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Course Overview

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Course Overview ...

Public District School Board Writing Partnership

Course Profile

    Mathematics for Everyday Life

Grade 11

    Workplace Preparation

    ; for teachers by teachers

    This sample course of study was prepared for teachers to use in meeting local classroom

    needs, as appropriate. This is not a mandated approach to the teaching of the course.

    It may be used in its entirety, in part, or adapted.

Fall 2000

    Course Profiles are professional development materials designed to help teachers implement the new Grade 11 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

Acknowledgments

    Public District School Board Writing Teams

Course Profile Writing Team

    Mary-Beth Fortune, Lead Writer, Peel District School Board

    Liisa Suurtamm, Lead Writer, Peel District School Board and Ontario Association of Mathematics

    Educators

    Jeff Brosseau, Greater Essex County District School Board

    Cathy Dunne, Peel District School Board

    Krysta Mehler, Greater Essex County District School Board

    Jim Vincent, Peel District School Board

Reviewers

    Bibiana Couto, Peel District School Board; John Cullen, La Mangia Cakes Bakery (Workplace

    Reviewer); Lucille Davies, Limestone District School Board; Ron Lewis, Rainbow District School

    Board; Shirley Scott, District School Board Of Niagara; Peter Wright, Grand Erie District School

    Board

Lead Board

    District School Board of Niagara

    Jacob Speijer, Project Manager, Ontario Mathematics Coordinators Association

Partner Boards

    Grand Erie District School Board, Greater Essex County District School Board, Limestone District

    School Board, Peel District School Board, Rainbow District School Board

Associations

    Ontario Association of Mathematics Educators (OAME)

    Ontario Mathematics Coordinators Association (OMCA)

Page 2 ; Mathematics for Everyday Life Workplace Preparation

Course Overview

    Mathematics, Grade 11, Workplace

    Identifying Information

    Course Title: Mathematics for Everyday Life

    Grade: 11

    Course Type: Workplace Preparation

    Ministry Course Code: MEL 3E

    Credit Value: 1.0

    Description/Rationale

    This course prepares students for the world of work and for the Grade 12 Mathematics for Everyday Life course. This course is intended for students who have, at minimum, successfully completed a Grade 9 Mathematics course. It enables students to broaden their understanding of mathematics as it applies to real-life financial contexts. Students use current information and technology to solve problems and make comparisons leading to informed decisions. Assessment and evaluation are done using a wide variety of strategies with an emphasis on performance-based approaches.

    Unit Titles (Time + Sequence)

    Unit 1 Working for your Money 15 hours

    Unit 2 Hello, Good Buy! 12 hours

    Unit 3 Bank On It! 17 hours

    Unit 4 Making your Money Work 11 hours

    Unit 5 It‟s in your Best Interest 13 hours

    Unit 6 You Auto Know 17 hours

    Unit 7 Planes, Trains and Automobiles (and Buses too!) 13 hours

    Unit 8 Touring With The Band (Summative Activity) 12 hours

    Unit Descriptions

    Unit 1: Working for your Money

    Time: 15 hours

    Description

    Students investigate renumeration and personal taxation. Students use appropriate technology to develop a working knowledge of salary, hourly rate, overtime, commission, and personal income tax. Utilizing this information, students investigate the relationship between net pay and gross pay. Opportunities are given for students to explore various spending habits as related to pay period. Students investigate the resources necessary for the completion of personal income tax returns. Throughout this unit, students utilize charts, spreadsheets, and appropriate technology to support their understanding of personal income. Strand(s) and Expectations

    Strand(s): Earning, Paying Taxes, and Purchasing

    Overall Expectations: EPV.01; EPV.02.

    Specific Expectations: EP1.01; EP1.02; EP1.03; EP1.04; EP1.05; EP2.02; EP2.03.

    Page 3 ; Mathematics for Everyday Life Workplace Preparation

Unit 2: Hello, Good Buy!

    Time: 12 hours

    Description

    Throughout this unit, students are involved in various investigations and activities that allow them to apply responsible decision-making to purchasing situations. Students are given the opportunity to make correct change, perform cost comparisons, and calculate discounts, sale prices, and taxes. Students also identify and compare various purchase plans. Technology is used to enhance student understanding. Students are encouraged to utilize estimation to ensure that their calculated results are reasonable. Strand(s) and Expectations

    Strand(s): Earning, Paying Taxes, and Purchasing

    Overall Expectations: EPV.02; EPV.03.

    Specific Expectations: EP2.01; EP2.04; EP3.01; EP3.02; EP3.03; EP3.04; EP3.05; EP3.06; EP3.07.

    Unit 3: Bank on It!

    Time: 18 hours

    Description

    Students explore the world of financial institutions as it relates to saving their money. Particular emphasis is placed on simple and compound interest. Students identify and investigate various financial services in the context of real-life situations. Applying appropriate technology, students calculate investment growth, examine differences between simple interest and compound interest, and compare savings alternatives. Strand(s) and Expectations

    Strand(s): Saving, Investing, and Borrowing

    Overall Expectations: SIV.01; SIV.02.

    Specific Expectations: SI1.01; SI1.02; SI1.03; SI1.04; SI1.05; SI1.06; SI2.01; SI2.02; SI2.03.

    Unit 4: Making your Money Work

    Time: 11 hours

    Description

    Students investigate different types of investment strategies and associated characteristics. Students examine both long-term and short-term investments. Applications of both simple interest and compound interest with varying compounding periods are compared. Using appropriate technology, students analyse expected growth of investments and their associated risks. The results of this analysis enable students to make informed decisions regarding money management to optimize investment opportunities. Strand(s) and Expectations

    Strand(s): Saving, Investing, and Borrowing

    Overall Expectations: SIV.01; SIV.02.

    Specific Expectations: SI1.04; SI1.06; SI2.05; SI2.04; SI2.06; SI2.07; SI2.08.

    Unit 5: It’s in your Best Interest

    Time: 13 hours

    Description

    Students investigate the features and conditions of credit cards, debit cards, and short-term loans. Using spreadsheet software, students examine the financial implications of delayed credit card payments and of personal loan features. The total interest paid is compared to the principal amount to determine advantages or disadvantages of borrowing options. Various payment alternatives are explored to make informed decisions regarding available loan features.

    Page 4 ; Mathematics for Everyday Life Workplace Preparation

Strand(s) and Expectations

    Strand(s): Earning, Paying Taxes, and Purchasing; Saving, Investing, and Borrowing

    Overall Expectations: EPV.03; SIV.01; SIV.03.

    Specific Expectations: EP3.05; EP3.08; SI1.01; SI3.01; SI3.02; SI3.03; SI3.04; SI3.05; SI3.06; SI3.07. Unit 6: You Auto Know

    Time: 17 hours

    Description

    Students investigate the costs of owning and operating both new and used vehicles by collecting data from current resources such as newspapers, Internet, and local car dealers. The long-term fixed and variable-operating costs of buying and leasing vehicles will be compared to the costs of using public transportation. Students explore issues relating to vehicle insurance, to obtaining a driver‟s license, and to the consequences of irresponsible operation of a vehicle. Particular emphasis is placed on making informed financial decisions. Appropriate technology is used to aid in the analysis of data.

    Strand(s) and Expectations

    Strand(s): Transportation and Travel

    Overall Expectations: TTV.01; TTV.02.

    Specific Expectations: TT1.01; TT1.02; TT1.03; TT1.04; TT1.05; TT1.06; TT1.07; TT2.02.

    Unit 7: Planes, Trains, and Automobiles (and Buses too!)

    Time: 13 hours

    Description

    Students access authentic resources, e.g., automobile association, Internet, travel guides, to plan an automobile trip, and to both identify and estimate any associated costs. Students explore the costs of completing this trip using alternate modes of transportation, such as by airplane, bus, and train. By examining and evaluating the advantages and the disadvantages of these options, students justify and present a decision on the most appropriate choice for their trip.

    Strand(s) and Expectations

    Strand(s): Transportation and Travel

    Overall Expectations: TTV.01; TTV.02; TTV.03.

    Specific Expectations: TT1.08; TT2.01; TT2.02; TT2.03; TT3.01; TT3.02; TT3.03; TT3.04.

    Unit 8: Touring With The Band (Summative Activity)

    Time: 12 hours

    Description

    In this summative unit, students create a fictitious local music band that they manage. In an effort to raise money for new band equipment, the band manager plans a tour consisting of four consecutive weekend performances. Students estimate expenses and potential revenue to anticipate profits, which determines if the tour is feasible. Particular emphasis is placed on estimating expenses related to renting and maintaining a touring vehicle, accommodation, and food, as well as projecting potential revenue from ticket sales and souvenir sales. Findings are presented in the form of an organized tour proposal summary. Critical thinking skills are demonstrated throughout the unit as student investigations result in making informed decisions and justifying choices.

    Strand(s) and Expectations

    Strand(s): Earning, Paying Taxes, and Purchasing; Transportation and Travel

    Overall Expectations: EPV.01; EPV.02; EPV.03; TTV.01; TTV.02.

    Page 5 ; Mathematics for Everyday Life Workplace Preparation

Specific Expectations: EP1.01; EP1.02; EP1.03; EP2.01; EP3.03; EP3.04; EP3.06; TT1.06; TT2.01;

    TT2.02; TT2.03.

    Course Notes

    Students in this course will benefit from the following strategies:

    ; Fostering Students‟ Employability Skills

    Because these students may soon be entering the work force, teachers should cultivate students‟

    understanding the importance of regular attendance, of punctuality, of taking initiative, and of being

    prepared, as it relates to employee behaviour in the workplace. Students should be active learners in the

    classroom. It is imperative that problem-solving skills be developed and that students are taught to be

    resourceful. Teachers should encourage students to develop a respect for others‟ point of view.

    ; Teaching Skills Within Context

    It is beneficial for students to widen their views of mathematics in order to recognize its usefulness and

    relevance both inside and outside of school. Teachers need to take time to develop specific skills but

    should do so within a larger context. Activities and problems are presented in real-life situations and

    opportunities are given for students to access community resources and to seek out current information.

    It is important that students connect ideas within the various areas of mathematics. It may be necessary

    for teachers to highlight these connections for students, as they may not see them on their own. ; Providing a Structured Learning Environment

    It is important that routines be structured with well-communicated expectations. These students

    typically need their teacher to be consistent yet flexible. Tasks should be divided into small components

    and accompanied by regular feedback.

    ; Creating a Positive Learning Environment

    In order to help alleviate students‟ math anxiety, the teacher‟s approach should be positive, welcoming,

    and low-risk. Timelines should be realistic and flexible. To address the varied needs of the students,

    especially during performance-based activities, teachers may find it advantageous to keep a variety of

    teaching strategies in mind to allow them to deal with the unexpected as it arises. It may be necessary

    to both re-teach skills and to provide opportunities for practice as the need arises. ; Using Technology as a Tool For Learning

    Technology is an important teaching tool in this course as it provides students with a tactile and visual

    connection to concepts. Students should recognize the role of technology in their everyday life and in

    the world of work. A variety of technological tools should be used and the emphasis should be on using

    technology to analyse results of investigations as opposed to rote calculation. Time must be allotted for

    orientation to technology, as required.

    Teaching/Learning Strategies

    Opportunities will be provided throughout the course to apply a variety of both teaching and learning strategies.

    In applying this course profile, teachers should:

    ; become familiar with any student IEPs and make appropriate accommodations based on student needs; ; use current and local information to promote relevance;

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

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

    ; provide many opportunities for student success;

    ; provide extension opportunities;

    ; provide regular, constructive feedback;

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

    Page 6 ; Mathematics for Everyday Life Workplace Preparation

; provide review and remediation where appropriate;

    ; integrate technology when appropriate;

    ; draw from a workplace setting.

    In achieving the expectations of this course, students:

    ; communicate their understanding using a number of different mediums;

    ; develop increasing responsibility for their own learning by attending class regularly, being punctual,

    and coming prepared;

    ; become independent and active learners;

    ; recognize the importance of math in the workplace and in daily life;

    ; investigate and explore concepts using technology;

    ; apply and develop individual and group learning skills;

    ; utilize a variety of resources to solve problems;

    ; become informed consumers and develop personal financial management skills;

    ; use estimation to judge the reasonableness of their answers;

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

    Assessment and Evaluation

    Assessment is a systematic process of collecting information or evidence about student learning. Assessment should be used to gather information for diagnostic, formative, and summative purposes. Evaluation is the judgement teachers make about the assessments of student learning based on established criteria. Evaluation requires that the teacher not simply average marks. In forming an evaluative judgement, the teacher should consider students‟ performance in the four categories of the Achievement Chart. Assessment and evaluation strategies and tools must address the variety of learning styles and needs. A balanced assessment and evaluation program is based on the provincial curriculum expectations and the achievement levels.

    It is important to note that assessment and evaluation will be criterion referenced, comparing student performance to the Ministry standard, not to other students. Level 3 is defined as the provincial standard. Level 4 performance requires a consistent, but not constant, pattern of well-communicated higher level thinking and not simply technically correct solutions. Level 4 does not require a student to perform beyond grade level expectations.

    Teachers should use a variety of assessment methods for example:

    ; assess Understanding/Knowledge through tests, quizzes, and observation of performance tasks; ; assess Thinking/Inquiry/Problem Solving through performance assessment, observation, conferencing,

    and projects;

    ; assess Communication through journals, portfolios, performance assessments, observations, and

    presentations;

    ; assess Application in familiar settings through tests, quizzes, and performance assessment.

Learning Skills can be assessed through journals, portfolios, and observation.

    Assessment and Evaluation tools to be used throughout the course may include:

    ; the four-level Achievement Chart for Mathematics;

    ; rubrics;

    ; checklists;

    ; rating scales;

    ; marking schemes;

    ; anecdotal comments.

    Page 7 ; Mathematics for Everyday Life Workplace Preparation

    When teachers use a variety of these assessment tools, it is necessary to ensure that a consistent standard is maintained. That is, a 70-79% performance using an objective marking scheme should be equivalent to a Level 3 performance. Teachers may find it more appropriate to use rubrics to assess Inquiry/Problem Solving and Communication, and objective scales for Knowledge/Understanding and Application, as they are beginning to gather data in the categories of the Achievement Chart. In doing so, it is important that they keep in mind that Level 3 and 70-79% are the provincial standard. Performance task and tests should be set with the Expectations in the policy documents as the criteria for this standard. A selection of these tools is designed for this course profile to accompany specific assessment and evaluation activities. Teachers are encouraged to use them and to develop similar tools for other assessment activities. Some suggestions for increasing scoring consistency include:

    ; involving other teachers in the department in the creation of rubrics for assessment; ; involving students in the setting of criteria, and in the use of self-assessment and peer assessment; ; gathering exemplars of student work at the four levels, so that teachers and students can get a better

    image of what achievement at these levels looks like.

    In this course profile, assessment and evaluation of the expectations using the four levels of the Achievement Chart is ongoing throughout the units. Assessment and evaluation tools are designed to allow students to demonstrate performance at the full range of student learning.

    To facilitate the completion of the summative assessment unit, it is recommended that teachers use a portfolio or folder to collect student work throughout the course. This enables students to draw from their portfolio to assist them with their summative activities. The teacher can use this portfolio either as the actual summative assessment or to facilitate students with completing the summative activities. It should be noted that:

    ; Tests that include only questions that ask students to perform algorithms and to apply their knowledge

    do not necessarily offer an opportunity for students to demonstrate overall Level 4 performance. ; It is often easier to pose questions with the expectation of Level 1 to 4 responses in the Inquiry/Problem

    Solving and Communication categories of the Achievement Chart than the Knowledge/Understanding

    and routine Application categories.

    ; Teachers must expand their understanding of applications to include non-routine applications. This

    newer view of Applications requires a shift from thinking of them as being tied to specific content, to

    applications of mathematics in general.

    ; The issue of communication is complex. Teachers need to ask students to communicate their

    understanding of their knowledge, their stages of thought in an inquiry, and their process of applying

    mathematics to a problem, in order to assess Level 1 to 4 performances in the other three categories of

    the Achievement Chart. Then, they need to report on the Communications category separately from

    those categories.

    ; The expectations of the course include a wide range of skills, all of which must be addressed. Those

    who have not demonstrated the expected level of achievement earlier in the course should be given

    additional opportunities, after more learning has happened, to demonstrate improved levels of

    achievement.

    Accommodations

    Appropriate accommodations should be part of the planning of each unit activity with respect to the particular students in the class and their specific needs. Instructional, assessment, and evaluation activities must take into account the strengths, needs, learning expectations and accommodations as identified in the Individual Education Plan (IEP) whether students are formally identified or not (Regulation 181/98). Page 8 ; Mathematics for Everyday Life Workplace Preparation

The following accommodations should be made for ESL/ELD students:

    ; Have students work with partners, peer tutors, or classmates who share the same linguistic background.

    ; Provide extensive student/teacher conferencing.

    ; Use peer conferencing to reinforce instructions/information.

    ; Ask an ESL/ELD teacher to review questions, assignments, or assessment instruments. ; Provide sets of reference notes, outlines of critical information, and models of charts, timelines, or

    diagrams.

    ; Reinforce main ideas by using think/pair/share.

    ; Pair written instructions with verbal instructions.

    ; Use key visuals to illustrate definitions for the students‟ dictionary of key words.

    ; Simplify instructions.

    ; Highlight key words or phrases.

    ; Brainstorm in groups in first language if English is limited.

    ; Provide opportunities for students to practise oral presentation skills. ; Provide visual/auditory cues.

    The following accommodations should be make for students with learning disabilities: ; Provide extensive student/teacher conferencing.

    ; Pair students.

    ; Provide a list of terminology (possibly simplified) before any activity begins. ; Adjust handouts in terms of language and content used, and in terms of size and easy-to-read font. ; Allow assignments to be completed in alternate formats or in longer timelines. ; Keep manipulatives, grid paper, formula sheets, and other aids available for needs that arise. ; Contact parent/guardian for support and suggestions.

    ; Provide oral preplanning of activities with students.

    ; Allow the use of specialized equipment and assistance, e.g., some students may require calculators with

    large keys.

    ; Allow students to work in alternative settings, e.g., resource room, where students can receive

    assistance with problems that are language-based.

    Resources

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

    Andrini, B. Cooperative Learning and Mathematics: A Multi-Structural Approach. California: Resources

    for Teachers. 1991.

    Baker, E. Making Performance Assessment Work: The Road Ahead. Educational Leadership 51,

    (1994): 6:58-62.

    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.

    Charles, L. and M.R. Brummet. Connections 8: Linking Manipulatives to Mathematics. California:

    Creative Publications, 1996.

    Countryman, J. Writing to Learn Mathematics. Portsmouth: Heinemann, 1992.

    Fisher, S., Shelley, S., and J. Gravelle. Complete Idiot’s Guide To Personal Finance In Your 20s and 30s For Canadians. Scarborough: Prentice Hall, 1999.

    Hibbard, K.M., et al. A Teacher’s Guide to Performance-Based Learning and Assessment. Alexandria,

    VA: Association for Supervision and Curriculum Department, 1996.

    Page 9 ; Mathematics for Everyday Life Workplace Preparation

Lambdin, D.V., et al. Emphasis on Assessment: Readings from NCTM’s School-Based Journals. Reston,

    VA: National Council of Teachers of Mathematics, 1996.

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

    VA: National Council of Teachers of Mathematics, 1997.

    O‟Neil, J. “Putting Performance Assessment to the Test.” Educational Leadership 49, 8: 14-19. 1992.

    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.

    Stepien, W. and S. Gallagher. “Problem-Based Learning: As Authentic As It Gets.” Educational

    Leadership. 50, 7: 25-28. 1993.

    Course Evaluation

    Course improvement should be viewed as an ongoing, collaborative process among mathematics teachers. As new resources, new technology, and new insights about the programs develop, teachers must adapt their programs to better serve the needs of their students. Teachers may also choose to make revisions to the course as they work with teachers from other schools.

    To meet these goals, teachers should evaluate the effectiveness of their courses using a variety of information sources. While students‟ performances on summative tasks are obvious indicators of success, many other sources exist. These include student feedback, student attitudes, parental feedback, and performance of students in subsequent mathematics courses.

Page 10 ; Mathematics for Everyday Life Workplace Preparation

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