Michels Academy

Grade 12 Mathematics Course Outline

MAP4C

School: Michels Academy
Department: Mathematics
Course Developer: Henry Michels
Course Development Date: August, 2010
Course Reviser/ revision date: Henry Michels/May 2011
Course title/grade /course: Foundations for College Mathematics/Grade 12
Ministry course code: MAP4C
Course Type:College Preparation
Credit Value: 1 credit
All material on this course outline has been developed based on the Ontario Curriculum Grades 11 and 12 Mathematics Policy Document (Revised), published in 2007.
Prerequisite: Foundations for College Mathematics, Grade 11 College Preparation, or Functions and Applications, Grade 11, University/College Preparation

Course Description

This course enables students to broaden their understanding of real-world applications of mathematics. Students will analyse data using statistical methods; solve problems involving applications of geometry and trigonometry; solve financial problems connected with annuities, budgets, and renting or owning accommodation; simplify expressions; and solve equations. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This course prepares students for college programs in areas such as business, health sciences, and human services, and for certain skilled trades.

Mathematical Process Expectations

The mathematical processes will be integrated into student learning in all areas of this course.

Throughout this course, students will:

1.Problem Solve - develop, select, apply, compare, and adapt a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding;

2.Reason and Prove - develop and apply reasoning skills (e.g., use of inductive reasoning, deductive reasoning, and counter-examples; construction of proofs) to make mathematical conjectures, assess conjectures, and justify conclusions, and plan and construct organized mathematical arguments;

3.Reflect - demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);

4.Select Tools and Computational Strategies - select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;

5.Connect - make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports);

6.Represent - create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;

7.Communicate - communicate mathematical thinking orally, visually, and in writing, using precise mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.

Overall Expectations

By the end of this course, students will:

A. MATHEMATICAL MODELS

1. evaluate powers with rational exponents, simplify algebraic expressions involving exponents, and solve problems involving exponential equations graphically and using common bases;

2. describe trends based on the interpretation of graphs, compare graphs using initial conditions and rates of change, and solve problems by modelling relationships graphically and algebraically;

3. make connections between formulas and linear, quadratic, and exponential relations, solve problems using formulas arising from real-world applications, and describe applications of mathematical modelling in various occupations.

B. PERSONAL FINANCE

1. demonstrate an understanding of annuities, including mortgages, and solve related problems using technology;

2. gather, interpret, and compare information about owning or renting accommodation, and solve problems involving the associated costs;

3. design, justify, and adjust budgets for individuals and families described in case studies, and describe applications of the mathematics of personal finance.

C. GEOMETRY AND TRIGONOMETRY

1. solve problems involving measurement and geometry and arising from real-world applications;

2. explain the significance of optimal dimensions in real-world applications, and determine optimal dimensions of two-dimensional shapes and three-dimensional figures;

3. solve problems using primary trigonometric ratios of acute and obtuse angles, the sine law, and the cosine law, including problems arising from real-world applications, and describe applications of trigonometry in various occupations.

D. DATA MANAGEMENT

1. collect, analyse, and summarize two-variable data using a variety of tools and strategies, and interpret and draw conclusions from the data;

2. demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations.

Outline of Course Content

Topic / Overall Expectations / Specific Expectations / Hours / Assessment for, as Learning / Assessment of Learning
Measurement and Geometry / A3
C1
C2 / A3.2; A3.4;
C1.1 - C1.3;
C2.1 - C2.3 / 11 / Drop Boxes
#1 - #5
On-Line Quiz / Test
Assignment # 1
Optimization Investigation
Trigonometry / C3 / C3.1 - C3.5 / 11 / Drop Boxes
#6 - #10
On-Line Quiz / Test
Assignment # 2
Trigonometry Task
One and Two Variable Statistics / D1 / D1.1 - D1.8 / 11 / Drop Boxes
#11 - 16
On-Line Quiz / Test
Assignment # 3
Survey Project
Statistical Measures and Critical Analysis / D2 / D2.1- D2.5 / 11 / Drop Boxes
#17 - #22
On-Line Quiz / Test
Graphical Models / A2 / A2.1 - A2.6 / 11 / Drop Boxes
#22 - #27
On-Line Quiz / Test
Assignment # 4
Real-World Exponential Analysis
Algebraic Models / A1
A3 / A1.1 – A1.7
A3.1- A3.2 / 11 / Drop Boxes
#28 - #33
On-Line Quiz / Test
Assignment # 5
Real-World Exponential Analysis
Annuities and Mortgages / A3
B1 / A3.3-A3.5
B1- B1.8 / 11 / Drop Boxes
#34 - #39
On-Line Quiz / Test
Assignment # 6
Wedding Budget
Budgeting / B2
B3 / B2.1-B2.3
B3.1- B3.6 / 15 / Drop Boxes
#40 - #43B
On-Line Quiz / Test
Assignment # 7
Renting vs Owning
Personal Budget
Culminating Activity
(30% of the course mark) / A1; A2; A3
B1; B2; B3
C1; C2; C3
D1; D2; / 10 hrs.
4 classes / Review
Student/Teacher conferencing / Section 1: Mathematical Modelling
Section 2: Budgeting a Trip
Section 3: Statistics Garbage Disposal
Section 4: Careers and Math

Note: Although 7 assignments have been noted in the Assessment of Learning Column, students need to only complete 4 of them in order to demonstrate mastery of curriculum expectations. Assignments #3 and #4 must be completed by all students.

Teaching and Learning Strategies

Strategies will be used which will build on students’ prior knowledge and to assess where students are in their learning. Students are encouraged to share learning strategies with their teacher which help them improve their learning. Students are encouraged to share the types of learning strategies which best meet their learning style with the instructor. Examples of teaching/learning strategies which will be used throughout the course include but are not limited to:

Socratic Method / Independent work
Large/small group work / Teacher directed learning / Field Excursions (investigation of use of student learnings in architecture/construction/banking, etc)
Project based learning / Use of computer software/technology / Student/teacher conferencing
Use of visual representations / Investigative inquiry
Problem solving exercises / Guest Presenters
Cooperative learning / Reflective Questioning

Assessment and Evaluation Strategies

In order to ensure that assessment and evaluation are valid and reliable, and lead to improvement of student learning, teachers of this course use a variety of the following strategies to assess student learning and to provide them with feedback:

Type / Why? / Examples
Assessment for learning / To inform teaching practices and to select instructional strategies that meet the needs of the learner /
  • Observation
  • Quizzes
  • Student/teacher conferences
  • Homework checks
  • Level of student participation
  • Questioning techniques
  • Student attendance
  • Student behaviour
  • performance tasks,

Assessment as Learning / To help student understand what he/she knows and still needs to learn /
  • Quizzes
  • Homework completion
  • Use of “student voice”

Assessment of Learning / To judge the quality of the student work based on his/her mastery of curriculum expectations, as defined by the Ministry of Education /
  • Tests
  • Assignments
  • Culminating tasks
  • Examinations
  • Computer lab work

Evaluation refers to the process of judging the quality of student work on the basis of established criteria, and assigning a value to represent that quality. Only work that is completed by students individually will form part of the final grade of the student. Evaluation is the responsibility of the teacher and is based on individual student demonstration of course expectations. Evaluated group tasks likewise must reflect individual accountability for learning and demonstration of course expectations through work submitted. Teachers will use their professional judgement in the determination of the final grade based on the most recent and most consistent achievement/performance levels of the students.

Student achievement will be communicated formally to students and parents by means of the Provincial Report Card, Grades 9–12. The percentage grade represents the quality of the student's overall achievement of the expectations for the course and reflects the corresponding level of achievement. Learning skills (responsibility; organization; independent work; collaboration; initiative; self-regulation) will also be assessed separately from the achievement of the learning expectations and will be reported on the provincial report card.

A final grade is recorded and a credit is granted and recorded where the student's grade is 50% or higher. The final grade for each course in Grades 9–12 will be determined as follows:

• Seventy per cent of the grade will be based on evaluations conducted throughout the course. This portion of the grade will reflect the student's most consistent level of achievement throughout the course, although special consideration will be given to more recent evidence of achievement. Tests and projects/presentations which enable students to apply their learning will form the basis for the term mark.

• Thirty per cent of the grade will be based on a final culminating activity:

  • Section 1: Mathematical Modelling
  • Section 2: Budgeting a Trip
  • Section 3: Statistics Garbage Disposal
  • Section 4: Careers and Math

All tests and the final culminating activity will be weighted according to the achievement chart as follows:

Knowledge and Understanding / 25 %
Thinking and Inquiry / 25 %
Communication / 25 %
Application / 25 %

Considerations for Program Planning:

In developing the mathematics program at Michels Academy, special consideration has been given to ensure that:

  • Health and safety regulations have been met in the classrooms
  • Students who have special learning needs can be successful due to a variety of differentiated learning strategies being provided;
  • Students who are English Language Learners can be successful due to the inclusion of differentiated learning strategies being provided;
  • Antidiscrimination education will ensure that all students have access to materials that reflect diversity with respect to gender, race, culture, and ability.
  • Students will be encouraged to develop critical thinking skills through the use of investigations
  • Students have numerous opportunities to demonstrate their oral, written and visual communication;
  • Students will be provided with numerous opportunities to use computer technology, both as a research tool and a tool to highlight their learnings;
  • Students are aware of the various career opportunities available to them which build on the learnings in the classroom

Resources:

Students will be expected to supply their own laptops. A major portion of the course work will be completed using an on-line program, available through the instructor.

Students will have access to:

(1) Workbook “Foundations for College Mathematics 12: Practise and Homework Book”, McGraw-Hill Ryerson 2009 (hardcopy)

(2)Dropbox As Learning Exercise Notes (hardcopy)

(3)Textbook “Foundations for College Mathematics 12: Practise and Homework Book”, McGraw-Hill Ryerson 2009

(4)Michels Academy Online Learning Environment at