Written by Region 3, Approved for Region 4

Mathematics 18

Written by Region 3, approved for Region 4

Mathematics 18

Rationale

This program offers a fresh start for students whose educational needs cannot be met in the regular education program. Students are encouraged to stay in school, experience success, learn employment skills, and develop a strong sense of self worth. Graduates of the program greatly enhance their opportunity of finding meaningful employment and becoming productive citizens.

Mathematics skills and applications will be taught in the context of real-life situations and materials. Activities and materials will enable the student to acquire the basic performance skills required for successful transition from school to the world of work and independent living.

Instructional Approaches

Instruction should be built on the belief that each student has differing learning styles, skills and abilities. Therefore, instructional approaches should be flexible and constantly changing, depending on the individual that is being dealt with. The first step should be to build the students’ self-esteem, so that they begin to believe they can learn, then to establish a relationship of trust so that cooperative learning can begin. The time frame for this may vary widely from one student to another.

To help each student achieve success, a wide variety of instructional approaches are encouraged.

A few suggestions are:

Direct Instruction. This strategy includes methods such as lecture, compare and contrast, guides for reading, listening or viewing, practice and drill, videos, speakers, and demonstrations. This also involves a great deal of one on one interaction and intervention with the student.

Indirect Instruction. This strategy includes methods such as reflective instruction, concept formation, case studies, close procedure, problem solving, and guided inquiry.

Interactive Instruction. This strategy includes methods such as role-playing, brainstorming, discussion, group work, problem solving, and interviewing. This may be carried out in class discussions, small group discussions or projects, student pairs working on assignments together, etc.

Experiential Learning. This learning strategy includes simulations, field trips, games, experiments, role-playing, and surveys.

Independent Study. This Learning strategy includes projects, essays, homework, assigned questions, and computer assisted instruction.

Examples of Assessment and Evaluation Techniques

Students should be on an ongoing basis using; in class performance, attitude, attendance, responsibility for homework, assignments, and such examinations as the teacher deems appropriate. In addition, there may student/parent interviews held to discuss student progress. It is suggested that an extensive written report be presented to each student at the end of the year. Parents should be encouraged to contact the school any time. Interviews may be requested by home or the school at any time during the school year.

Students should be encouraged to attend school regularly and punctually. A passing grade should be set at 50% on chosen evaluations.

The following is a list of possible performance criteria for Mathematics 18:

Individual Assessments ~ focus is on individual student progress. Assessment activities constructed and collaborating to complete assessment activities organized by the teacher.

Group Assessments ~ focus on the progress of a group of students has been made by cooperating and collaborating to complete assessment activities organized by the teacher.

Self-Assessment ~ refers to the students’ own assessment of their progress in knowledge, skills, processes, or attitudes.

Peer-Assessment ~ refers to the student assessment of other students. Peer-Assessments may be conducted either individually or collaboratively in groups.

Portfolios ~ a collection of student work that assists the student and teacher to make judgements about student learning progress. Samples of work to be included may be selected by the student, by the teacher, or by the teacher and student in consultation.

Anecdotal Record ~ written descriptions of student progress that a teacher keeps on a day-to-day basis.

Observation Checklists ~ lists of criteria a teacher determines are important to observe in students at a particular time. Besides each of the criteria, a notation is made as to whether that particular criterion was observed.

Rating Scales ~ record the degree to which skills are found or the quality of the performance.

Written Assignments ~ this may include questions, paragraphs, essays, reports, written and visual work, summaries, notebooks, journals, problem solving steps and strategies, etc. (ex: An investigation into what financial institution offers the best perks or benefits may be presented in a written report. The report would include methods of investigation, method of evaluation, etc.)

Presentations ~ these may accompany the written assignments and student performance assessment. They may be done on an individual or group basis, be organized into assessment stations or contracts, be self-and/or peer-assessed, and be included in portfolios. Checklists, rating scales, and anecdotal records may be used to record assessment information.

Performance Assessment ~ Students may be assessed on various forms of performance. Performance may be individual- or group-based, may be organized into contracts or assessment stations, may involve self-assessment and/or peer-assessments as components, and may involve written assignments and presentations. The recording of assessment information may be done by checklists, rating scales, or anecdotal records.

Homework ~ assignments students are given that are completed during their time away from the classroom. Students are evaluated on the quality of the work as well as the responsibility taken in meeting due dates.

Quizzes & Tests ~ may involve unit tests or final examinations. The types are as follows: Oral Assessment Items, Performance Test Items, Essay Questions, Short-Answer Items, Matching Items, Multiple-choice Items, True/False Items and Fill in the Blank Items.

*****Note: It is suggested that there be a pre-evaluation completed at the beginning of the year to provide the teacher with an overview of strengths and weakness. This may be in the form of a locally developed evaluation or a standardized test. Based on the needs of the student, chose the applicable level of instructional material. At the end of the year retest the students with the same test given at the beginning of the year as a way to measure improvement in mathematical skills.

**** Daily Lessons: Concepts are often forgotten so a few daily review questions at the beginning of the class will help to reinforce previously learned concepts.

**** Materials: A variety of materials have been suggested for this math course ranging from easy to more difficult material. Not all materials or all objectives will be suitable for all students.

Common Essential Learning (CELS)

Communication: Development of communication skills through mathematical language.

Critical and Creative Thinking: Students will use mathematical skills and knowledge in

problem-solving and decision-making as a consumer,

within daily routines and during community-based

activities.

3. Independent Learning: The long-term goal of instruction is the application of mathematical

concepts to enable students to participate independently in the

community and to adapt to changing demands and routines.

4. Numeracy: Students will develop and apply skills in computation, measurement and

problem-solving.

Personal & Social Values and Skills: Students will develop skills to communicate in a

socially appropriate and respectful manner.

Technology Literacy: Students’ knowledge will be utilized in increasing access to and

operation of tools and equipment. Instruction will incorporate the

appropriate use of calculators.

COMPARISON OF MAJOR CONCPEPTS

MATH 11/Math 18

Some concepts taught in Math 11 probably won't be taught in Math 18. Those particular concepts have been replaced with concepts that students at the alternate level often need.

Math 11

Graphing, Variations & Proportion

Part I: Interpreting data and reading graphs

Charts and tables
Graphs

Part II: Theory

Graphing on the cartesian plane
Linear functions

Part III: Applications

Ratios and rates
Direct variations

Consumer Math

Part I: Percent
Part II: Income
Part III: Budget

Geometry

Angles
Triangles
Quadrilaterals
Pythagorean theorem

Math 18

Graphing

Interpreting data and reading graphs

Charts and tables
Graphs

Time

Telling time
Analog
Digital
Calendar

Consumer Math

Part I: Money
Part II: Counting Money & GST Purchasing
Part III: Budget
Part IV: Basic Banking

Geometry

Shapes

COMPARISON OF MAJOR CONCEPTS

MATH 11/Math 18

…continued

Math 11

Algebra Skills

Part I: Fractions & IntegersPart II: Rational Numbers
Part III: Exponents
Part IV: Polynomials

Solving Equations

Part I: Solve EquationsPart II: Problem Solving
Part III: Exponents
Part IV: Polynomials /

Math 18

Measurement

Part I: Linear Measurement

Metric ~ mm, cm, m, etc.
Imperial ~ inches, feet, etc.

Part II: Quantity Measurement

Liquids ~ ml, L, etc.
Solids ~ g, kg, etc.

Numeration Skills

Part I: NumerationPart II: Basic Computation
Part III: Fractions

Problem Solving

Part I: One-Step ProblemsPart II: Two-Step Problems

Unit 1 – NumeracyMathematics 18

Level (18,28,38) Development

Foundational ObjectivesLearning ObjectivesCELSAwareness = A

Emerging = E

Progressing = P

______

182838

______

1) Students will develop math skills1) Read numerals 1 to 100,000#1 Communication P

which can be applied to

Independent living.2) Hear a number and write#2 Numeracy P

the numeral.

2) Students will increase their#5 Personal and P

ability to perform calculations 3) Recognize a decimal number social values

involving whole numbers, factorsand be able to give its value to and skills

decimals, and percentages.the nearest whole number.

3) To develop and understanding 4) Compare numbers and decide#4 Technology P

of the basic operations usingwhich is largest or smallest using: Literacy

whole numbers. a) whole numbers

b) decimal numbers

c) money

5) Add, subtract, multiple, and

divide up to 10 by memory using

fingers, pen and paper (show

understanding of what each

concept means).

6) Use a calculator to add,

subtract, multiply, and divide whole

and decimal numbers.

Effective Instructional Adaptations toAuthentic Assess-Resources

StrategiesAccommodate Diversity ment Strategies

1) Place Value Games1) Box Cars and One Eyed

-Set up place value chart, emphasize- math maniuplatives- correct visual Jocks Games

the pattern. rods/cubes placement

-Look at the digits in a numeral.

Identify the place value.- place value charts- untimed written

2) Teach lower number strategy test2) Make worksheets

(very good strategy to teach lower - visual representation- individual oraleg. Monopoly, Game of Life

priced item). of larger vs. smaller assessment or Payday

a) What is a digit? How many digits numbers- greater than/less

are in each numeral? Than untimed test

b) Compare number of digits (before- use maniuplatives- grocery lists, menus4) Manipulatives

the decimal). The one with fewer- going to a store and eg. Base blocks

digits is lower. purchasing with real

c) Make a vertical chart of numbers- Power of 10 game money5) Enright Computation Series

9 to 10 – which number is lower - include source

d) What if there are the same - order from Internet6) Access to Math Series

number of digits before the decimal? - compare/contract ~ “Whole Numbers & Integers” Book - visual representation

Compare each digit that is different, >5, rounding off ~ “Decimals” Booklet

The number that is lower on the

chart is the smaller number.7) Mathematics Workshop Series

e) Introduce decimals: ~”Basic Skills 1” Booklet

-follow the steps above ~”Basic Skills 2” Booklet

-if every number is the same than

compare each number after the

decimal

-if the digit is lower on the chart

it is the lower item.

f) Compare money using the above

steps. Discuss the meaning of

decimals and zeros. Circle the

lower number.

Eg.(1) 0.05 or 0.09

(2) 0.26 or 0.26

(3) 0.27 or 0.39

(4) $5 or $5.00

(5) $0.05 or $0.5. Discuss

meaning of the 0 on the calculator.

g) Use flyers to compare prices

of items.

-use grocery item

-use actual money
Unit II – FractionsMathematics 18

Level (18,28,38) Development

Foundational ObjectivesLearning ObjectivesCELSAwareness = A

Emerging = E

Progressing = P

______

182838

1) Students will develop math skills1) Recognize the meaning of #1 Communication P

which can be applied toa fraction.

independent living.#2 Numeracy P

2) Identify fractions equivalent to 1.

2) Students will increase their #4 Technology P

ability to perform calculations3) Identify simple fractions that are Literacy

involving whole numbers, fractions,equivalent such as 2/4=1/2.

decimals, and percentages.

3) To develop and understanding

of the basic operations using

fractions

Effective Instructional Adaptations toAuthentic Assess-Resources

StrategiesAccommodate Diversity ment Strategies

1) Introduce which fraction is larger/- paper folding/paper- visual representation1) Skills in Mathematics 1 –

smaller. Cutting activities paper of fractionsCambridge Skills Series – pg 89

eg. Would you rather have 1/4, 1/8, colouring- correct amount of

1/64, or 1/190 of this chocolate bar?- measuring instruments for ingredients to make2) Keys to Fractions food edible

a recipe

2) Know what 1/4, 1/2, 1/3,- math manipulatives3) Enright Computation Series

1/8 means.- paper assessment

4) Manipulatives

3) Make a bar chart using strips of - on-line math games- math manipulatives

colored paper to make/show5) Access to Math Series

equivalent fractions.- fraction blocks ~ “Fractions” Booklet

- chocolate bars
Unit III – Problem SolvingMathematics 18

Level (18,28,38) Development

Foundational ObjectivesLearning ObjectivesCELSAwareness = A

Emerging = E

Progressing = P

______

182838

______

1) Students will develop the skills to1) Figure out 1 step problems by#1 Communication P

solve real world problems usingadding, subtracting, dividing and

various problem solving strategies.multiplying#3 Critical and P

Creative Thinking

Effective Instructional Adaptations toAuthentic Assess-Resources

StrategiesAccommodate Diversity ment Strategies

1) Teach problem solving skills- task analysis, one step at - visual representation1) Understanding Math Story

throughout each unit. a time Problems

- guided practice- written breakdown - model of each step

- visual representation of

2) Draw diagrams etc. problem (role play, use- recipe cards2) Solving Word Problems manipulatives . . . ) (write down what

- set up a store for money learning)

3) Teach strategies to solve the solving problems3) Access to Math Series

problem.~“Problem Solving Strategies” Book

~“One and Two Step Problems” Book

4) Mathematics Workshop Series

~ “Problem Solving 1” Booklet

~ “Problem Solving 2” Booklet

Mathematics 18

Unit IV – Interpreting Data & Reading Graphs

Level (18,28,38) Development

Foundational ObjectivesLearning ObjectivesCELSAwareness = A

Emerging = E

Progressing = P

______

182838

______

1) To demonstrate an understanding1) To read and interpret a variety of#1 Communication P

of how to read and interpret graphstables and charts.

and charts.#3 Critical and

2) To read and interpret informationCreative Thinking E

2) The student should demonstratefrom graphs.

knowledge and understanding of#6 Independent A

why, and how to collect, organize,3) To use ordered pairs in the CartesianLearning

and interpret numerical data.Coordinate.

3) To graph ordered pairs in the

Cartesian coordinate plane

Effective Instructional Adaptations toAuthentic Assess-Resources

StrategiesAccommodate Diversity ment Strategies

PART IPART 1

1) Read a school day timetable- more time to complete- oral assessment1) Applications in Mathematics

2) Read a simple pictograph assignments- visual assessment Chapter 1

3) Make a tally chart- working in small groups/pairs- computer based2) What Do They Tell You? Tables,

4) Read a TV Schedule- computer generated graphs assessment Charts and Graphs – Scholastic

5) Read a distance chart from a map- generate examples 3) Clock and Calendar Skills

6) Read a postal rate chart Weston Watch

7) Use the phone book to figure4) Schedules – Janus Survival Guide

out telephone rates5) Mathematics Skills Workshop –

8) Read a sales tax chart Globe Book Company

9) Read an income tax chart 6) Phone Book

7) Various Maps

8) School Timetable

9) TV schedule for local listings 10) Payroll charts/tax charts

11) Access to Math Series:

~"Graphing and Interpreting Data”

PART ll

1) Practice finding information from

variety of the following graphs:

pictographs, bar graphs, line

PART lll- visual representationPART ll

1) Play Battleship, Bingo (note of graph1) Applications in Mathematics

letter first then numeral) Chapter 1

2) Use a map of the world, or- accommodate based2) What Do They Tell You> Tables,

province to show the location of on need of students Charts and Graphs – Scholastic

various cities and tourists areas.3) Mathematics Skills Workshop –

(This is a practical example of using Globe Book Company

coordinates to locate points).

3) Discuss jobs that use coordinatePART lll

systems ex: air traffic controllers.1) Battleship Game

2) Maps/Atlas

Unit V – Telling TimeMathematics 18

Level (18,28,38) Development

Foundational ObjectivesLearning ObjectivesCELSAwareness = A

Emerging = E

Progressing = P

______

182838

______

1) The student should demonstratePART IPART I P

an ability to measure time and use1) Recognize the difference between#3 Critical and

appropriate measurementa.m. and p.m.Creative Thinking

techniques and to apply measure-

ment to real life.2) To be able to tell time to the #4 Technological P

hours and half hour.Literacy

3) To tell time to the hour/half hour P

using an analog clock.

4) To tell time to the hour/half hour P

using a digital clock

PART IIPART II

1) Identify present day, month, year.#1 Communication P

2) Locate a date on a calendar for#3 Critical and P

a specific purpose.Creative Thinking

3) Identify the four seasons. P

4) Identify holidays with a season P

and date.

5) Write = Identify Dates P

ex: (a) words = January 25th, 2002

(b) numerals = 01/25/02.

Effective Instructional Adaptations toAuthentic Assess-Resources

StrategiesAccommodate Diversity ment Strategies

PART lPART l

1) Make a collage of a.m. and p.m.- use of picture graph- marks for effort1) Magazines

activities detailing agenda for a.m.2) Student Timetables

2) Student Timetable: distinguish and p.m.- represent a.m./p.m.3) Clock and Calendar Skills –

between a.m./p.m. activities- is clock visually correct Weston Watch pg. 4-7

3) Make a clock with moving hands4) Time – Miliken

4) To begin – make hour hand and- individual assessment5) Time Clock Stamps

minute hand different colors- pictorial assessment

5) During the day, have students- oral testingPART ll

identify what time it is.1) Clock and Calendar Skills –

6) Have available both digital and Weston Watch pg. 106-115

analog clocks/watches to display2) Calendar, Agenda Book

the same time.3) Calendars from various years

4) Clock and Calendar Skills –

PART ll Weston Watch pg. 122-125