Problem Solving
Communication
Application

Design a household improvement.

2

AMV.02, AM2.05, AM2.06
CGE4b

Knowledge/Understanding

Construct scale drawings using technology.

3

AMV.02, AM2.07
CGE5a

Application

Design and build 3-D scale model.

4

AMV.03, AM3.01
CGE4b, CGE5a

Knowledge/Understanding
Communication

Analyse symmetrical designs using technology.

5

AMV.03, AM3.02, AM3.03
CGE3c

Knowledge/Understanding
Application
Communication

Construct a personal logo using technology.

6

AMV.03, AM3.04, AM3.05
CGE4f, CGE5h

Thinking/Inquiry/Problem Solving

Apply tiling principles to the construction of tiling designs with technology.

7

AMV.02, AMV.03, AM2.05, AM2.09, AM3.02, AM3.05
CGE5h

Knowledge/Understanding
Communication
Thinking/Inquiry/Problem Solving
Application

Making design and purchase decisions.

Note: 0.75 hours have been allotted for introducing the Transform menu on Geometers Sketchpad.

Unit 7:  Making Your Mark

Time:  12 hours

Unit Description

This profile encourages the development of the critical thinking skills that are required to analyse choices and make informed decisions. The summative activities should address the key expectations that support the development of these skills. Due to the complexity of the task, teachers may consider pairing students. These expectations can be clustered into four categories:

Cluster 1 – addresses the expectations that require students to analyse statistical information in order to make informed choices.

Cluster 2 – is represented by the expectations that engage students in planning and adjusting personal budgets.

Cluster 3 – is represented by expectations that require students to apply their knowledge about perimeter, area, and scale in order to plan and cost home improvement projects.

Cluster 4 – focuses on the decision-making skills that underlie the design process.

In the development of the summative unit, it is suggested that a scenario reflecting local conditions provide the unifying theme for the activities. The following is a suggestion:

A single female with a young child plans to open a small video business in her community. She decides to survey the population in her area to gather information about the type of videos she should order for her store. In anticipation of her grand opening, she is considering a raffle for door prizes in order to attract customers. She has saved some money and plans to buy a house in the area. In addition to calculating her monthly costs, she must adjust her current household budget to account for the additional expenses of home ownership and the video business. She plans to renovate one of the rooms in her house to provide a separate office space for the business. A two-dimensional drawing of the room should help her decide how to arrange the office furniture. The perimeter and area of the office is required so that she can estimate the cost of flooring and wall coverings. She plans to design a business logo for the video store’s stationery in addition to a screen saver for her office computer that features Escher-like tessellations.

Unit Overview Chart

Cluster

Learning Expectations

Assessment Categories

Focus

1

SPV.01, SPV.02, SPV.03, SP1.01, SP1.02, SP1.03, SP2.02, SP2.03, SP2.04, SP3.01, SP3.02, SP3.03
CGE2c, CGE4f, CGE5a

Knowledge/Understanding
Communication
Thinking/Inquiry/Problem Solving

Construct and interpret graphs based on survey data. Apply understanding of probability to experimental results.

2

EFV.02, EFV.03, AMV.02, EF2.01, EF2.04, EF3.03, EF3.04, EF3.05, AM2.09
CGE3c, CGE4b, CGE5h

Application
Communication
Thinking/Inquiry/Problem Solving

Determine the type of housing available for a given budget. Design and adjust a budget to reflect changes in the family income.

3

AMV.02, AM2.02, AM2.06
CGE2b, CGE5a

Knowledge/Understanding
Application
Communication

Determine the perimeter and area of a room and create a two-dimensional drawing.

4

AMV0.3, AM3.03, AM3.05
CGE2c, CGE3c

Knowledge/Understanding
Application

Design a business logo and computer screen saver.

Teaching/Learning Strategies

Students will benefit from multiple experiences with applications that are relevant to their daily lives and will prepare them for the workplace. Large tasks should be sequenced into logical steps and connections to prior learning should be made and reinforced as necessary. A flexible teaching style that recognizes individual strengths, engages students in their learning, and provides frequent and varied feedback will ensure a greater likelihood of student success.

In planning the delivery of this course, teachers should:

·         become familiar with exceptional students’ IEPs and make appropriate accommodations based on student needs;

·         identify and build on student’s prior knowledge;

·         provide a variety of learning experiences that focus on active learning and draw from the workplace setting;

·         use a variety of instructional strategies to address varied learning styles;

·         include a balance of whole class, small group, and individual instruction;

·         use mini-lessons to introduce skills as necessary;

·         provide many and varied opportunities for student success using regular, constructive feedback;

·         use positive reinforcement to foster students’ confidence in their mathematical abilities;

·         provide students with activities that involve developing critical thinking and decision-making skills;

·         provide review, remediation, and extension when appropriate;

·         integrate technology when appropriate;

·         use current and local information to promote relevance.

In achieving the expectations of this course, students will:

·         recognize the importance of math in the workplace;

·         utilize a variety of resources to solve problems;

·         develop practical decision-making and organizational skills;

·         use estimation to judge the reasonableness of answers;

·         work individually as well as cooperatively;

·         increase proficiency with technology as it pertains to the course material;

·         become informed consumers;

·         investigate and explore concepts using technology;

·         create a glossary of terms and add to it on an on-going basis.

Assessment & Evaluation of Student Achievement

·         To effectively assess student achievement, a balance of diagnostic, formative, and summative assessment instruments should be used.

·         Seventy per cent of the grade will be based on assessment and evaluations conducted throughout the course.

·         Thirty per cent of the grade will be based on a final evaluation in the form of an examination, performance, essay, and/or other methods of evaluation.

·         High quality assessments should motivate students to improve their own learning, inform teachers about the effectiveness of instruction, and identify areas for improvement in both teaching and learning.

·         In order for assessment and evaluation to be valid, it must reflect the instructional framework of the course. Students must be provided with a variety of ways to demonstrate their understanding and be given opportunities to achieve these expectations throughout the course.

·         Parents, students and teachers work together to set future goals for student self-improvement.

·         Evaluation of student achievement is based on the criteria provided by the Achievement Chart categories.

Specific tools, which may be considered, are suggested below. These lists, while not comprehensive, may serve as a guide for assessing and evaluating student achievement. Generic rubrics that can be adapted to specific tasks are provided at the OAME/OMCA website: www.oame.on.ca. These materials are available under “CARE Package.”

Knowledge/Understanding

Achievement in this category reflects the student’s ability to demonstrate an understanding of mathematical concepts and to perform algorithms.

Assessment/evaluation may include the use of:

·         skill-based calculations on assignments, tests, exams;

·         student-teacher conferencing;

·         accuracy of mathematical answers in reports and presentations.

Application

Achievement in this category reflects the student’s ability to apply concepts and procedures to familiar and unfamiliar settings.

Assessment/evaluation may include the use of:

·         problems requiring the selection and application of formulas;

·         appropriate application of technological tools.

Thinking/Inquiry/Problem Solving

Achievement in this category reflects the student’s ability to demonstrate reasoning and to apply the steps of the inquiry/problem solving process effectively. This category is especially conducive to the use of rubrics due to the open-ended nature of many of the problems.

Assessment/evaluation may include the use of:

·         open-ended questions;

·         exploration tasks requiring interpretation of the results;

·         observations of problem solving strategies used in group work;

·         student-teacher conferencing;

·         tasks requiring complexity of mathematical reasoning in reports and presentations.

Communication

Achievement in this category reflects the student’s ability to communicate his/her reasoning using appropriate mathematical language, symbols, and conventions. Rubrics are effective and efficient tools for this type of evaluation.

Assessment/evaluation may include the use of:

·         verbal presentation of solutions and homework;

·         appropriate use of mathematical language on tests and assignments;

·         journals;

·         visual aids during presentations;

·         reports and assignments;

·         student-teacher conferencing.

To Assess Learning Skills

While learning skills are not to be included in the determination of the student’s grade, teachers and students should be aware of the importance that these skills have on the student’s performance. In addition, these skills need to be reported on the report card, and thus need to be tracked throughout the course.

The following is a partial list of suggested indicators of learning skills:

Organization

·         preparedness (materials for class)

·         work is submitted on time

·         notebook

Work Habits

·         regular completion of homework

·         use of class time

·         attendance and punctuality

Team Work

·         cooperation in group settings

·         respect for the opinions of others

Initiative

·         participates in class discussion

·         responsibility for own learning, e.g., tutoring

Works Independently

·         commitment to task

·         effort to solving problems individually

Accommodations

Appropriate accommodations should be a part of the planning of each unit and reflect the needs of the students in the class. When planning instructional and assessment activities, teachers must consider the students’ strengths and needs in light of the learning expectations and accommodations identified in the students’ IEPs (whether the students are formally identified or not) (Regulation 181/98).

Special Considerations for Students

·         Provide flexible timelines with respect to the completion of projects and assignments.

·         Allow students to work in alternate settings where students can receive assistance with problems.

·         Provide alternate formats for assignments, e.g., demonstration, oral presentation, written report.

·         Provide multiple opportunities for success by employing a variety of assessments.

·         Allow accommodations with respect to test/exam writing environments, e.g., extra time, use of technology, cueing, etc.

Accommodations for Students with Learning Disabilities

·         Change the style of presentation.

·         Provide access to technology and specialized equipment when appropriate.

·         Provide additional time and alternate formats for assessment.

·         Include more concrete experiences where appropriate.

·         Vary the pace of learning.

·         Subdivide tasks.

·         Pair students.

·         Use easy to read fonts and layouts in handouts with concise instructions.

·         Provide models and templates.

·         Provide alternate environments in which to complete tests.

·         Reinforce instructions on an individual basis.

Accommodations for ESL/ELD Students

·         Use peer tutoring to reinforce instructions and provide models.

·         Provide extensive student/teacher conferencing.

·         Limit complex sentence structures in oral and written formats.

·         Provide visual/auditory clues.

·         Use a word wall for subject-specific terminology.

·         Partner students with the same linguistic background.

·         Combine written instructions with verbal instructions.

·         Highlight key words or phrases.

·         Provide opportunities to practise oral presentation skills.

Resources

Units in the Course Profile make reference to the use of specific websites. Teachers need to consult their board policies regarding use of any copyrighted materials. Before reproducing materials for student use from printed publications, teachers need to ensure that their board has a Cancopy licence and that this licence covers the resources they wish to use. Before screening videos/films with their students, teachers need to ensure that their board/school has obtained the appropriate public performance videocassette licence from an authorized distributor, e.g., Audio Cine Films Inc. Teachers are reminded that much of the material on the Internet is protected by copyright. The copyright is usually owned by the person or organization that created the work. Reproduction of any work or substantial part of any work on the Internet is not allowed without the permission of the owner.

Websites

The URLs for the websites were verified by the writers prior to publication. Given the frequency with which these designations change, teachers should always verify the websites prior to assigning them for student use.

http://www.cmhc.ca/banner1/

http://www.rona.ca/

http://www.nycenet.edu/oit/math-kitecture/index.htm

http://mathforum.org/workshops/sum98/participants/sanders/

www.scalemodel.net/

http://www.schools.ash.org.au/stkierans-manly/Classes/Yr6/6B/Symmetry/page1.html

http://www.gopromos.com/idea_center/stock_art_alpha.asp?type=L

http://www2.spsu.edu/math/tile/index.htm

http://155.187.10.12/flags/flags.html

www.style-line.com

http://mathforum.com/geometry/rugs/

http://library.thinkquest.org/16661/

http://www.izzy.net/~jc/EscherTiles/EscherTiles.html

http://www.col-ed.org/cur/math/math48.txt

http://www.uiowa.edu/~tutimp/modules/probstat/spinners/makespin.htm

http://www.shazam.econ.ubc.ca/flip/

http://www.ti.com/calc

Print

Bennett, Dan. Exploring Geometry with the Geometer’s Sketchpad. Berkeley: Key Curriculum Press. 1999. ISBN: 1-55953-289-0

Gibbs, J. Tribes: A New Way of Learning Together. Concord: Irwin Publishing, 1994.
ISBN: 0-7725-2118-2

Lee, Kevin. TesselMania. 1995.

Readers Digest. New Complete Do-It-Yourself Manual. Montreal: Reader’s Digest Canada 1991.
ISBN: 0888501781

Seymour, Dale and Jill Britton. Introduction to Tessellations. CA: Dale Seymour Publications, 1989. ISBN 94303-0879

Wyatt, K., A. Lawrence, and G. Foletta. Geometry Activities for Middle School Students with the Geometer’s Sketchpad. Berkeley: Key Curriculum Press. 1998. ISBN: 1-55953-299-8

Airasian, P.W. Classroom Assessment. New York: McGraw-Hill, 1994.

Burz, H.L. and K. Marshall. Performance-Based Curriculum for Mathematics. California: Sage, 1996.

Bush, W.S. and A.S. Greer, eds. Mathematics Assessment – A Practical Handbook for Grades 9-12. Retson, VA: The National Council of Teachers of Mathematics, 1999.

Coxford, A.F. and N.L. Webb, eds. Assessment in the Mathematics Classroom. Reston, VA: The National Council of Teachers of Mathematics, Inc., 1993.

Hibbard, K.M., et al. A Teacher’s Guide to Performance-Based Learning and Assessment. Alexandria, VA: Association for Supervision and Curriculum Department, 1996.

Marzano, R.J., D. Pickering, and J. McTighe. Assessing Student Outcomes: Performance Assessment Using the Dimensions of Learning Model. Alexandria, VA: Association for Supervision and Curriculum Development, 1993.

National Council of Teachers of Mathematics. Assessment Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics, 1997.

Rogers, S. and S. Graham. The High Performance Toolbox: Succeeding with Performance Tasks, Projects, and Assessments. Peak Learning Systems, 1997.

Romberg, T.A., ed. Reform in School Mathematics and Authentic Assessment. New York: State University of New York Press, 1995.

Romberg, T.A., ed. Mathematics Assessment and Evaluation: Imperatives for Mathematics Educators. New York: State University of New York Press, 1992.

Silver, E.A., et al. Thinking Through Mathematics: Fostering Inquiry and Communication in Mathematics Classrooms. New York: College Entrance Examination Board, 1990.

Wiggins, G. Assessment: Authenticity, Context, and Validity. Phi Delta Kappan, 1993. 75, 3: 200-14

Wiggins, G. and J. McTighe. Understanding by Design. Alexandria, VA: Association for Supervision of Curriculum Development, 1998.

OSS Considerations

The following list of resources supports many of the Ontario Secondary School Policies as well as the Ontario Catholic Secondary School Graduate Expectations:

Ministry of Education Policy and Reference Documents

·         Choices into Action: Guidance and Career Education Program Policy

·         Cooperative Education: Policies and Procedures for Ontario Secondary Schools

·         Individual Education Plans: Standards for Development, Program Planning, and Implementation, 2000

·         Mathematics, Grades 9-10

·         Mathematics, Grades 11-12

·         Ontario Schools Code of Conduct

·         Ontario Secondary Schools, Grades 9 to 12: Program and Diploma Requirements

·         Program Planning and Assessment, Grades 9-12

·         Violence-Free Schools Policy

 

The Ministry of Education has also published several resource documents, brochures, and policy/program memoranda in support of its OSS policies. They are available online at the Ministry of Education website, http://www.edu.gov.on.ca/eng/document/document.html.

Publications Concerning Faith Development

·         Blueprints (Catholic Curriculum Cooperative - Central Ontario Region)

·         Catholicity Across The Curriculum (Ontario Catholic School Trustees’ Association)

·         Educating the Soul (Institute for Catholic Education)

·         Ontario Catholic Secondary School Graduate Expectations (Institute for Catholic Education)

·         This Moment of Promise (Ontario Conference of Catholic Bishops)

·         Creating Catholic Curriculum (Eastern Ontario Catholic Curriculum Cooperative)

Career Goals/Cooperative Education Programs

·         Ontario Youth Apprenticeship Program

·         Youth Employment Skills Program

Community Partnerships

Refer to local board policies, e.g., Relations with Business - Corporate Donations, Sponsorships and Agreements.


Coded Expectations, Mathematics for Everyday Life, Grade 12,
Workplace Preparation, MEL4E

Statistics and Probability

Overall Expectations

SPV.01 · construct and interpret graphs;

SPV.02 · formulate questions, and collect and organize data related to the questions;

SPV.03 · apply principles of probability to familiar situations;

SPV.04 · interpret statements about statistics and probability arising from familiar situations and the media.

Specific Expectations

Constructing and Interpreting Graphs

SP1.01 – represent given data in a variety of graphical forms, using spreadsheets or other suitable graphing technology;

SP1.02 – select an effective graphical form for a given set of data and explain reasons for the choice;

SP1.03 – interpret graphs by identifying trends and describing the meaning of the trends within the context of the data.

Collecting and Organizing Data

SP2.01 – identify issues or questions of interest and collect related data, using an appropriate sampling technique;

SP2.02 – construct tables and graphs to represent collected data, using spreadsheets or other suitable graphing technology;

SP2.03 – draw appropriate conclusions about questions or issues on the basis of the interpretation of graphs;

SP2.04 – explain conclusions clearly.

Applying Principles of Probability

SP3.01 – express probabilities of simple events as the number of favourable outcomes divided by the total number of outcomes;

SP3.02 – express probabilities as fractions, decimals, and percents, and interpret probabilities expressed in each of these forms;

SP3.03 – describe the results obtained in carrying out probability experiments related to familiar situations involving chance (e.g., rolling dice, spinning spinners, flipping coins);

SP3.04 – compare predicted and experimental results for familiar situations involving chance, using technology to extend the number of experimental trials (e.g., using a random number generator on a spreadsheet or on a graphing calculator);

SP3.05 – simulate familiar situations involving chance and explain the choice of simulation (e.g., simulate the gender of children in a family by the repeated flipping of a coin and explain why coin flipping was used).

Interpreting Statements About Statistics and Probability

SP4.01 – interpret information about probabilities to assist in making informed decisions in a variety of situations (e.g., evaluating risk versus reward in the purchase of lottery tickets);

SP4.02 – interpret and assess statistical and probabilistic information used in the media and in common conversation (e.g., vague statements such as “four out of five dentists recommend”; statements about odds; scales on graphs).

Everyday Financing

Overall Expectations

EFV.01 · determine the costs involved in renting an apartment;

EFV.02 · determine the costs involved in buying a house;

EFV.03 · design household budgets for given circumstances.

Specific Expectations

Determining the Costs of Renting an Apartment

EF1.01 – determine, through investigation, the costs of apartment rentals in the surrounding community;

EF1.02 – describe the alternatives available (e.g., leasing, renting month to month) and the procedures involved (e.g., paying a deposit) in renting an apartment;

EF1.03 – describe the rights and responsibilities of an apartment tenant and an apartment landlord;

EF1.04 – calculate the monthly costs involved in maintaining an apartment.

Determining the Costs of Buying a House

EF2.01 – determine, through investigation, patterns in the cost of housing in the surrounding community (e.g., what kind of house can be purchased for $75 000? $140 000? $250 000? $400 000?);

EF2.02 – describe the procedures and costs involved in purchasing a house;

EF2.03 – identify the costs involved in maintaining a house;

EF2.04 – calculate the monthly costs involved in maintaining a given house.

Designing Budgets

EF3.01 – identify typical components (e.g., accommodation, food, savings) and their dispersion in a household budget;

EF3.02 – determine the type of housing affordable in the surrounding community by a person with a given income and family responsibilities;

EF3.03 – design an appropriate monthly budget for a person living in the surrounding community who has a given income, family responsibilities, and long-term savings goals;

EF3.04 – present a budget in a clear fashion, using appropriate mathematical forms (e.g., written or oral explanations, charts, tables, graphs, calculations);

EF3.05 – investigate the effect on an overall budget of changing one component, using a given spreadsheet template or budgeting software.

Applications of Measurement and Geometry

Overall Expectations

AMV.01 · use measurement and strategies of estimation in a variety of applications;

AMV.02 · solve problems involving measurement and design;

AMV.03 · apply transformation geometry in creating effective designs.

Specific Expectations

Measuring and Estimating

AM1.01 – demonstrate a working knowledge of the metric system;

AM1.02 – measure lengths accurately, using the metric system and the imperial system;

AM1.03 – estimate distances in metric units and in imperial units by applying personal referents (e.g., the width of a finger is approximately 1 cm; the length of a piece of standard loose-leaf paper is about 1 foot);

AM1.04 – estimate capacities in metric units by applying personal referents (e.g., a can of pop is about 350 mL);

AM1.05 – estimate, with reasonable accuracy, large numbers that are illustrated visually (e.g., books on a wall in a library, pictures of crowds, populations of high-rise buildings), and explain the strategies used.

Solving Problems Involving Measurement and Design

AM2.01 – demonstrate an understanding of the Pythagorean theorem, by constructing on a floor a rectangular region having accurate right-angled corners;

AM2.02 – determine the perimeter and area of regular and irregular figures from given diagrams;

AM2.03 – estimate, with reasonable accuracy, perimeters and areas of large regions (e.g., a playing field), and explain the strategies used;

AM2.04 – demonstrate an understanding of the effect on the area of familiar objects (e.g., a photograph, a television screen, a road map) of multiplying each dimension by the same factor;

AM2.05 – make a two-dimensional scale drawing of a room, using design or drawing software effectively;

AM2.06 – create a three-dimensional drawing of the interior of a room, using design or drawing software effectively;

AM2.07 – construct, with reasonable accuracy, a scale model of an environment of personal interest (e.g., a building, a garden, a bridge);

AM2.08 – estimate and calculate the surface area and volume of objects and containers in the surrounding environment that approximate the shape of rectangular prisms and cylinders;

AM2.09 – investigate the making of a household improvement (e.g., landscaping a property, decorating a room), design the improvement, and estimate and calculate the cost, using technology (e.g., spreadsheets, design or drawing software).

Applying Transformation Geometry

AM3.01 – describe the use of translations, reflections, rotations, and dilatations as they relate to symmetry and design in logos, with the aid of technology (e.g., dynamic geometry software, design or drawing software);

AM3.02 – analyse the geometric aspects of interesting and appealing applications (e.g., logos found in advertising, designs found in fabric or wallpaper);

AM3.03 – create a personal logo, using the mathematics of symmetry, translations, reflections, rotations, or dilatations, with the aid of technology (e.g., dynamic geometry software, design or drawing software);

AM3.04 – determine, through investigations, using concrete materials and technology, the characteristics of shapes that will tile the plane;

AM3.05 – create designs involving tiling patterns (e.g., Escher-type designs, wallpaper or fabric designs), using technology (e.g., dynamic geometry software, design or drawing software).

 


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.

 

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